exact penalty results for mathematical programs with vanishing constraints a mathematical program with vanishing constraints mpvc is a constrained optimization problem arising in certain engineering applications the feasible set has a complicated structure so that the most familiar constraint qualifications are usually violated this in turn implies that standard penalty functions are typically non exact for mpvcs we therefore develop a new mpvc tailored penalty function which is shown to be exact under reasonable assumptions this new penalty function can then be used to derive or recover suitable optimality conditions for mpvcs

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

a relation between trinucleotide comma free codes and trinucleotide circular codes the comma free codes and circular codes are two important classes of codes in code theory and in genetics fifty years ago before the discovery of the genetic code a trinucleotide triletter comma free code was proposed for associating the codons of genes with the amino acids of proteins more recently in the last ten years trinucleotide circular codes have been identified statistically in different genomes here we identify a relation between these two classes of trinucleotide codes by constructing a hierarchy of comma free and circular codes

strong duality and kkt conditions in nonconvex optimization with a single equality constraint and geometric constraint some topological and geometric characterizations of strong duality for a non convex optimization problem under a single equality and geometric constraints are established in particular a hidden convexity of the conic hull of joint range of the pair of functions associated to the original problem is obtained applications to derive a characterization of the validity of kkt conditions without standard constraints qualification are also discussed it goes beyond the exact penalization technique several examples showing our results provide much more information than those appearing elsewhere are given finally the standard quadratic problem involving a non necessarily polyhedral cone is analyzed in detail

a classification of 20 trinucleotide circular codes trinucleotide comma free codes and trinucleotide circular codes are two important classes of codes in code theory and theoretical biology a trinucleotide circular code containing exactly 20 elements is called here a 20 trinucleotide circular code in this paper solving a combinatorial problem of hard computational complexity we extend and improve our results of c j michel g pirillo and m a pirillo 2008 14 concerning the small class of 528 self complementary 20 trinucleotide circular codes to the complete class of the 20 trinucleotide circular codes which contains 12 964 440 elements a surprising relation with the symmetric group s 4 appears but it remains unexplained so far

stationary conditions for mathematical programs with vanishing constraints using weak constraint qualifications abstract we consider a class of optimization problems that is called a mathematical program with vanishing constraints mpvc for short this class has some similarities to mathematical programs with equilibrium constraints mpecs for short and typically violates standard constraint qualifications hence the well known karush kuhn tucker conditions do not provide necessary optimality criteria in order to obtain reasonable first order conditions under very weak assumptions we introduce several mpvc tailored constraint qualifications discuss their relation and prove an optimality condition which may be viewed as the counterpart of what is called m stationarity in the mpec field

a new regularization method for mathematical programs with complementarity constraints with strong convergence properties mathematical programs with equilibrium or complementarity constraints mpecs form a difficult class of optimization problems the feasible set has a very special structure and violates most of the standard constraint qualifications therefore one typically applies specialized algorithms in order to solve mpecs one very prominent class of specialized algorithms are the regularization or relaxation methods the first regularization method for mpecs is due to scholtes siam j optim 11 2001 pp 918 936 but in the meantime there exist a number of different regularization schemes which try to relax the difficult constraints in different ways however almost all regularization methods converge to c stationary points only which is a very weak stationarity concept an exception is a recent method by kadrani dussault and benchakroun siam j optim 20 2009 pp 78 103 whose limit points are shown to be m stationary here we provide a new regularization method which also converges to m sta

a newly developed qp relaxation method for element connectivity parameterization to achieve stress based topology optimization for geometrically nonlinear structures the aim of this work is to present a novel computational approach to employ the stress based topology optimization method stom to minimize the volume subject to the locally defined stress constraints of a geometrically nonlinear structure in the framework of the element connectivity parameterization ecp method considering the locally defined stress constraints in topology optimization to is a classic and challenging engineering problem and successful optimization procedures have recently been developed using the density based to method for linear elastic structures however no study has yet considered the static failure constraint when using to for a geometrically nonlinear structure therefore the present study develops a novel computational approach for the stom for a geometrically nonlinear structure to successfully optimize a geometrically nonlinear structure the unstable element issue must be properly addressed in addition to the stress singularity issue the existence of a large number of constraints and the highly nonlinear behavior of the local stress constraints to effectively resolve these issues this research adopts the ecp method to interpolate and optimize the connectivities among solid finite elements furthermore we find that a stress singularity issue linked to the local optima issue arises in the ecp method that is different from that of the density based to by investigating the singularity behavior in detail we develop a new qp relaxation method that is suitable for the ecp method to demonstrate the improved capability of the proposed ecp method with the modified qp relaxation several two dimensional to problems are solved

the coc algorithm part ii topological geometrical and generalized shape optimization abstract after outlining analytical methods for layout optimization and illustrating them with examples the coc algorithm is applied to the simultaneous optimization of the topology and geometry of trusses with many thousand potential members the numerical results obtained are shown to be in close agreement up to twelve significant digits with analytical results finally the problem of generalized shape optimization finding the best boundary topology and shape is discussed

global optimization of minimum weight truss topology problems with stress displacement and local buckling constraints using branch and bound we present a convergent continuous branch and bound algorithm for global optimization of minimum weight truss topology problems with displacement stress and local buckling constraints valid inequalities which strengthen the problem formulation are derived the inequalities are generated by solving well defined convex optimization problems computational results are reported on a large collection of problems taken from the literature most of these problems are for the first time solved with a proof of global optimality copyright 2004 john wiley sons ltd

a quadratic approximation for structural topology optimization in topology optimization it is customary to use reciprocal like approximations which result in monotonically decreasing approximate objective functions in this paper we demonstrate that efficient quadratic approximations for topology optimization can also be derived if the approximate hessian terms are chosen with care to demonstrate this we construct a dual sao algorithm for topology optimization based on a strictly convex diagonal quadratic approximation to the objective function although the approximation is purely quadratic it does contain essential elements of reciprocal like approximations for self adjoint problems our approximation is identical to the quadratic or second order taylor series approximation to the exponential approximation we present both a single point and a two point variant of the new quadratic approximation

a mixed fem approach to stress constrained topology optimization we present an alternative topology optimization formulation capable of handling the presence of stress constraints in a straightforward fashion the main idea is to adopt a mixed finite element discretization scheme wherein not only displacements as usual but also stresses are the variables entering the formulation by doing so any stress constraint may be handled within the optimization procedure without resorting to post processing operation typical of displacement based techniques that may also cause a loss in accuracy in stress computation if no smoothing of the stress is performed two dual variational principles of hellinger reissner type are presented in continuous and discrete form that which included in a rather general topology optimization problem in the presence of stress constraints that is solved by the method of moving asymptotes int j numer meth engng 1984 24 3 359 373 extensive numerical simulations are performed and ongoing extensions outlined including the optimization of elastoplastic and incompressible media copyright 2007 john wiley sons ltd

characterizing fj and kkt conditions in nonconvex mathematical programming with applications in this paper we analyze the fritz john and karush kuhn tucker kkt conditions for a g teaux differentiable nonconvex optimization problem with inequality constraints and a geometric constraint set the fritz john condition is characterized in terms of an alternative theorem which covers beyond standard situations while characterizations of kkt conditions without assuming constraints qualifications are related to strong duality of a suitable linear approximation of the given problem and the properties of its associated image mapping such characterizations are suitable for dealing with some problems in structural optimization where most of the known constraint qualifications fail in particular several examples are given showing the usefulness and optimality in a certain sense of our results which provide much more information than those including the mordukhovich normal cone or clarke s appearing elsewhere the case with a single inequality constraint is discussed in detail by establishing

on the time transformation of mixed integer optimal control problems using a consistent fixed integer control function nonlinear control systems with instantly changing dynamical behavior can be modeled by introducing an additional control function that is integer valued in contrast to a control function that is allowed to have continuous values the discretization of a mixed integer optimal control problem miocp leads to a non differentiable optimization problem and the non differentiability is caused by the integer values the paper is about a time transformation method that is used to transform a miocp with integer dependent constraints into an ordinary optimal control problem differentiability is achieved by replacing a variable integer control function with a fixed integer control function and a variable time allows to change the sequence of active integer values in contrast to other contributions so called control consistent fixed integer control functions are taken into account here it is shown that these control consistent fixed integer control functions allow a better accuracy in the resulting trajectories in particular in the computed switching times the method is verified on analytical and numerical examples

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

the second moment and the autocovariance function of the squared errors of the garch model since bollerslev and taylor indepedently introduced the garch model almost a decade ago many questions have remained unanswered this paper addresses two of them first what is the autocovariance structure of the squared errors and second what is the condition on the parameters of the garch p q model in order for the

varieties of comma free codes new varieties of comma free codes cfc of length 3 on the 4 letter alphabet are defined and analysed self complementary comma free codes ccfc c 3 comma free codes c 3cfc c 3 self complementary comma free codes c 3ccfc self complementary maximal comma free codes cmcfc c 3 maximal comma free codes c 3mcfc and c 3 self complementary maximal comma free codes c 3cmcfc new properties with words of length 3 4 5 and 6 in comma free codes are used for the determination of growth functions in the studied code varieties

mathematical programs with vanishing constraints optimality conditions and constraint qualifications we consider a difficult class of optimization problems that we call a mathematical program with vanishing constraints problems of this kind arise in various applications including optimal topology design problems of mechanical structures we show that some standard constraint qualifications like licq and mfcq usually do not hold at a local minimum of our program whereas the abadie constraint qualification is sometimes satisfied we also introduce a suitable modification of the standard abadie constraint qualification as well as a corresponding optimality condition and show that this modified constraint qualification holds under fairly mild assumptions we also discuss the relation between our class of optimization problems with vanishing constraints and a mathematical program with equilibrium constraints

optimization of large scale truss structures using sparse sand formulations sparsity features of simultaneous analysis and design sand formulations are studied and exploited for optimization of large scale truss structures three formulations are described and implemented with an existing analysis code sand formulations have large number of variables however gradients of the functions and hessian of the lagrangian are quite sparsely populated therefore this structure of the problem is exploited and an optimization algorithm with sparse matrix capability is used to solve large scale problems an existing analysis software is integrated with an optimizer based on a sparse sequential quadratic programming sqp algorithm to solve sample problems the formulations and algorithms work quite well for the sample problems and their performances are compared and discussed for all the cases considered the sand formulations out perform the conventional formulation except one case further research is suggested to fully study and utilize sparse features of the alternative sand formulations and to develop more efficient sparse solvers for large scale and more complex applications

the application of a unified bayesian stopping criterion in competing parallel algorithms for global optimization abstract the unconstrained global programming problem is addressed using a multistart multialgorithminfrastructure in which different algorithms compete in parallel for a contribution towards a single global stopping criterion denoted the unified bayesian global stopping criterion the use of different algorithms is motivated by the observation that no single global optimization algorithm consistently outperforms all other algorithms when applied to large sets of problems from different classes the bayesian stopping criterion is based on the single assumption that the probability of each algorithm converging to the global optimum is at least as large as the probability of convergence to any other local minimum this assumption is often valid in the case of practical problems of physical origin e g determining physical configurations corresponding to minimum potential energy results for parallel clusters of up to 128 machines are presented

testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression abstract broad classes of diagnostics for serial correlation and or dynamic conditional heteroskedasticity of regression disturbances are considered the classes include statistics with good power against strongly dependent alternatives along with the usual ones that test against weak dependence and many others limiting null distributions are obtained under mild conditions on the dependence structure of the alternative against which the test is derived on moments of the disturbances and on the regressors the various test statistics have a similar overall structure and while tests against strongly dependent alternatives entail more computation than ones against weakly dependent alternatives the difference can be slight if the fast fourier transform is used

stationarity conditions and constraint qualifications for mathematical programs with switching constraints in optimal control switching structures demanding at most one control to be active at any time instance appear frequently discretizing such problems a so called mathematical program with switching constraints is obtained although these problems are related to other types of disjunctive programs like optimization problems with complementarity or vanishing constraints their inherent structure makes a separate consideration necessary since standard constraint qualifications are likely to fail at the feasible points of switching constrained optimization problems stationarity notions which are weaker than the associated karush kuhn tucker conditions need to be investigated in order to find applicable necessary optimality conditions furthermore appropriately tailored constraint qualifications need to be formulated in this paper we introduce suitable notions of weak mordukhovich and strong stationarity for mathematical programs with switching constraints and present some associated constraint qualifications our findings are exploited to state necessary optimality conditions for discretized optimal control problems with switching constraints furthermore we apply our results to optimization problems with either or constraints first a novel reformulation of such problems using switching constraints is presented second the derived surrogate problem is exploited to obtain necessary optimality conditions for the original program

optimal design in conductivity under locally constrained heat flux this paper addresses the relaxation of an optimal design problem in conductivity under a point wise constraint on the heat flux by using a variational approach developed by the authors in a previous work we obtained a complete relaxation involving the explicit computation of constrained quasiconvex envelopes this relaxed formulation turns out to be very simple in the remarkable compliance case for which numerical simulations are performed those simulations show that our approach and results are interesting from a theoretical point of view as well as from a practical perspective the emphasis of our work is placed on the local constraint on the heat flux which seems to be a new ingredient for this kind of optimal design problems

stationarity and the existence of moments of a family of garch processes abstract this paper investigates some structural properties of a family of garch processes a simple sufficient condition for the existence of the order stationary solution of the processes is derived where 0 1 and 0 the solution is strictly stationary and ergodic and the causal expansion of the family of garch processes is also established furthermore the necessary and sufficient condition for the existence of the moments is obtained the technique used in this paper for the moment conditions is different from that used in he and terasvirta j econom 92 1999a 173 and avoids the assumption that the process started at some finite value infinitely many periods ago moreover the conditions for the strict stationarity of the model and the existence of its moments are simple to check and should prove useful in practice

a mixed integer programming for robust truss topology optimization with stress constraints this paper presents a mixed integer programming mip formulation for robust topology optimization of trusses subjected to the stress constraints under the uncertain load a design dependent uncertainty model of the external load is proposed for dealing with the variation of truss topology in the course of optimization for a truss with the discrete member cross sectional areas it is shown that the robust topology optimization problem can be reduced to an mip problem which is solved globally numerical examples illustrate that the robust optimal topology of a truss depends on the magnitude of uncertainty

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

eulerian shape design sensitivity analysis and optimization with a fixed grid conventional shape optimization based on the finite element method uses lagrangian representation in which the finite element mesh moves according to shape change while modern topology optimization uses eulerian representation in this paper an approach to shape optimization using eulerian representation such that the mesh distortion problem in the conventional approach can be resolved is proposed a continuum geometric model is defined on the fixed grid of finite elements an active set of finite elements that defines the discrete domain is determined using a procedure similar to topology optimization in which each element has a unique shape density the shape design parameter that is defined on the geometric model is transformed into the corresponding shape density variation of the boundary elements using this transformation it has been shown that the shape design problem can be treated as a parameter design problem which is a much easier method than the former a detailed derivation of how the shape design velocity field can be converted into the shape density variation is presented along with sensitivity calculation very efficient sensitivity coefficients are calculated by integrating only those elements that belong to the structural boundary the accuracy of the sensitivity information is compared with that derived by the finite difference method with excellent agreement two design optimization problems are presented to show the feasibility of the proposed design approach

topology optimization with local stress constraint based on level set evolution via reaction diffusion abstract this work focuses the structural topology optimization problem of mass minimization subject to local stress constraints to this aim two related issues are addressed the first one is the successful strategy used to define local stress constraints by means of an augmented lagrangian approach the second and main contribution of the present paper is the use of a reaction diffusion equation to guide via evolution of a level set the design optimization sequence the advantages of this strategy are twofold firstly it allows the creation of new holes during the optimization process a significant feature for a true topological optimization method secondly reinitialization steps usually found in classical hamilton jacobi based evolution are eliminated with a significant improvement in convergence ease a set of benchmark examples in two dimensions are presented numerical results show the efficiency of the algorithm to create new holes identify stress concentrations and to provide stable optimization sequences converging to local minima defined by stress saturated designs

the distribution of realized exchange rate volatility using high frequency data on deutschemark and yen returns against the dollar we construct model free estimates of daily exchange rate volatility and correlation that cover an entire decade our estimates termed realized volatilities and correlations are not only model free but also approximately free of measurement error under general conditions which we discuss in detail hence for practical purposes we may treat the exchange rate volatilities and correlations as observed rather than latent we do so and we characterize their joint distribution both unconditionally and conditionally noteworthy results include a simple normality inducing volatility transformation high contemporaneous correlation across volatilities high correlation between correlation and volatilities pronounced and persistent dynamics in volatilities and correlations evidence of long memory dynamics in volatilities and correlations and remarkably precise scaling laws under temporal aggregation

optimal design and relaxation of variational problems iii abstract this paper has attempted a synthesis of three subjects that have developed separately optimal design homogenization and relaxation in the calculus of variations the underlying theme is that of oscillations they occur with certain definite patterns in minimizing sequences for the variational problem the same patterns recur in nearly optimal designs and in the coefficients of the equation being homogenized each problem is resolved by determining the structure of those oscillations and above all their macroscopic averages it is those averages that solve the relaxed problem they also determine the optimal design and the solution of the homogenized equation we emphasize also the role of optimization the homogenized equations and composite materials of interest here come not from arbitrary mixtures but from those that are extremal since they correspond to minimizing sequences for the variational problem the effective properties of these composites attain the optimal bounds for given materials in fixed proportions

topological derivative based topology optimization of structures subject to drucker prager stress constraints abstract an algorithm for topology optimization of elastic structures under plane stress subject to the drucker prager stress constraint is presented the algorithm is based on the use of the topological derivative of the associated objective functional in conjunction with a level set representation of the structure domain in this context a penalty functional is proposed to enforce the point wise stress constraint and a closed formula for its topological derivative is derived the resulting algorithm is of remarkably simple computational implementation it does not require post processing procedures of any kind and features only a minimal number of user defined algorithmic parameters this is in sharp contrast with current procedures for topological structural optimization with local stress constraints the effectiveness and efficiency of the algorithm presented here are demonstrated by means of numerical examples the examples show in particular that it can easily handle structural optimization problems with underlying materials featuring strong asymmetry in their tensile and compressive yield strengths

stability of finite element models for distributed parameter optimization and topology design abstract we address a problem of numerical instability that is often encountered in finite element solutions of distributed parameter optimization and variable topology shape design problems we show that the cause of this problem is numerical rather than physical in nature we consider a two field distributed parameter optimization problem involving a design field and a response field and show that the optimization problem corresponds to a mixed variational problem an improper selection of the discrete function spaces for these two fields leads to grid scale anomalies in the numerical solutions to optimization problems similar to those that are sometimes encountered in mixed formulations of the stokes problem we present a theoretical framework to explain the cause of these anomalies and present stability conditions for discrete models the general theoretical framework is specialized to analyze the stability of specific optimization problems and stability results for various mixed finite element models are presented we propose patch tests that are useful in identifying unstable elements

topology optimization with mixed finite elements on regular grids abstract recently new families of mixed finite elements have been proposed to address the analysis of linear elastic bodies on regular grids adopting a limited number of degrees of freedom per element a two dimensional mixed discretization is implemented to formulate an alternative topology optimization problem where stresses play the role of main variables and both compressible and incompressible materials can be dealt with the structural compliance is computed through the evaluation of the complementary energy whereas the enforcement of stress constraints is straightforward numerical simulations investigate the features of the proposed approach comparisons with a conventional displacement based scheme are provided for compressible materials stress constrained solutions for structures made of incompressible media are introduced

stability of random coefficient arch models and aggregation schemes in this paper we consider arch models with nonnegative random coefficients necessary and sufficient conditions for the existence of first and second moments are established the arch models with deterministic coefficients are shown to be always short memory processes the effect of small perturbations of the parameters is investigated the results obtained are applied to some aggregation schemes

a hierarchical method for discrete structural topology design problems with local stress and displacement constraints in this paper we present a hierarchical optimization method for finding feasible true 0 1 solutions to finite element based topology design problems the topology design problems are initially modelled as non convex mixed 0 1 programs the hierarchical optimization method is applied to the problem of minimizing the weight of a structure subject to displacement and local design dependent stress constraints the method iteratively treats a sequence of problems of increasing size of the same type as the original problem the problems are defined on a design mesh which is initially coarse and then successively refined as needed at each level of design mesh refinement a neighbourhood optimization method is used to treat the problem considered the non convex topology design problems are equivalently reformulated as convex all quadratic mixed 0 1 programs this reformulation enables the use of methods from global optimization which have only recently become available for solving the problems in the sequence numerical examples of topology design problems of continuum structures with local stress and displacement constraints are presented copyright 2006 john wiley sons ltd

homogenization and optimal bounds in linear elasticity in their celebrated paper of 1963 hashin shtrikman 1 addressed the problem of determining optimal bounds for the bulk and shear moduli of a statistically isotropic elastic composite material with arbitrary isotropic phase geometry they derived a set of bounds for these moduli in the physically meaningful case of three dimensional elasticity in the case of a two phase composite let k 1 1 and k 2 2 respectively denote the bulk and shear moduli for the first and the second phase let k denote their analogues for the composite and let 0 stand for the volume fraction of the first phase in the composite under the ordering restriction that both

solutions to shape and topology eigenvalue optimization problems using a homogenization method a solution strategy to find the shape and topology of structures that maximize a natural frequency is presented the methodology is based on a homogenization method and the representation of the shape of the structure as a material property the problem is formulated as a reinforcement problem in which a given structure is reinforced using a prescribed amount of material two dimensional plane elasticity problems are considered examples are presented for illustration

on the superlinear local convergence of a filter sqp method transition to superlinear local convergence is shown for a modified version of the trust region filter sqp method for nonlinear programming introduced by fletcher leyffer and toint 8 hereby the original trust region sqp steps can be used without an additional second order correction the main modification consists in using the lagrangian function value instead of the objective function value in the filter together with an appropriate infeasibility measure moreover it is shown that the modified trust region filter sqp method has the same global convergence properties as the original algorithm in 8

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

lipschitz and holder stability of optimization problems and generalized equations this paper studies stability aspects of solutions of parametric mathematical programs and generalized equations respectively with disjunctive constraints we present sufficient conditions that under some constraint qualifications ensuring metric subregularity of the constraint mapping continuity results of upper lipschitz and upper holder type respectively hold furthermore we apply the above results to parametric mathematical programs with equilibrium constraints and demonstrate how some classical results for the nonlinear programming problem can be recovered and even improved by our theory

a level set approach for topology optimization with local stress constraints summary the purpose of this work is to present a level set based approach for the structural topology optimization problem of mass minimization submitted to local stress constraints the main contributions are threefold first the inclusion of local stress constraints by means of an augmented lagrangian approach within the level set context second the proposition of a constraint procedure that accounts for a continuous activation deactivation of a finite number of local stress constraints during the optimization sequence finally the proposition of a logarithmic scaling of the level set normal velocity as an additional regularization technique in order to improve the minimization sequence a set of benchmark tests in two dimensions achieving successful numerical results assesses the good behavior of the proposed method in these examples it is verified that the algorithm is able to identify stress concentrations and drive the design to a feasible local minimum copyright 2014 john wiley sons ltd

modelling topology optimization problems as linear mixed 0 1 programs this paper deals with topology optimization of discretized continuum structures it is shown that a large class of non linear 0 1 topology optimization problems including stress and displacement constrained minimum weight problems can equivalently be modelled as linear mixed 0 1 programs the modelling approach is applied to some test problems which are solved to global optimality