achieving minimum length scale in topology optimization using nodal design variables and projection functions a methodology for imposing a minimum length scale on structural members in discretized topology optimization problems is described nodal variables are implemented as the design variables and are projected onto element space to determine the element volume fractions that traditionally define topology the projection is made via mesh independent functions that are based upon the minimum length scale a simple linear projection scheme and a non linear scheme using a regularized heaviside step function to achieve nearly 0 1 solutions are examined the new approach is demonstrated on the minimum compliance problem and the popular simp method is used to penalize the stiffness of intermediate volume fraction elements solutions are shown to meet user defined length scale criterion without additional constraints penalty functions or sensitivity filters no instances of mesh dependence or checkerboard patterns have been observed copyright 2004 john wiley sons ltd

shape optimization of three dimensional continuum structures via force approximation techniques the existing need to develop methods whereby the shape design efficiency can be improved through the use of high quality approximation methods is addressed an efficient approximation method for stress constraints in three dimensional shape design problems is proposed based on expanding the nodal forces in taylor series with respect to shape variations the significance of this new method is shown through elementary beam theory calculations and via numerical computations using three dimensional solid finite elements numerical examples including the classical cantilever beam structure and realistic automotive parts like the engine connecting rod are designed for optimum shape using the proposed method the numerical results obtained from these methods are compared with other published results to assess the efficiency and the convergence rate of the proposed method it is concluded that by taking advantage of this high quality approximation the total number of finite element analyses required for structural shape optimization can be reduced significantly resulting in the same level of efficiency achieved previously in sizing problems

topology optimization using polytopes abstract meshing complex engineering domains is a challenging task arbitrary polyhedral meshes can provide the much needed flexibility in automated discretization of such domains the geometric property of polyhedral meshes such as its unstructured nature and the connectivity of faces between elements makes them specially attractive for topology optimization applications numerical anomalies in designs such as the single node connections and checkerboard pattern can be naturally circumvented with polyhedrons in the current work we solve the governing three dimensional elasticity state equation using the virtual element method vem approach the main characteristic difference between vem and standard finite element methods fem is that in vem the canonical basis functions are not constructed explicitly rather the stiffness matrix is computed directly utilizing a projection map which extracts the linear component of the deformation such a construction guarantees the satisfaction of the patch test used by engineers as an indicator of optimal convergence of numerical solutions under mesh refinement finally the computations reduce to the evaluation of matrices which contain purely geometric surface facet quantities the present work focuses on the first order vem in which the degrees of freedom are associated with the vertices the features of the current optimization approach are demonstrated using numerical examples for compliance minimization and compliant mechanism problems

sensitivity analysis with the modified heaviside function for the optimal layout design of multi component systems two kinds of design variables i e pseudo density variables associated with the framework structure and location design variables associated with connected components are involved in the layout design of multi component systems although sensitivities with respect to the first ones can easily be carried out as in topology optimization the semi analytical method sam is often used for sensitivity analysis with respect to the location design variables due to the geometric perturbation of the finite element mesh the latter can then be regarded as a geometric perturbation model gpm in this paper we propose a material perturbation model mpm using fixed finite element fe mesh for sensitivity analysis with respect to location design variables the material discontinuity across the boundary between each component and the framework structure is smoothed approximately by means of a modified heaviside function when a location design variable of a certain component is perturbed attached finite elements to the component boundary are assumed to undertake only a shift of material properties while the finite element mesh itself remains geometrically unchanged as a result analytical sensitivities with respect to location design variables are achieved as easily as for pseudo density variables the computing efficiency is thus improved because the velocity field for the mesh perturbation in the semi analytical scheme is no longer needed the mpm is illustrated by means of numerical tests especially the design optimization of 3d multi component systems

structural optimization a new dual method using mixed variables a new and powerful mathematical programming method is described which is capable of solving a broad class of structural optimization problems the method employs mixed direct reciprocal design variables in order to get conservative first order approximations to the objective function and to the constraints by this approach the primary optimization problem is replaced with a sequence of explicit subproblems each subproblem being convex and separable it can be efficiently solved by using a dual formulation an attractive feature of the new method lies in its inherent tendency to generate a sequence of steadily improving feasible designs examples of application to real life aerospace structures are offered to demonstrate the power and generality of the approach presented

stress constrained shape and topology optimization with fixed mesh a b spline finite cell method combined with level set function abstract in this paper we develop an efficient and flexible design method that integrates the b spline finite cell method b spline fcm and the level set function lsf for stress constrained shape and topology optimization any structure of complex geometry is embedded within an extended regular and fixed eulerian mesh no matter how the structure is optimized high order b spline shape functions are further implemented to ensure precisions of stress analysis and sensitivity analysis meanwhile level set functions i e implicit functions are used to enable topological changes of the considered structure through smooth boundary variations involved parameters rather than the conventional discrete form of lsf are directly taken as design variables to facilitate the numerical computing process to be specific the lsf is constructed by means of r functions that incorporate cubic splines as implicit functions to offer flexibilities for shape optimization within the framework of fixed mesh while the compactly supported radial basis functions cs rbfs are employed as implicit functions for stress constrained topology optimization it is shown the proposed fcm lsf method is a convenient approach that makes it possible to calculate stress and stress sensitivities with high precision representative examples of shape and topology optimization with and without stress constraints are solved with success demonstrating the advantages of the fcm lsf method

a computational procedure for response statistics based optimization of stochastic non linear fe models abstract an approach for an efficient solution of response statistics based optimization problems of non linear fe systems under stochastic loading is presented a sequential approximate optimization approach where approximate stochastic analyses are used during portions of the optimization process is implemented in the proposed formulation in this approach analytical approximations of the performance functions in terms of the design variables are considered during the optimization process the analytical approximations are constructed by combining a mixed linearization approach with a stochastic response sensitivity analysis the state of the system is defined in terms of the statistical second moment characteristics of the structural response the stochastic loading and the response of the system are represented by an orthogonal series expansion of the corresponding covariance matrices in particular a truncated karhunen loeve k l expansion is applied the system of non linear equations is replaced by a statistical equivalent linear system the evaluation of the k l vectors is carried out by an efficient procedure that combines local linearization modal analysis and static response of higher structural modes an illustrative example is presented that shows the efficiency of the proposed methodology it considers a building finite element model enforced with non linear hysteretic devices and subject to a stochastic ground acceleration two types of problems are considered a minimum structural weight design problem and an optimal non linear device design problem

structural optimization using beam elements techniques for handling beam elements in structural optimization are investigated the complexities of evaluating the geometrical properties of a section stress recovery and design variable selection are successfully handled by the concept of an element library use of equivalent stress and separation of sensitivity variables and design variables program implementation is based on the use of an existing finite element analysis package and a numerical optimizer the quality of linearization of the behavior constraint functions is also investigated

an efficient approximation technique for frequency constraints in frame optimization an efficient approximation technique is presented for dealing with frequency constraints in frame optimization the method is based on a linear approximation of the eigenvalues with respect to the member section properties using this an approximate optimization problem is solved treating the physical dimensions of the beams as design variables when the eigenvalues are required the section properties are first calculated then using the approximation the eigenvalues are estimated and returned to the optimizer when the approximate optimum is found a detailed analysis is performed and the process is repeated examples are presented to demonstrate the method the method is simple yet treats the physical dimensions of the structure as design variables and allows for large move limits during the approximate optimization

minimum ber linear transceivers for mimo channels via primal decomposition this paper considers the employment of linear transceivers for communication through multiple input multiple output mimo channels with channel state information csi at both sides of the link the design of linear mimo transceivers has been studied since the 1970s by optimizing simple measures of the quality of the system such as the trace of the mean square error matrix subject to a power constraint recent results showed how to solve the problem in an optimal way for the family of schur concave and schur convex cost functions in particular when the constellations used on the different transmit dimensions are equal the bit error rate ber averaged over these dimensions happens to be a schur convex function and therefore it can be optimally solved in a more general case however when different constellations are used the average ber is not a schur convex function and the optimal design in terms of minimum ber is an open problem this paper solves the minimum ber problem with arbitrary constellations by first reformulating the problem in convex form and then proposing two solutions one is a heuristic and suboptimal solution which performs remarkably well in practice the other one is the optimal solution obtained by decomposing the convex problem into several subproblems controlled by a master problem a technique borrowed from optimization theory for which extremely simple algorithms exist thus the minimum ber problem can be optimally solved in practice with very simple algorithms

multi material topology optimization considering interface behavior via xfem and level set method abstract in most of the existing topology optimization studies of multi material structures the interface of different materials was assumed to be perfectly bonded optimal design based on the perfect interface assumption may introduce the risk of failure caused by interface debonding this paper presents an efficient multi material topology optimization strategy for seeking the optimal layout of structures considering the cohesive constitutive relationship of the interface based on the color level set method to describe the topology and the interface the interface behavior is simulated by combining the extended finite element method xfem and the cohesive model on fixed mesh this enables modeling of possible separation of material interfaces and thus provides a more realistic model of multi material structures furthermore this interface modeling technique avoids the difficulty of re meshing when tracking the moving cohesive interface positions during the optimization process in the topology optimization model the normal velocities defined on the level set points are considered as design variables in conjunction with the adjoint variable sensitivity analysis these design variables are updated by using the mathematical programming approach and then used to interpolate the boundary velocities these boundary velocities are extrapolated to the whole domain with the fast marching method and used to advance the structural boundary through the hamilton jacobi equation this topology optimization technique can handle multiple constraints easily in the framework of level set method and at the same time preserve the signed distance property of the level set functions two numerical examples are given to demonstrate the effectiveness of the present method it is also revealed that the optimal design considering interface behavior may exhibit tension compression non symmetric topology in which material interfaces mainly undergo compression

optimal structural design considering flexibility a topology optimization method based on the homogenization method the homogenization design method has been successfully applied to a variety of optimization problems such as the stiffness maximization problem and the eigen frequency maximization problem in this study a methodology to obtain the optimal structure design considering flexibility is developed as a new extension of the homogenization design method first flexibility is formulated using the mutual energy concept second a new multi objective function is proposed to obtain optimal solutions incorporating flexibility and stiffness next the topology optimization procedure is constructed using the homogenization method and sequential linear programming slp finally some examples are presented to confirm that the methodology presented here can provide flexible structures satisfying the problem specifications

separable convex optimization problems with linear ascending constraints separable convex optimization problems with linear ascending inequality and equality constraints are addressed in this paper an algorithm that explicitly characterizes the optimum point in a finite number of steps is described the optimum value is shown to be monotone with respect to a partial order on the constraint parameters moreover the optimum value is convex with respect to these parameters this work generalizes the existing algorithms of morton von randow and ringwald math programming 32 1985 pp 238 241 and viswanath and anantharam ieee trans inform theory 48 2002 pp 1295 1318 to a wider class of separable convex objective functions computational experiments that compare the proposed algorithm with a standard convex optimization tool are also provided

beyond the regret minimization barrier optimal algorithms for stochastic strongly convex optimization we give novel algorithms for stochastic strongly convex optimization in the gradient oracle model which return a o 1 t approximate solution after t iterations the first algorithm is deterministic and achieves this rate via gradient updates and historical averaging the second algorithm is randomized and is based on pure gradient steps with a random step size his rate of convergence is optimal in the gradient oracle model this improves upon the previously known best rate of o log t t which was obtained by applying an online strongly convex optimization algorithm with regret o log t to the batch setting we complement this result by proving that any algorithm has expected regret of log t in the online stochastic strongly convex optimization setting this shows that any online to batch conversion is inherently suboptimal for stochastic strongly convex optimization this is the first formal evidence that online convex optimization is strictly more difficult than batch stochastic convex optimization

efficient accurate reanalysis for structural optimization the combined approximations method developed recently is an efficient reanalysis method providing high quality results through the use of this approach the computed terms of a series expansion are used as basis vectors in a reduced basis expression by solving a reduced system of equations first and second order approximations were demonstrated in previous studies for small structures the efficiency and the accuracy of the method are improved and results are illustrated for larger structures by the utilization of a gram schmidt orthogonalization procedure new set of basis vectors is generated and normalized such that the reduced system of equations becomes uncoupled the advantage in using the latter vectors is that all expressions for evaluating the displacements are explicit functions of the design variables consequently additional vectors can be considered without modifying the calculations that have already been carried out in addition the uncoupled system is more well conditioned some considerations related to the efficiency of the solution process and the accuracy of the results are discussed and the effect of various parameters on the accuracy is studied numerical results are demonstrated for several medium and large scale structures it is shown that accurate and efficient approximations are achieved for very large changes in the design

feasible methods for nonconvex nonsmooth problems with applications in green communications we propose a general feasible method for nonsmooth nonconvex constrained optimization problems the algorithm is based on the inexact solution of a sequence of strongly convex optimization subproblems followed by a step size procedure key features of the scheme are i it preserves feasibility of the iterates for nonconvex problems with nonconvex constraints ii it can handle nonsmooth problems and iii it naturally leads to parallel distributed implementations we illustrate the application of the method to an open problem in green communications whereby the energy consumption in mimo multiuser interference networks is minimized subject to nonconvex quality of service constraints

a mass constraint formulation for structural topology optimization with multiphase materials this work is focused on the topology optimization of lightweight structures consisting of multiphase materials instead of adopting the common idea of using volume constraint a new problem formulation with mass constraint is proposed meanwhile recursive multiphase materials interpolation rmmi and uniform multiphase materials interpolation ummi schemes are discussed and compared based on numerical tests and theoretical analysis it is indicated that the nonlinearity of the mass constraint introduced by rmmi brings numerical difficulties to attain the global optimum of the optimization problem on the contrary the ummi 2 scheme makes it possible to formulate the mass constraint in a linear form with separable design variables one such formulation favors very much the problem resolution by means of mathematical programming approaches especially the convex programming methods moreover numerical analysis indicates that fully uniform initial weighting is beneficial to seek the global optimum when ummi 2 scheme is used besides the relationship between the volume constraint and mass constraint is theoretically revealed the filtering technique is adapted to avoid the checkerboard pattern related to the problem with multiphase materials numerical examples show that the ummi 2 scheme with fully uniform initial weighting is reliable and efficient to deal with the structural topology optimization with multiphase materials and mass constraint meanwhile the mass constraint formulation is evidently more significant than the volume constraint formulation copyright 2011 john wiley sons ltd

a multi resolution approach for multi material topology optimization based on isogeometric analysis abstract a novel multi resolution scheme to perform the multi material topology optimization in the framework of isogeometric analysis iga is proposed to create high resolution optimized designs with a lower computational cost a new variable parameter space is supplemented to define design density variables and represent the optimal material distribution utilizing the bivariate b spline basis functions these functions are simply obtained by k refinement strategy in the iga the non uniform rational b spline nurbs basis functions are employed to exactly describe geometric domains and approximate unknown solutions in finite element analysis fea as well an alternating active phase algorithm associated with the block gauss seidel method is employed to convert a multiphase topology optimization problem under multiple volume fraction constraints into many binary phase topology optimization sub problems with only one volume fraction constraint accordingly the number of design variables depends only on one active phase in each of those sub problems regardless of the number of material phases and is significantly decreased in comparison with the original problem the optimality criteria oc method is used as an optimizer to update solutions for such sub problems the effectiveness and robustness of the proposed method are verified via testing various benchmark examples

duality and optimization for generalized multi hop mimo amplify and forward relay networks with linear constraints we consider a generalized multi hop mimo amplify and forward af relay network with multiple sources destinations and arbitrarily number of relays we establish two dualities and the corresponding dual transformations between such a network and its dual respectively under single network linear constraint and per hop linear constraint a unified optimization framework is proposed to find a stationary point for an important class of nonconvex optimization problems of af relay networks based on a local lagrange dual method where the primal algorithm only finds a stationary point for the inner loop problem of maximizing the lagrangian w r t the primal variables the input covariance matrices are shown to satisfy a polite water filling structure at a stationary point of the inner loop problem the duality and polite water filling are exploited to design fast primal algorithms compared with the existing algorithms the proposed optimization framework with duality based primal algorithms can be used to solve more general problems with lower computation cost

explicit constraint approximation forms in structural optimization part 1 analyses and projections abstract an analytical study of several alternative forms of constraint approximation relevant to problems in structural design is presented limitations of the existing forms of the constraint approximations are stated and methods are outlined to improve them a new generalized form of constraint approximation is proposed for optimal design problems with and without design variable linking a power form of constraint approximation is derived for bending types of finite elements having nonlinear size stiffness relationships a detailed analysis to determine the relative effectiveness of the various forms is included a rating guideline is proposed to quantify the characteristics of chosen approximations or family of approximations on grounds of accuracy and of conservatism of remaining feasible

high quality approximation of eigenvalues in structural optimization a new function for approximating natural frequency constraints during structural optimization is presented the rayleigh quotient approximation rqa presented here icreases the quality of the approximate frequency constraint by approximating the modal strain and kinetic energies instead of the frequency eigenvalue itself

a multi material level set based topology and shape optimization method abstract this paper proposes a new multi material level set mm ls topology description model for topology and shape optimization of structures involving multiple materials each phase is represented by a combined formulation of different level set functions with a total number of m level set functions this approach provides a representation of m materials and one void phase totally m 1 phases the advantages of the proposed method include 1 it can guarantee that each point contains exactly one phase without overlaps between each two phases and redundant regions within the design domain 2 it possesses an explicit mathematical expression which greatly facilitates the design sensitivity analysis and 3 it retains the merits of the level set method including smooth boundary and distinct interface a parametric level set method is applied to evolve the topology and shape of multi material structures with a high computational efficiency several numerical examples are presented to demonstrate the effectiveness of the proposed method

asynchronous stochastic coordinate descent parallelism and convergence properties we describe an asynchronous parallel stochastic proximal coordinate descent algorithm for minimizing a composite objective function which consists of a smooth convex function added to a separable convex function in contrast to previous analyses our model of asynchronous computation accounts for the fact that components of the unknown vector may be written by some cores simultaneously with being read by others despite the complications arising from this possibility the method achieves a linear convergence rate on functions that satisfy an optimal strong convexity property and a sublinear rate 1 k on general convex functions near linear speedup on a multicore system can be expected if the number of processors is o n 1 4 we describe results from implementation on 10 cores of a multicore processor

a new multi material level set topology optimization method with the length scale control capability abstract multi material level set topology optimization methods conventionally rely on the overlap of multiple level set functions to realize the multi material structural representation however this representation may produce redundant material phases and the signed distance information is no longer available within the individual material regions to fix these issues a new multi material level set topology optimization method is proposed in this paper where m level set functions represent m material phases plus the void and the signed distance information is straightforwardly available in each material phase to be specific each level set function corresponds to a material phase and the overlapping areas are filled with an artificial material type the property of which is weaker than any of the involved material types this artificial material plays the role of penalizing the overlap areas to vanish which is different from the close to zero property material type for the void hence the optimization process starts with any multi level set interpolated input and the overlapping areas will gradually vanish based on this new method we have successfully realized the component length scale control on multi material structures and innovatively an approach has been proposed to realize the uniform component thickness control without need of pre specifying the thickness target

optimum linear joint transmit receive processing for mimo channels with qos constraints this paper considers vector communications through multiple input multiple output mimo channels with a set of quality of service qos requirements for the simultaneously established substreams linear transmit receive processing also termed linear precoder at the transmitter and linear equalizer at the receiver is designed to satisfy the qos constraints with minimum transmitted power the exact conditions under which the problem becomes unfeasible are given although the original problem is a complicated nonconvex problem with matrix valued variables with the aid of majorization theory we reformulate it as a simple convex optimization problem with scalar variables we then propose a practical and efficient multilevel water filling algorithm to optimally solve the problem for the general case of different qos requirements the optimal transmit receive processing is shown to diagonalize the channel matrix only after a very specific prerotation of the data symbols for situations in which the resulting transmit power is too large we give the precise way to relax the qos constraints in order to reduce the required power based on a perturbation analysis we also propose a robust design under channel estimation errors that has an important interest for practical systems numerical results from simulations are given to support the mathematical development of the problem

arock an algorithmic framework for asynchronous parallel coordinate updates finding a fixed point to a nonexpansive operator i e x tx abstracts many problems in numerical linear algebra optimization and other areas of data science to solve fixed point problems

topology optimization of continuum structures with local stress constraints we introduce an extension of current technologies for topology optimization of continuum structures which allows for treating local stress criteria we first consider relevant stress criteria for porous composite materials initially by studying the stress states of the so called rank 2 layered materials then on the basis of the theoretical study of the rank 2 microstructures we propose an empirical model that extends the power penalized stiffness model also called simp for solid isotropic microstructure with penalization for inter mediate densities in a second part solution aspects of topology problems are considered to deal with the so called singularity phenomenon of stress constraints in topology design an constraint relaxation of the stress constraints is used we describe the mathematical programming approach that is used to solve the numerical optimization problems and show results for a number of example applications 1998 john wiley sons ltd

topology optimization of nonlinear heat conduction problems involving large temperature gradient abstract in this work we develop a topology optimization method for steady state nonlinear heat conduction problems involving large temperature gradient to minimize the maximum structural temperature temperature dependent material properties tdmps are taken into account to break the widely used assumption of constant material properties cmps in conventional topology optimization the kreisselmeier steinhauser function is adopted as an aggregated measure of the maximum temperature over a specific region and the adjoint method is used to derive the sensitivity expressions to effectively solve the well known unsymmetric adjoint problem caused by material nonlinearity an engineering oriented stationary iterative method esim is constructed to transform the unsymmetric adjoint problem into a symmetric one with a series of right hand sides that can be efficiently solved with mature linear system solvers both 2d and 3d numerical examples are provided to illustrate the validity and utility of the proposed method including the accuracy and convergence of the esim the results show that the assumption of cmps can result in significant inaccuracy in the analysis and design of heat conduction systems working under large temperature gradient on the contrary by considering tdmps and employing the proposed method reasonable designs are achieved and thermal performance is greatly improved

an efficient direct solution of cave filling problems waterfilling problems subjected to peak power constraints are solved which are known as cave filling problems cfp the proposed algorithm finds both the optimum number of positive powers and the number of resources that are assigned the peak power before finding the specific powers to be assigned the proposed solution is non iterative and results in a computational complexity which is of the order of m o m where m is the total number of resources which is significantly lower than that of the existing algorithms given by an order of m 2 o m 2 under the same memory requirement and sorted parameters the algorithm is then generalized both to weighted cfp wcfp and wcfp requiring the minimum power these extensions also result in a computational complexity of the order of m o m finally simulation results corroborating the analysis are presented

practical algorithms for a family of waterfilling solutions many engineering problems that can be formulated as constrained optimization problems result in solutions given by a waterfilling structure the classical example is the capacity achieving solution for a frequency selective channel for simple waterfilling solutions with a single waterlevel and a single constraint typically a power constraint some algorithms have been proposed in the literature to compute the solutions numerically however some other optimization problems result in significantly more complicated waterfilling solutions that include multiple waterlevels and multiple constraints for such cases it may still be possible to obtain practical algorithms to evaluate the solutions numerically but only after a painstaking inspection of the specific waterfilling structure in addition a unified view of the different types of waterfilling solutions and the corresponding practical algorithms is missing the purpose of this paper is twofold on the one hand it overviews the waterfilling results existing in the literature from a unified viewpoint on the other hand it bridges the gap between a wide family of waterfilling solutions and their efficient implementation in practice to be more precise it provides a practical algorithm to evaluate numerically a general waterfilling solution which includes the currently existing waterfilling solutions and others that may possibly appear in future problems

local stress constrained and slope constrained sand topology optimisation summary we study the alternative simultaneous analysis and design sand formulation of the local stress and slope constrained topology design problem it is demonstrated that a standard trust region lagrange newton sequential quadratic programming sqp type algorithm based in this case on strictly convex and separable approximate subproblems may converge to singular optima of the local stress constrained problem without having to resort to relaxation or perturbation techniques moreover due to the negation of the sensitivity analyses in sand the density and displacement variables are independent and the immense sparsity of the sand problem solutions to large scale problem instances may be obtained in a reasonable amount of computation time this article is protected by copyright all rights reserved

alternative approximation concepts for space frame synthesis a structural synthesis methodology for the minimum mass design of 3 dimensionall frame truss structures under multiple static loading conditions and subject to limits on displacements rotations stresses local buckling and element cross sectional dimensions is presented a variety of approximation concept options are employed to yield near optimum designs after no more than 10 structural analyses available options include a formulation of the nonlinear mathematcal programming problem in either reciprocal section property rsp or cross sectional dimension csd space b two alternative approximate problem structures in each design space and c three distinct assumptions about element end force variations fixed element design element linking and temporary constraint deletion features are also included the solution of each approximate problem in either its primal or dual form is obtained using conmin a feasible directions program the frame truss synthesis methodology is implemented in the compass computer program and is used to solve a variety of problems these problems were chosen so that in addition to exercising the various approximation concepts options the results could be compared with previously published work

scale related topology optimization of cellular materials and structures the integrated optimization of lightweight cellular materials and structures are discussed in this paper by analysing the basic features of such a two scale problem it is shown that the optimal solution strongly depends upon the scale effect modelling of the periodic microstructure of material unit cell muc i e the so called representative volume element rve however with the asymptotic homogenization method used widely in actual topology optimization procedure effective material properties predicted can give rise to limit values depending upon only volume fractions of solid phases properties and spatial distribution of constituents in the microstructure regardless of scale effect from this consideration we propose the design element de concept being able to deal with conventional designs of materials and structures in a unified way by changing the scale and aspect ratio of the de scale related effects of materials and structures are well revealed and distinguished in the final results of optimal design patterns to illustrate the proposed approach numerical design problems of 2d layered structures with cellular core are investigated

perturbed iterate analysis for asynchronous stochastic optimization we introduce and analyze stochastic optimization methods where the input to each update is perturbed by bounded noise we show that this framework forms the basis of a unified approach to analyzing asynchronous implementations of stochastic optimization algorithms by viewing them as serial methods operating on noisy inputs using our perturbed iterate framework we provide new analyses of the hogwild algorithm and asynchronous stochastic coordinate descent that are simpler than earlier analyses remove many assumptions of previous models and in some cases yield improved upper bounds on the convergence rates we proceed to apply our framework to develop and analyze kromagnon a novel parallel sparse stochastic variance reduced gradient svrg algorithm we demonstrate experimentally on a 16 core machine that the sparse and parallel version of svrg is in some cases more than four orders of magnitude faster than the standard svrg algorithm

asynchronous parallel algorithms for nonconvex optimization we propose a new asynchronous parallel block descent algorithmic framework for the minimization of the sum of a smooth nonconvex function and a nonsmooth convex one subject to both convex and nonconvex constraints the proposed framework hinges on successive convex approximation techniques and a novel probabilistic model that captures key elements of modern computational architectures and asynchronous implementations in a more faithful way than current state of the art models other key features of the framework are 1 it covers in a unified way several specific solution methods 2 it accommodates a variety of possible parallel computing architectures and 3 it can deal with nonconvex constraints almost sure convergence to stationary solutions is proved and theoretical complexity results are provided showing nearly ideal linear speedup when the number of workers is not too large

globally convergent optimization algorithm using conservative convex separable diagonal quadratic approximations we implement and test a globally convergent sequential approximate optimization algorithm based on convexified diagonal quadratic approximations the algorithm resides in the class of globally convergent optimization methods based on conservative convex separable approximations developed by svanberg at the start of each outer iteration the initial curvatures of the diagonal quadratic approximations are estimated using historic objective and or constraint function value information or by building the diagonal quadratic approximation to the reciprocal approximation at the current iterate during inner iterations these curvatures are increased if no feasible descent step can be made although this conditional enforcement of conservatism on the subproblems is a relaxation of the strict conservatism enforced by svanberg global convergence is still inherited from the conservative convex separable approximations framework developed by svanberg a numerical comparison with the globally convergent version of the method of moving asymptotes and the nonconservative variants of both our algorithm and method of moving asymptotes is made

an efficient reliability based optimization scheme for uncertain linear systems subject to general gaussian excitation a very efficient methodology to carry out reliability based optimization of linear systems with random structural parameters and random excitation is presented the reliability based optimization problem is formulated as the minimization of an objective function for a specified reliability the probability that design conditions are satisfied within a given time interval is used as a measure of the system reliability approximation concepts are used to construct high quality approximations of dynamic responses in terms of the design variables and uncertain structural parameters during the design process the approximations are combined with an efficient simulation technique to generate explicit approximations of the reliability measures with respect to the design variables in particular an efficient importance sampling technique is used to estimate the failure probabilities the number of dynamic analyses as well as reliability estimations required during the optimization process are reduced dramatically several example problems are presented to illustrate the effectiveness and feasibility of the suggested approach

the method of moving asymptotes a new method for structural optimization a new method for non linear programming in general and structural optimization in particular is presented in each step of the iterative process a strictly convex approximating subproblem is generated and solved the generation of these subproblems is controlled by so called moving asymptotes which may both stabilize and speed up the convergence of the general process

on the precoder design of a wireless energy harvesting node in linear vector gaussian channels with arbitrary input distribution a wireless energy harvesting node wehn operating in linear vector gaussian channels with arbitrarily distributed input symbols is considered in this paper the precoding strategy that maximizes the mutual information along n independent channel accesses is studied under non causal knowledge of the channel state and harvested energy commonly known as offline approach it is shown that at each channel use the left singular vectors of the precoder are equal to the eigenvectors of the gram channel matrix additionally an expression that relates the optimal singular values of the precoder with the energy harvesting profile through the minimum mean square error mmse matrix is obtained then the specific situation in which the right singular vectors of the precoder are set to the identity matrix is considered in this scenario the optimal offline power allocation named mercury water flowing is derived and an intuitive graphical representation is presented two optimal offline algorithms to compute the mercury water flowing solution are proposed and an exhaustive study of their computational complexity is performed moreover an online algorithm is designed which only uses causal knowledge of the harvested energy and channel state finally the achieved mutual information is evaluated through simulation

a hybrid optimal synthesis method for truss structures considering shape material and sizing variables a generalized hybrid optimal synthesis method is developed for truss structures in which the design variables are the co ordinates of the panel points cross sectional areas and discrete material kinds of member elements the primary design problem is formulated in terms of the shape material and sizing variables and approximated to a sequence of convex and separable subproblems by using mixed direct reciprocal design variables each subproblem is solved by a dual method in which the continuous shape and sizing variables are optimized by a newton type algorithm and the discrete material and continuous sizing variables are improved by a discrete sensitivity analysis using the proposed method discrete material kinds shape and sizing variables can be systematically improved to obtain an optimum solution the rigourness reliability and efficiency of the method are demonstrated by applying it to the minimum cost design of trusses subjected to stress and displacement constraints

a unified parametric design approach to structural shape optimization this paper presents a general parametric design approach for 2 d shape optimization problems this approach has been achieved by integrating practical design methodologies into numerical procedures it is characterized by three features i automatic selection of a minimum number of shape design variables based on the cad geometric model ii integration of sequential convex programming algorithms to solve equality constrained optimization problems iii efficient sensitivity analysis by means of the improved semi analytical method it is shown that shape design variables can be either manually or systematically identified with the help of equality constraints describing the relationship between geometric entities numerical solutions are performed to demonstrate the applicability of the proposed approach a discussion of the results is also given

convex separable problems with linear constraints in signal processing and communications in this work we focus on separable convex optimization problems with box constraints and a set of triangular linear constraints the solution is given in closed form as a function of some lagrange multipliers that can be computed through an iterative procedure in a finite number of steps graphical interpretations are given casting valuable insights into the proposed algorithm and allowing to retain some of the intuition spelled out by the water filling policy it turns out that it is not only general enough to compute the solution to different instances of the problem at hand but also remarkably simple in the way it operates we also show how some power allocation problems in signal processing and communications can be solved with the proposed algorithm

topology optimization with multiple materials via moving morphable component mmc method summary with the fast development of additive manufacturing am technology topology optimization involving multiple materials has received ever increasing attention traditionally this kind of optimization problem is solved within the implicit solution framework using the simp solid isotropic material with penalization or level set method this treatment however will inevitably lead to a large number of design variables especially when many types of materials are involved and three dimensional 3d problems are considered this is due to the fact that for each type of material a corresponding density field level function defined on the entire design domain must be introduced to describe its distribution in the present paper a novel approach for topology optimization with multiple materials is established based on the moving morphable component mmc framework with use of this approach topology optimization problems with multiple materials can be solved with much less numbers of design variables and degrees of freedom numerical examples provided demonstrate the effectiveness of the proposed approach

on the equivalence of optimality criterion and sequential approximate optimization methods in the classical topology layout problem we study the classical topology optimization problem in which minimum compliance is sought subject to linear constraints using a dual statement we propose two separable and strictly convex subproblems for use in sequential approximate optimization sao algorithms respectively the subproblems use reciprocal and exponential intermediate variables in approximating the non linear compliance objective function any number of linear constraints or linearly approximated constraints are provided for the relationships between the primal variables and the dual variables are found in analytical form for the special case when only a single linear constraint on volume is present we note that application of the ever popular optimality criterion oc method to the topology optimization problem combined with arbitrary values for the heuristic numerical damping factor proposed by bendsoe results in an updating scheme for the design variables that is identical to the application of a rudimentary dual sao algorithm in which the subproblems are based on exponential intermediate variables what is more we show that the popular choice for the damping factor 0 5 is identical to the use of sao with reciprocal intervening variables finally computational experiments reveal that subproblems based on exponential intervening variables result in improved efficiency and accuracy when compared to sao subproblems based on reciprocal intermediate variables and hence the heuristic topology oc method hitherto used this is attributed to the fact that a different exponent is computed for each design variable in the two point exponential approximation we have used using gradient information at the previously visited point copyright 2007 john wiley sons ltd

multimaterial topology optimization by volume constrained allen cahn system and regularized projected steepest descent method abstract a new computational algorithm is introduced in the present study to solve multimaterial topology optimization problems it is based on the penalization of the objective functional by the multiphase volume constrained ginzburg landau energy functional the update procedure is based on the gradient flow of the objective functional by a fractional step projected steepest descent method in the first step the new design is found based on the projected steepest descent method to ensure the reduction in the objective functional simultaneously satisfying the control constraints in the second step regularization step an h 1 regularity of the solution is ensured while keeping the feasibility of solution with respect to the set of control constraints the presented algorithm could be accounted as a constrained h 1 optimization algorithm which according to our knowledge has not been reported to solve such kind of problems yet the success and efficiency of the presented method are shown through several test problems numerical results show that the presented algorithm ends with a near 0 1 topology and its computational cost scales sub linearly by the number of phases for the sake of reader convenience and the ease of further extension the matlab implementation of the presented algorithm is included in the appendix

topology optimization on two dimensional manifolds abstract this paper presents topology optimization on general two dimensional manifolds for phenomena described by second order partial differential equations where the material interpolation is implemented by using the material distribution method when a physical field is defined on a two dimensional manifold the material interpolation is implemented on a material parameter in the partial differential equation used to describe the distribution of the physical field when the physical field is defined on a three dimensional domain with its boundary conditions defined on a two dimensional manifold corresponding a surface or an interface of this three dimensional domain the material density is used to formulate a mixed boundary condition of the partial differential equation for the physical field and implement the penalization between two different boundary types based on the homeomorphic property of two dimensional manifolds typical two dimensional manifolds e g sphere torus mobius strip and klein bottle are included in the numerical tests which are used to demonstrate this topology optimization approach for the design problems of fluidic mechanics heat transfer and electromagnetics

optimal training design for channel estimation in decode and forward relay networks with individual and total power constraints in this paper we study the channel estimation and the optimal training design for relay networks that operate under the decode and forward df strategy with the knowledge of the interference covariance in addition to the total power constraint on all the relays we introduce individual power constraint for each relay which reflects the practical scenario where all relays are separated from one another considering the individual power constraint for the relay networks is the major difference from that in the traditional point to point communication systems where only a total power constraint exists for all colocated antennas two types of channel estimation are involved maximum likelihood ml and minimum mean square error mmse for ml channel estimation the channels are assumed as deterministic and the optimal training results from an efficient multilevel waterfilling type solution that is derived from the majorization theory for mmse channel estimation however the second order statistics of the channels are assumed known and the general optimization problem turns out to be nonconvex we instead consider three special yet reasonable scenarios the problem in the first scenario is convex and could be efficiently solved by state of the art optimization tools closed form waterfilling type solutions are found in the remaining two scenarios of which the first one has an interesting physical interpretation as pouring water into caves

randomized smoothing for stochastic optimization we analyze convergence rates of stochastic optimization algorithms for nonsmooth convex optimization problems by combining randomized smoothing techniques with accelerated gradient methods we obtain convergence rates of stochastic optimization procedures both in expectation and with high probability that have optimal dependence on the variance of the gradient estimates to the best of our knowledge these are the first variance based rates for nonsmooth optimization we give several applications of our results to statistical estimation problems and provide experimental results that demonstrate the effectiveness of the proposed algorithms we also describe how a combination of our algorithm with recent work on decentralized optimization yields a distributed stochastic optimization algorithm that is order optimal

a novel method of non probabilistic reliability based topology optimization corresponding to continuum structures with unknown but bounded uncertainties abstract a new non probabilistic reliability based topology optimization nrbto method for detailed design of continuum structures is proposed in this paper in which the unknown but bounded ubb uncertainties existing in material and external loads are considered simultaneously based on the interval set theoretic model traditional displacement constraint is transformed into the non probabilistic reliability format in which a novel measuring index namely the optimization feature distance is defined by a combination of the area ratio ideas thus the optimal layout issue is converted by the lightweight design problem with displacement reliability constraints moreover the interval parametric vertex approach and the adjoint vector method are also employed to obtain the sensitivity information between the reliability measurement and design variables by utilizing the method of moving asymptotes mma the optimization problem that is investigated can be solved iteratively two engineering examples are eventually presented to demonstrate the validity and effectiveness of the methodology that has been developed and numerical results show that considering the ubb uncertainty effects during the whole procedure of topology optimization may have a significant influence on the final structural configurations

framework for the buckling optimization of variable angle tow composite plates variable angle tow describes fibers in a composite lamina that have been steered curvilinearly in doing so substantially enlarged freedom for stiffness tailoring of composite laminates is enabled variable angle tow composite structures have been shown to have improved buckling and postbuckling load carrying capability when compared to straight fiber composites however their structural analysis and optimal design is more computationally expensive due to the exponential increase in number of variables associated with spatially varying planar fiber orientations in addition to stacking sequence considerations in this work an efficient two level optimization framework using lamination parameters as design variables has been enhanced and generalized to the design of variable angle tow plates new explicit stiffness matrices are found in terms of component material invariants and lamination parameters the convex hull property of b splines is exploited to ensure pointwise feasibility of lamination paramet

structural reanalysis for general layout modifications a procedure for reanalysis of structures subjected to various layout modifications is presented the procedure is based on exact analysis of the initial design it is suitable for all types of layout changes including the general case in which some members and joints are added other members and joints are deleted and some joint coordinates are modified in the particular and challenging case of addition of joints where the number of degrees of freedom is increased a simple reanalysis of a modified initial design is first carried out further changes are then applied to the latter design it is shown that for changes in a limited number of members of a truss structure an exact solution is readily achieved for changes in numerous members of a general structure an approximate solution can be efficiently obtained high quality approximations are demonstrated for various types of layout modifications

an approximation concepts approach to shape optimal design abstract in the past much of the work done in structural optimization consisted in resizing the members of fixed configuration models in that case a powerful design procedure has now emerged which is based on the coordinate use of explicit high quality approximations of the behavior constraints and dual methods of mathematical programming there is however a large class of problems for which the main degrees of freedom for the designer correspond to the shape of the structure itself the main objectives of this paper are to recall briefly a convenient geometric representation in which the boundaries of the structure are represented by bezier or b spline curves and then to discuss the choice of optimization algorithm it is shown that cost efficient methods for structural sizing may be advantageously extended to shape optimal design problems different approximation schemes are tested and a new general optimization algorithm is presented that combines mixed approximations and dual methods many large scale applications are treated to demonstrate the generality and the efficiency of the new formulation finally considerations are given about an integrated approach including cad computer codes and finite element optimization software

convex primal decomposition for multicarrier linear mimo transceivers the design of linear transceivers for multiple input multiple output mimo communication systems with channel state information is particularly challenging for two main reasons first since several substreams are established through the mimo channel it is not even clear how the quality of the system should be measured second once a cost function has been chosen to measure the quality the optimization of the system according to such criterion is generally difficult due to the nonconvexity of the problem recent results have solved the problem for the wide family of schur concave convex functions resulting in simple closed form solutions when the system is modeled as a single mimo channel however with several mimo channels such as in multi antenna multicarrier systems the solution is generally more involved leading in some cases to the need to employ general purpose interior point methods this problem is specifically addressed in this paper by combining the closed form solutions for single mimo channels with a primal decomposition approach resulting in a simple and efficient method for multiple mimo channels the extension to functions that are not schur concave convex is also briefly considered relating the present work with a recently proposed method to minimize the average bit error rate ber of the system

power minimization for cdma under colored noise rate constrained power minimization pmin over a code division multiple access cdma channel with correlated noise is studied pmin is shown to be an instance of a separable convex optimization problem subject to linear ascending constraints pmin is further reduced to a dual problem of sumrate maximization rmax the results highlight the underlying unity between pmin rmax and a problem closely related to pmin but with linear receiver constraints subsequently conceptually simple sequence design algorithms are proposed to explicitly identify an assignment of sequences and powers that solve pmin the algorithms yield an upper bound of 2n 1 on the number of distinct sequences where n is the processing gain the sequences generated using the proposed algorithms are in general real valued if a rate splitting and multi dimensional cdma approach is allowed the upper bound reduces to n distinct sequences in which case the sequences can form an orthogonal set and be binary plusmn1 valued

new approximation method for stress constraints in structural synthesis a new approximation method for dealing with stress constraints in structural synthesis is presented in previous methods it has been common to create an approximation of the actual constraints with respect to the design variables and then use this with optimization to produce a new candidate design in the present method the finite element nodal forces are instead approximated and these are used to create an explicit but often nonlinear approximation to the original problem the principal motivation is to create the best approximation possible in order to reduce the number of detailed finite element analyses needed to reach the optimum the method is shown to be quite simple while providing significant efficiency gains in the overall optimization task also the method produces such high quality approximations to the original problem that the need for move limits during the approximate optimization stage is greatly reduced examples are offered and compared with published results to demonstrate the efficiency and reliability of the proposed method it is concluded that there are considerable gains yet to be achieved through continued careful investigation of approximation techniques

optimal design of multiphase composites under elastodynamic loading abstract an algorithm is proposed to optimize the performance of multiphase structures composites under elastodynamic loading conditions the goal is to determine the distribution of material in the structure such that the time averaged total stored energy of structure is minimized a penalization strategy is suggested to avoid the checkerboard instability simultaneously to generate near 0 1 topologies as a result of this strategy the solutions of presented algorithm are sufficiently smooth and possess the regularity of h 1 function space a simple method for the continuum adjoint sensitivity analysis of the corresponding pde constrained optimization problem is presented it is general and can be easily applied to a wide range of alternative problems the success of the introduced algorithm is studied by numerical experiments on two dimensional model problems for different numbers of phases according to numerical results the objective functional is reduced monotonically with iterations moreover the final topologies at the optimal solutions are near 0 1 the dynamic behavior of optimal designs is compared to that of initial ones to show the impact of optimization on the performance of structures