optimum sensitivity derivatives of objective functions in nonlinear programming the feasibility of eliminating second derivatives from the input of optimum sensitivity analyses of optimization problems is demonstrated this elimination restricts the sensitivity analysis to the first order sensitivity derivatives of the objective function it is also shown that when a complete first order sensitivity analysis is performed second order sensitivity derivatives of the objective function are available at little additional cost an expression is derived whose application to linear programming is presented

exponential decay toward equilibrium via entropy methods for reaction diffusion equations abstract in this work we show how the entropy method enables to get in an elementary way and without linearization estimates of exponential decay towards equilibrium for solutions of reaction diffusion equations corresponding to a reversible reaction explicit rates of convergence combining the dissipative effects of diffusion and reaction are given

second order design sensitivity analysis of structural systems esign sensitivity analysis methods for calculation of first derivatives of structural performance with respect to design parameters have become quite well developed and applied 1 2 it is the purpose of this note to extend the adjoint method of design sensitivity analysis to calculation of second derivatives of performance with respect to design parameters the value of second deriva tive information in design optimization is well known using only first order gradient information optimization algorithms must resort to onedimensional search or heuristic step size selection methods if second derivative information is available at a reasonable computing cost much more powerful iterative optimization algorithms are possible 3 finite dimensional matrix structural models are considered here even though the methods presented can be extended to distributed parameter boundary value problem structural models structural design is presumed to be described by a vector of design parameters b b1 b2 bk t structural response is described by a vector of nodal displacement coordinates z zi z2 zn 7

second order sensitivity derivatives in structural analysis haug s 1981 expressions for the calculation of static constraint function second derivatives have resulted in an order of magnitude saving over conventional methods for the calculation of such derivatives a similar but simplified procedure is presented which results in a reduction of computational cost by an additional factor of two the results are presented in a notation that is different from that of haug but more common in other work on structural synthesis and analysis

local extremes runs strings and multiresolution the paper considers the problem of nonparametric regression with emphasis on controlling the number of local extremes two methods the run method and the taut string multiresolution method are introduced and analyzed on standard test beds it is shown that the number and locations of local extreme values are consistently estimated rates of convergence are proved for both methods the run method converges slowly but can withstand blocks as well as a high proportion of isolated outliers the rate of convergence of the taut string multiresolution method is almost optimal the method is extremely sensitive and can detect very low power peaks section 1 contains an introduction with special reference to the number of local extreme values the run method is described in section 2 and the taut string multiresolution method in section 3 low power peaks are considered in section 4 section 5 contains a comparison with other methods and section 6 a short conclusion the proofs are given in section 7 and the taut string algorithm is described in the appendix

optimum design of flexible structures under constraints on strain energy and asymptotic stability a new concept and optimization method are presented for designing a flexible structure that allows large deformation constraint is given for the minimum strain energy that can be stored for specified norm of displacement as well as asymptotic stability of the undeformed state within the region defined by the specified displacement norm the optimal solution is obtained by solving a two level optimization problem examples are given for 2 bar and 24 bar trusses asymptotic stability of the optimized truss is verified by carrying out dynamic analysis for given random initial velocity that is equivalent to the specified strain energy

sensitivity of optimum solutions of problem parameters solution of the optimum sensitivity problem yields the values of derivatives of the optimal objective function and design variables with respect to those physical quantities which were kept constant as problem parameters during optimization examples of these sensitivity derivatives might include derivatives of cross section al area and structural mass with respect to allowable stress and derivatives of fuel consumed and wing aspect ratio with respect to aircraft range derivation of the sensitivity equations that yield the sensitivity derivatives directly which avoids the costly and inaccurate perturb and reoptimize approach is discussed and solvability of the equations is examined the equations apply to optimum solutions obtained by direct search methods as well as those generated by procedures of the sequential unconstrained minimization technique sumt class applications are discussed for the use of the sensitivity derivatives in extrapolation of the optimal objective function and design variable values for incremented parameters optimization with multiple objectives and decomposition of large optimization problems several aspects of these applications and verification of the sensitivity equations are presented through numerical examples

multiplier methods for engineering optimization multiplier methods used to solve the constrained engineering optimization problem are described these methods solve the problem by minimizing a sequence of unconstrained problems defined using the cost and constraint functions the methods proposed in 1969 have been determined to be quite robust although not as efficient as other algorithms they can be more effective for some engineering applications such as optimum design and control oflarge scale dynamic systems since 1969 several modifications and extensions of the methods have been developed therefore it is important to review the theory and computational procedures of these methods so that more efficient and effective ones can be developed for engineering applications recent methods that are similar to the multiplier methods are also discussed these are continuous multiplier update exact penalty and exponential penalty methods

on total variation minimization and surface evolution using parametric maximum flows in a recent paper boykov et al lncs vol 3953 pp 409 422 2006 propose an approach for computing curve and surface evolution using a variational approach and the geo cuts method of boykov and kolmogorov international conference on computer vision pp 26 33 2003 we recall in this paper how this is related to well known approaches for mean curvature motion introduced by almgren et al siam journal on control and optimization 31 2 387 438 1993 and luckhaus and sturzenhecker calculus of variations and partial differential equations 3 2 253 271 1995 and show how the corresponding problems can be solved with sub pixel accuracy using parametric maximum flow techniques this provides interesting algorithms for computing crystalline curvature motion possibly with a forcing term

a new asymptotic preserving scheme based on micro macro formulation for linear kinetic equations in the diffusion limit we propose a new numerical scheme for linear transport equations it is based on a decomposition of the distribution function into equilibrium and nonequilibrium parts we also use a projection technique that allows us to reformulate the kinetic equation into a coupled system of an evolution equation for the macroscopic density and a kinetic equation for the nonequilibrium part by using a suitable time semi implicit discretization our scheme is able to accurately approximate the solution in both kinetic and diffusion regimes it is asymptotic preserving in the following sense when the mean free path of the particles is small our scheme is asymptotically equivalent to a standard numerical scheme for the limit diffusion model a uniform stability property is proved for the simple telegraph model various boundary conditions are studied our method is validated in one dimensional cases by several numerical tests and comparisons with previous asymptotic preserving schemes

sensitivity of control augmented structure obtained by a system decomposition method the verification of a method for computing sensitivity derivatives of a coupled system is presented the method deals with a system whose analysis can be partitioned into subsets that correspond to disciplines and or physical subsystems that exchange input output data with each other the method uses the partial sensitivity derivatives of the output with respect to input obtained for each subset separately to assemble a set of linear simultaneous algebraic equations that are solved for the derivatives of the coupled system response this sensitivity analysis is verified using an example of a cantilever beam augmented with an active control system to limit the beam s dynamic displacements under an excitation force the verification shows good agreement of the method with reference data obtained by a finite difference technique involving entire system analysis the usefulness of a system sensitivity method in optimization applications by employing a piecewise linear approach to the same numerical example is demonstrated the method s principal merits are its intrinsically superior accuracy in comparison with the finite difference technique and its compatibility with the traditional division of work in complex engineering tasks among specialty groups

existence of bounded discrete steady state solutions of the van roosbroeck system on boundary conforming delaunay grids the classic van roosbroeck system describes the carrier transport in semiconductors in a drift diffusion approximation its analytic steady state solutions fulfill bounds for some mobility and recombination generation models the main goal of this paper is to establish the identical bounds for discrete in space steady state solutions on 3d boundary conforming delaunay grids and the classical scharfetter gummel scheme together with a uniqueness proof for small applied voltages and the known dissipativity continuous as well as space and time discrete these discretization techniques carry over the essential analytic properties to the discrete case the proofs are of interest for deriving averaging schemes for space or state dependent material parameters which preserve these qualitative properties too to illustrate the properties of the scheme 1 4 16 elementary cells of a modified coolmos like structure are depleted by increasing the applied voltage until steady state avalanche breakdown occurs

locally adaptive regression splines in this paper least squares penalized regression estimates withtotal variation penalities are considered it is shown that theseestimators are least squares splines with locally data adaptive placed knotpoints algorithms and asymptotic properties are discussed

efficient asymptotic preserving ap schemes for some multiscale kinetic equations many kinetic models of the boltzmann equation have a diffusive scaling that leads to the navier stokes type parabolic equations as the small scaling parameter approaches zero in practical applications it is desirable to develop a class of numerical schemes that can work uniformly with respect to this relaxation parameter from the rarefied kinetic regimes to the hydrodynamic diffusive regimes an earlier approach in s jin l pareschi and g toscani siam j numer anal 35 1998 pp 2405 2439 reformulates such systems into the common hyperbolic relaxation system by jin and xin for hyperbolic conservation laws used to construct the relaxation schemes and then uses a multistep time splitting method to solve the relaxation system here we observe that the combination of the two time split steps may yield hyperbolic parabolic systems that are more advantageous in both stability and efficiency for numerical computations we show that such an approach yields a class of asymptotic preserving ap schemes which are suitable for the computation of multiscale kinetic problems we use the goldstein taylor and carleman models to illustrate this approach

energy estimates for continuous and discretized electro reaction diffusion systems abstract we consider electro reaction diffusion systems consisting of continuity equations for a finite number of species coupled with a poisson equation we take into account heterostructures anisotropic materials and rather general statistic relations we investigate thermodynamic equilibria and prove for solutions to the evolution system the monotone and exponential decay of the free energy to its equilibrium value here the essential idea is an estimate of the free energy by the dissipation rate which is proved indirectly the same properties are shown for an implicit time discretized version of the problem moreover we provide a space discretized scheme for the electro reaction diffusion system which is dissipative the free energy decays monotonously on a fixed grid we use for each species different voronoi boxes which are defined with respect to the anisotropy matrix occurring in the flux term of this species

structural optimization by multilevel decomposition a method for decomposing an optimization problem into a set of subproblems and a coordination problem that preserves coupling between the subproblems is described the decomposition is achieved by separating the structural element optimization subproblems from the assembled structural optimization problem each element optimization and optimum sensitivity analysis yields the cross sectional dimensions that minimize a cumulative measure of the element constraint violation as a function of the elemental forces and stiffness the assembled structural optimization produces the overall mass and stiffness distributions optimized for minimum total mass subject to constraints that include the cumulative measures of the element constraint violations extrapolated linearly with respect to the element forces and stiffnesses the method is introduced as a special case of a multilevel multidisciplinary system optimization and its algorithm is fully described for two level optimization for structures assembled of finite elements of arbitrary type numerical results are given as an example of a framework to show that the decomposition method converges and yields results comparable to those obtained without decomposition it is pointed out that optimization by decomposition should reduce the design time by allowing groups of engineers using different computers to work concurrently on the same large problem

asymptotic preserving particle in cell method for the vlasov poisson system near quasineutrality this paper deals with the numerical resolution of the vlasov poisson system in a nearly quasineutral regime by particle in cell pic methods in this regime classical pic methods are subject to stability constraints on the time and space steps related to the small debye length and large plasma frequency here we propose an asymptotic preserving pic scheme which is not subjected to these limitations additionally when the plasma period and debye length are small compared to the time and space steps this method provides a consistent pic discretization of the quasineutral vlasov equation we perform several one dimensional numerical experiments which provide a solid validation of the method and its underlying concepts and compare the method with classical pic and direct implicit methods

lower stretch spanning trees we show that every weighted connected graph g contains as a subgraph a spanning tree into which the edges of g can be embedded with average stretch o log 2 n log log n moreover we show that this tree can be constructed in time o m log n n log 2 n in general and in time o m log n if the input graph is unweighted the main ingredient in our construction is a novel graph decomposition technique our new algorithm can be immediately used to improve the running time of the recent solver for symmetric diagonally dominant linear systems of spielman and teng from m 2 o sqrt log n log log n to m log o 1 n and to o n log 2 n log log n when the system is planar our result can also be used to improve several earlier approximation algorithms that use low stretch spanning trees

convergent discretizations for the nernst planck poisson system we propose and compare two classes of convergent finite element based approximations of the nonstationary nernst planck poisson equations whose constructions are motivated from energy versus entropy decay properties for the limiting system solutions of both schemes converge to weak solutions of the limiting problem for discretization parameters tending to zero our main focus is to study qualitative properties for the different approaches at finite discretization scales like conservation of mass non negativity discrete maximum principle decay of discrete energies and entropies to study long time asymptotics

an asymptotic preserving scheme for the two fluid euler poisson model in the quasineutral limit this paper deals with the modeling of a plasma in the quasineutral limit using the two fluid euler poisson system in this limit explicit numerical schemes suffer from severe numerical constraints related to the small debye length and large plasma frequency here we propose an implicit scheme which reduces to a scheme for the quasineutral euler model in the quasineutral limit such a property is referred to as asymptotic preservation one of the distinctive features of this scheme is that it has a comparable numerical cost to that of an explicit scheme simply the poisson equation is replaced by a different but formally equivalent elliptic problem we present numerical simulations for two different one dimensional test cases they confirm the expected stability of the scheme in the quasineutral limit they also show that this scheme has some accuracy problems in the limit of small electron to ion mass ratio in reproducing the correct electron velocity but this problem is already present in the results of the classical algorithm numerical simulations are also performed for a two dimensional problem of a plasma expansion in vacuum between two electrodes

a finite volume scheme for convection diffusion equations with nonlinear diffusion derived from the scharfetter gummel scheme we propose a finite volume scheme for convection diffusion equations with nonlinear diffusion such equations arise in numerous physical contexts we will particularly focus on the drift diffusion system for semiconductors and the porous media equation in these two cases it is shown that the transient solution converges to a steady state solution as t tends to infinity the introduced scheme is an extension of the scharfetter gummel scheme for nonlinear diffusion it remains valid in the degenerate case and preserves steady states we prove the convergence of the scheme in the nondegenerate case finally we present some numerical simulations applied to the two physical models introduced and we underline the efficiency of the scheme to preserve long time behavior of the solutions

fast approximate energy minimization via graph cuts many tasks in computer vision involve assigning a label such as disparity to every pixel a common constraint is that the labels should vary smoothly almost everywhere while preserving sharp discontinuities that may exist e g at object boundaries these tasks are naturally stated in terms of energy minimization the authors consider a wide class of energies with various smoothness constraints global minimization of these energy functions is np hard even in the simplest discontinuity preserving case therefore our focus is on efficient approximation algorithms we present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves namely expansion moves and swap moves these moves can simultaneously change the labels of arbitrarily large sets of pixels in contrast many standard algorithms including simulated annealing use small moves where only one pixel changes its label at a time our expansion algorithm finds a labeling within a known factor of the global minimum while our swap algorithm handles more general energy functions both of these algorithms allow important cases of discontinuity preserving energies we experimentally demonstrate the effectiveness of our approach for image restoration stereo and motion on real data with ground truth we achieve 98 percent accuracy

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

extrapolation of optimum design based on sensitivity derivatives in many applications it is useful to have information regarding the effect of the perturbations of the design problem constants parameters on the optimum solution of the problem sobieszczanski sobieski et al 1981 have therefore proposed to utilize an optimum sensitivity analysis as a structural design tool to assess the parameter perturbation effects by extrapolations based on optimum sensitivity derivatives the present investigation is concerned with an example of optimum sensitivity analysis involving a composite panel the case was selected in connection with the nonlinearity of the constraints and the tendency for a set of active constraints to change when the parameters are disturbed under these adverse conditions sensitivity derivatives are used in linear extrapolations to extend optimization information over a limited range of variation for a typical parameter

sequential linearization method for multilevel optimization the proposed method is based on the concept of providing linearized information between the system level and subsystem level optimization tasks the advantages of the method are that it does not require optimum sensitivities nonlinear equality constraints are not needed and the method is relatively easy to understand and use the disadvantage is that the coupling between subsystems is not dealt with in a precise mathematical manner

minimax estimation via wavelet shrinkage we attempt to recover an unknown function from noisy sampled data using orthonormal bases of compactly supported wavelets we develop a nonlinear method which works in the wavelet domain by simple nonlinear shrinkage of the empirical wavelet coefficients the shrinkage can be tuned to be nearly minimax over any member of a wide range of triebel and besov type smoothness constraints and asymptotically minimax over besov bodies with p q linear estimates cannot achieve even the minimax rates over triebel and besov classes with p 2 so the method can significantly outperform every linear method e g kernel smoothing spline sieve in a minimax sense variants of our method based on simple threshold nonlinear estimators are nearly minimax our method possesses the interpretation of spatial adaptivity it reconstructs using a kernel which may vary in shape and bandwidth from point to point depending on the data least favorable distributions for certain of the triebel and besov scales generate objects with sparse wavelet transforms many real objects have similarly sparse transforms which suggests that these minimax results are relevant for practical problems sequels to this paper which was first drafted in november 1990 discuss practical implementation spatial adaptation properties universal near minimaxity and applications to inverse problems

finite volume methods for convection diffusion problems derivation stability and error analysis in both discrete h 1 and l 2 norms for cell centered finite volume approximations of convection diffusion problems are presented various upwind strategies are investigated the theoretical results are illustrated by numerical examples

uniform in time bounds for approximate solutions of the drift diffusion system in this paper we consider a numerical approximation of the van roosbroeck s drift diffusion system given by a backward euler in time and finite volume in space discretization with scharfetter gummel fluxes we first propose a proof of existence of a solution to the scheme which does not require any assumption on the time step the result relies on the application of a topological degree argument which is based on the positivity and on uniform in time upper bounds of the approximate densities secondly we establish uniform in time lower bounds satisfied by the approximate densities these uniform in time upper and lower bounds ensure the exponential decay of the scheme towards the thermal equilibrium as shown in 3

optimization of nonhierarchically decomposed problems the increasing computational power available to practitioners leads to challenging applications of optimization approaches to large scale systems to address such problems decomposition of the original or all in one aio problem into smaller and simpler subproblems is the approach taken by engineers analytical target cascading atc a hierarchical decomposition and coordination approach is extended to model and coordinate problems with nonhierarchical interactions among the subproblems convergence results for atc based on lagrangian duality theory are extended for the new approach under certain conditions the optimal solution of the aio problem can be achieved by independently solving the nonhierarchically interacting subproblems a mathematical example with several subproblems interacting in a network is included and new applications in engineering design are highlighted

the dfs fused lasso linear time denoising over general graphs the fused lasso also known as anisotropic total variation denoising is widely used for piecewise constant signal estimation with respect to a given undirected graph the fused lasso estimate is highly nontrivial to compute when the underlying graph is large and has an arbitrary structure but for a special graph structure namely the chain graph the fused lasso or simply 1d fused lasso can be computed in linear time in this paper we revisit a result recently established in the online classification literature herbster et al 2009 cesa bianchi et al 2013 and show that it has important implications for signal denoising on graphs the result can be translated to our setting as follows given a general graph if we run the standard depth first search dfs traversal algorithm then the total variation of any signal over the chain graph induced by dfs is no more than twice its total variation over the original graph this result leads to several interesting theoretical and computational conclusions letting m and n denote the number of edges and nodes respectively of the graph in consideration it implies that for an underlying signal with total variation t over the graph the fused lasso properly tuned achieves a mean squared error rate of t2 3n 2 3 moreover precisely the same mean squared error rate is achieved by running the 1d fused lasso on the dfs induced chain graph importantly the latter estimator is simple and computationally cheap requiring o m operations to construct the dfs induced chain and o n operations to compute the 1d fused lasso solution over this chain further for trees that have bounded maximum degree the error rate of t2 3n 2 3 cannot be improved in the sense that it is the minimax rate for signals that have total variation t over the tree finally several related results also hold for example the analogous result holds for a roughness measure defined by the l0 norm of differences across edges in place of the total variation metric

a finite volume scheme for nonlinear parabolic equations derived from one dimensional local dirichlet problems in this paper we propose a new method to compute the numerical flux of a finite volume scheme used for the approximation of the solution of the nonlinear partial differential equation u t div q f u u 0 in a 1d 2d or 3d domain the function is supposed to be strictly increasing but some values s such that s 0 can exist the method is based on the solution at each interface between two control volumes of the nonlinear elliptic two point boundary value problem q f 0 with dirichlet boundary conditions given by the values of the discrete approximation in both control volumes we prove the existence of a solution to this two point boundary value problem we show that the expression for the numerical flux can be yielded without referring to this solution furthermore we prove that the so designed finite volume scheme has the expected stability properties and that its solution converges to the weak solution of the continuous problem numerical results show the increase of accuracy due to the use of this scheme compared to some other schemes

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

two dimensional exponential fitting and applications to drift diffusion models a class of methods is introduced that generalizes the so called exponential fitting method to two dimensional problems and more specifically to equations of the type operatorname div underset raise0 3em hbox smash scriptscriptstyle nabla u u underset raise0 3em hbox smash scriptscriptstyle nabla psi f with psi given and underset raise0 3em hbox smash scriptscriptstyle nabla psi big in a part of the domain the basic idea is the following i write the equation as operatorname div e psi underset raise0 3em hbox smash scriptscriptstyle nabla rho f through the change of variables u rho e psi ii discretize the symmetric equation by means of a method that uses some kind of harmonic average for the coefficient e psi mixed hybrid etc iii write the discrete scheme in terms of the nodal values of u e psi rho this produces an m matrix

study of a fully implicit scheme for the drift diffusion system asymptotic behavior in the quasi neutral limit in this paper we are interested in the numerical approximation of the classical time dependent drift diffusion system near quasi neutrality we consider a fully implicit in time and finite volume in space scheme where the convection diffusion fluxes are approximated by scharfetter gummel fluxes we establish that all the a priori estimates needed to prove the convergence of the scheme do not depend on the debye length lambda this proves that the scheme is asymptotic preserving in the quasi neutral limit lambda to 0

an energy preserving finite difference scheme for the poisson nernst planck system we give a semi implicit finite difference method for poisson nernst planck systems we prove rigorously the mass conservation and energy decay property of the method our method is second order convergent in space and first order convergent in time our method can be easily extended to the case of multi ions in this paper we construct a semi implicit finite difference method for the time dependent poisson nernst planck system although the poisson nernst planck system is a nonlinear system the numerical method presented in this paper only needs to solve a linear system at each time step which can be done very efficiently the rigorous proof for the mass conservation and electric potential energy decay are shown moreover mesh refinement analysis shows that the method is second order convergent in space and first order convergent in time finally we point out that our method can be easily extended to the case of multi ions