a multi variant martensitic phase transformation model formulation and numerical implementation the development of models for shape memory alloys and other materials that undergo martensitic phase transformations has been moving towards a common generalized thermodynamic framework several promising models utilizing single martensitic variants and some with multiple variants have appeared recently in this work we develop a model in a general multi variant framework for single crystals that is based upon lattice correspondence variants and the use of dissipation arguments for the generation of specialized evolution equations the evolution equations that appear are of a unique nature in that not only are the thermodynamic forces restricted in range but so are their kinematic conjugates this unusual situation complicates the discrete time integration of the evolution equations we show that the trial elastic state method that is popular in metal plasticity is inadequate in the present situation and needs to be replaced by a non linear programming problem with a simple geometric interpretation the developed integration methodology is robust and leads to symmetric tangent moduli example computations show the behavior of the model in the pseudoelastic range of particular interest is the fact that the model can predict the generation of habit plane like variants solely from the lattice correspondence variants this is demonstrated through a comparison to the experimental work of shield j mech phys solids 43 1995 869

a perturbed parallel decomposition method for a class of nonsmooth convex minimization problems a perturbed parallel decomposition method for solving the following model problem is presented minimize f 0 x sum i 1 m f i x over all x in mathbb r n where f 0 is differentiable and strongly convex and the f i s are closed proper and convex but not necessarily differentiable an important feature of the proposed method is the ability to split the given problem into independent subproblems that contain only individual functions in that way the algorithm is suitable for parallel computation the approach also allows for inaccuracies and duality gaps during the iterative process furthermore convergence is established under perturbations on the f i s in the epiconvergence sense and under inexact minimizations at each iteration relations of the method with the recent work of han and lou on the same model problem are also discussed from the theoretical point of view this paper represents a significant improvement on the parallel decomposition algorithms of han and lou

stabilizing nonuniformly quantized compressed sensing with scalar companders this paper addresses the problem of stably recovering sparse or compressible signals from compressed sensing measurements that have undergone optimal nonuniform scalar quantization i e minimizing the common l2 norm distortion generally this quantized compressed sensing qcs problem is solved by minimizing the l1 norm constrained by the l2 norm distortion in such cases remeasurement and quantization of the reconstructed signal do not necessarily match the initial observations showing that the whole qcs model is not consistent our approach considers instead that quantization distortion more closely resembles heteroscedastic uniform noise with variance depending on the observed quantization bin generalizing our previous work on uniform quantization we show that for nonuniform quantizers described by the compander formalism quantization distortion may be better characterized as having bounded weighted lp norm p 2 for a particular weighting we develop a new reconstruction approach termed generalized basis pursuit denoise gbpdn which minimizes the l1 norm of the signal to reconstruct constrained by this weighted lp norm fidelity we prove that for standard gaussian sensing matrices and k sparse or compressible signals in rn with at least k logn k p 2 measurements i e under strongly oversampled qcs scenario gbpdn is l2 l1 instance optimal and stable recovers all such sparse or compressible signals the reconstruction error decreases as o 2 b p 1 given a budget of b bits per measurement this yields a reduction by a factor p 1 of the reconstruction error compared to the one produced by l2 norm constrained decoders we also propose an primal dual proximal splitting scheme to solve the gbpdn program which is efficient for large scale problems interestingly extensive simulations testing the gbpdn effectiveness confirm the trend predicted by the theory that the reconstruction error can indeed be reduced by increasing p but this is achieved at a much less stringent oversampling regime than the one expected by the theoretical bounds besides the qcs scenario we also show that gbpdn applies straightforwardly to the related case of cs measurements corrupted by heteroscedastic generalized gaussian noise with provable reconstruction error reduction

on the ergodic convergence rates of a first order primal dual algorithm we revisit the proofs of convergence for a first order primal dual algorithm for convex optimization which we have studied a few years ago in particular we prove rates of convergence for a more general version with simpler proofs and more complete results the new results can deal with explicit terms and nonlinear proximity operators in spaces with quite general norms

a modified forward backward splitting method for maximal monotone mappings we consider the forward backward splitting method for finding a zero of the sum of two maximal monotone mappings this method is known to converge when the inverse of the forward mapping is strongly monotone we propose a modification to this method in the spirit of the extragradient method for monotone variational inequalities under which the method converges assuming only the forward mapping is lipschitz continuous on some closed convex subset of its domain the modification entails an additional forward step and a projection step at each iteration applications of the modified method to decomposition in convex programming and monotone variational inequalities are discussed

approximate proximal methods in vector optimization abstract this paper studies the vector optimization problem of finding weakly efficient points for mappings in a banach space y with respect to the partial order induced by a closed convex and pointed cone c y with a nonempty interior the proximal method in vector optimization is extended to develop an approximate proximal method for this problem by virtue of the approximate proximal point method for finding a root of a maximal monotone operator in this approximate proximal method the subproblems consist of finding weakly efficient points for suitable regularizations of the original mapping we present both an absolute and a relative version in which the subproblems are solved only approximately weak convergence of the generated sequence to a weak efficient point is established in addition we also discuss an extension to bregman function based proximal algorithms for finding weakly efficient points for mappings

an augmented lagrangian method for distributed optimization we propose a novel distributed method for convex optimization problems with a certain separability structure the method is based on the augmented lagrangian framework we analyze its convergence and provide an application to two network models as well as to a two stage stochastic optimization problem the proposed method compares favorably to two augmented lagrangian decomposition methods known in the literature as well as to decomposition methods based on the ordinary lagrangian function

space decomposition multiplier method for constrained minimization problems abstract in this paper a new multiplier method that decomposes variable space into decomposed spaces is introduced this method allows constrained minimization problems to be decomposed into subproblems a potential constraint strategy that uses only part of the constraint set in the decomposed space subproblems is also presented to increase the efficiency of this new space decomposition multiplier method three examples are given to demonstrate this method and the potential constraint strategy

damage and plasticity in microplane theory the paper deals with the microplane model in which the stress strain relations are defined independently on planes of all possible orientations in the microstructure and the microplane stresses or strains are then constrained kinematically or statically to the macroscopic stress or strain tensor the existing formulations of the microplane constitutive model for concrete are mainly based on the kinematic constraint they have been shown capable of reproducing satisfactorily most experimental results available for concrete specimens with the advantages of great conceptual simplicity convenient numerical explicitness intrinsic induced anisotropy and microcrack opening closure conditions etc however from the theoretical viewpoint little has been said about how these formulations relate to classical constitutive models of elasto plasticity or continuum damage mechanics in this paper a new apemu of microplane theory is achieved by systematically intro ducing damage and plasticity concepts into the microplane framework new insight is provided on the role played by the split of the normal components and on the role of the different possible types of micro macro constraint specific formulations are developed and discussed within the new theoretical framework which can be easily related to von mises plasticity and to the existing models based on the second and fourth order damage tensors 0 1997 elsevier science ltd

linear array thinning exploiting almost difference sets this paper describes a class of linear thinned arrays with predictable and well behaved sidelobes the element placement is based on almost difference sets and the array power pattern is forced to pass through n uniformly spaced values that although neither equal nor constant as for difference sets are a priori known from the knowledge of the aperture size the number of active array elements k and the features of the correlation function such a property allows one to predict the bounds of the confidence range of the peak sidelobe of the admissible arrays obtainable through simple shift operations on a binary sequence the expected peak sidelobe performances turn out to be comparable with those from difference sets even though obtainable in a wider set of array configurations and improved in comparison with cut and try random placements

parameter selection for total variation based image restoration using discrepancy principle there are two key issues in successfully solving the image restoration problem 1 estimation of the regularization parameter that balances data fidelity with the regularity of the solution and 2 development of efficient numerical techniques for computing the solution in this paper we derive a fast algorithm that simultaneously estimates the regularization parameter and restores the image the new approach is based on the total variation tv regularized strategy and morozov s discrepancy principle the tv norm is represented by the dual formulation that changes the minimization problem into a minimax problem a proximal point method is developed to compute the saddle point of the minimax problem by adjusting the regularization parameter adaptively in each iteration the solution is guaranteed to satisfy the discrepancy principle we will give the convergence proof of our algorithm and numerically show that it is better than some state of the art methods in terms of both speed and accuracy

complex weight sparse linear array synthesis by bayesian compressive sampling an innovative method for the synthesis of maximally sparse linear arrays matching arbitrary reference patterns is proposed in the framework of sparseness constrained optimization the approach exploits the multi task mt bayesian compressive sensing bcs theory to enable the design of complex non hermitian layouts with arbitrary radiation and geometrical constraints by casting the pattern matching problem into a probabilistic formulation a relevance vector machine rvm technique is used as solution tool the numerical assessment points out the advances of the proposed implementation over the extension to complex patterns of and it gives some indications about the reliability flexibility and numerical efficiency of the mt bcs approach also in comparison with state of the art sparse arrays synthesis methods

a class of dantzig wolfe type decomposition methods for variational inequality problems we consider a class of decomposition methods for variational inequalities which is related to the classical dantzig wolfe decomposition of linear programs our approach is rather general in that it can be used with certain types of set valued or nonmonotone operators as well as with various kinds of approximations in the subproblems of the functions and derivatives in the single valued case also subproblems may be solved approximately convergence is established under reasonable assumptions we also report numerical experiments for computing variational equilibria of the game theoretic models of electricity markets our numerical results illustrate that the decomposition approach allows to solve large scale problem instances otherwise intractable if the widely used path solver is applied directly without decomposition

backward forward algorithms for structured monotone inclusions in hilbert spaces abstract in this paper we study the backward forward algorithm as a splitting method to solve structured monotone inclusions and convex minimization problems in hilbert spaces it has a natural link with the forward backward algorithm and has the same computational complexity since it involves the same basic blocks but organized differently surprisingly enough this kind of iteration arises when studying the time discretization of the regularized newton method for maximally monotone operators first we show that these two methods enjoy remarkable involutive relations which go far beyond the evident inversion of the order in which the forward and backward steps are applied next we establish several convergence properties for both methods some of which were unknown even for the forward backward algorithm this brings further insight into this well known scheme finally we specialize our results to structured convex minimization problems the gradient projection algorithms and give a numerical illustration of theoretical interest

convergence rates with inexact non expansive operators in this paper we present a convergence rate analysis for the inexact krasnosel ski mann iteration built from non expansive operators the presented results include two main parts we first establish the global pointwise and ergodic iteration complexity bounds then under a metric sub regularity assumption we establish a local linear convergence for the distance of the iterates to the set of fixed points the obtained results can be applied to analyze the convergence rate of various monotone operator splitting methods in the literature including the forward backward splitting the generalized forward backward the douglas rachford splitting alternating direction method of multipliers and primal dual splitting methods for these methods we also develop easily verifiable termination criteria for finding an approximate solution which can be seen as a generalization of the termination criterion for the classical gradient descent method we finally develop a parallel analysis for the non stationary krasnosel ski mann iteration

bayesian compressive sampling for pattern synthesis with maximally sparse non uniform linear arrays a numerically efficient technique based on the bayesian compressive sampling bcs for the design of maximally sparse linear arrays is introduced the method is based on a probabilistic formulation of the array synthesis and it exploits a fast relevance vector machine rvm for the problem solution the proposed approach allows the design of linear arrangements fitting desired power patterns with a reduced number of non uniformly spaced active elements the numerical validation assesses the effectiveness and computational efficiency of the proposed approach as a suitable complement to existing state of the art techniques for the design of sparse arrays

applications of the method of partial inverses to convex programming decomposition a primal dual decomposition method is presented to solve the separable convex programming problem convergence to a solution and lagrange multiplier vector occurs from an arbitrary starting point the method is equivalent to the proximal point algorithm applied to a certain maximal monotone multifunction in the nonseparable case it specializes to a known method the proximal method of multipliers conditions are provided which guarantee linear convergence

space decomposition minimization method for large scale minimization problems abstract this paper introduces a set of new algorithms called the space decomposition minimization sdm algorithms that decomposes the minimization problem into subproblems if the decomposed space subproblems are not coupled to each other they can be solved independently with any convergent algorithm otherwise iterative algorithms presented in this paper can be used furthermore if the design space is further decomposed into one dimensional decomposed spaces the solution can be found directly using one dimensional search methods a hybrid algorithm that yields the benefits of the sdm algorithm and the conjugate gradient method is also given an example that demonstrates application of sdm algorithm to the learning of a single layer perceptron neural network is presented and five large scale numerical problems are used to test the sdm algorithms the results obtained are compared with results from the conjugate gradient method

hybrid design of non regular linear arrays with accurate control of the pattern sidelobes the hybridization of an analytical thinning technique based on almost difference sets adss and a convex programming cp strategy is proposed for designing non regular linear arrays over a half wavelength lattice that fit arbitrary upper bounds on the far field pattern the proposed approach combines the efficiency of the ads procedure in defining a low sidelobe thinned arrangement with the effectiveness of the cp approach in deducing the optimal tapering to control the beam shape a set of numerical results is presented to assess features and potentialities of the ads cp method

applications of splitting algorithm to decomposition in convex programming and variational inequalities recently han and lou proposed a highly parallelizable decomposition algorithm for minimizing a strongly convex cost over the intersection of closed convex sets it is shown that their algorithm is in fact a special case of a splitting algorithm analyzed by gabay for finding a zero of the sum of two maximal monotone operators gabay s convergence analysis for the splitting algorithm is sharpened and new applications of this algorithm to variational inequalities convex programming and the solution of linear complementarily problems are proposed for convex programs with a certain separable structure a multiplier method that is closely related to the alternating direction method of multipliers of gabay mercier and of glowinski marrocco but which uses both ordinary and augmented lagrangians is obtained

on the use of non linear transformations for the evaluation of anisotropic rotationally symmetric directional integrals application to the stress analysis in fibred soft tissues microsphere based constitutive models are a helpful tool in the modelling of materials with a microstructure composed of contributing elements directionally arranged this is the case for instance for fibred soft tissues in these models the macroscopic mechanical behaviour is obtained from the integration of the micro structural contribution of each component e g each fibre over the surface of an underlying microsphere which allows incorporating the mechanical features of the micro constituents to the macroscopic response the combination of this sort of models and the associated numerical techniques constitutes a powerful modelling tool for which an efficient integration scheme is required in this regard the unit sphere discretizations proposed by bazant and oh zamm j appl math mech z angew math mech 1986 66 1 37 49 have been used for the integration of the microscopic contributions in isotropic materials nevertheless the inclusion of anisotropy has important implications with regard to the integration scheme since very fine discretizations are needed to perform the integration accurately causing the integration process to be very costly in addition the storage of internal variables at each integration direction of every integration point is required for constitutive models based on the use of internal variables at the micro structural level which renders this approach rather complex and memory demanding in order to reduce the number of necessary integration directions several non linear transformations for the integration of rotationally symmetric functions over the surface of the unit sphere are here presented their accuracy in the integration of the von mises orientation distribution function is evaluated furthermore a hyperelastic microsphere based constitutive law for the modelling of soft biological tissues is used in order to check the accuracy and computational efficiency of the proposed transformations within a finite element context in inhomogeneous deformation problems simulation results show the suitability of the proposed methodology in order to accurately approximate the value of the integrals within reasonable computational costs copyright c 2009 john wiley sons ltd less

recovering low rank and sparse components of matrices from incomplete and noisy observations many problems can be characterized by the task of recovering the low rank and sparse components of a given matrix recently it was discovered that this nondeterministic polynomial time hard np hard task can be well accomplished both theoretically and numerically via heuristically solving a convex relaxation problem where the widely acknowledged nuclear norm and l 1 norm are utilized to induce low rank and sparsity this paper studies the recovery task in the general settings that only a fraction of entries of the matrix can be observed and the observation is corrupted by both impulsive and gaussian noise we show that the resulting model falls into the applicable scope of the classical augmented lagrangian method moreover the separable structure of the new model enables us to solve the involved subproblems more efficiently by splitting the augmented lagrangian function hence some splitting numerical algorithms are developed for solving the new recovery model some preliminary numerical experiments verify that these augmented lagrangian based splitting algorithms are easily implementable and surprisingly efficient for tackling the new recovery model

a new technique for nonconvex primal dual decomposition of a large scale separable optimization problem the primal dual approach is quite effective in decomposing a convex separable optimization problem into several subproblems of smaller sizes in this paper we present a new technique which extends the primal dual approach to nonconvex problems since a straightforward application of the multiplier method destroys separability a new lagrangian function is proposed which preserves separability based on this new function we develop a new iterative method for finding an optimal solution to the problem and show that the method is locally convergent to an optimal solution furthermore the effect of certain parameters on the ratio of convergence is investigated and simple examples are given to illustrate the proposed approach

autocorrelation driven synthesis of antenna arrays the case of ds based planar isophoric thinned arrays a new methodology for the design of isophoric thinned arrays with a priori controlled pattern features is introduced a fully analytical and general i e valid for any lattice and set of weights relationship between the autocorrelation of the array excitations and the power pattern samples is first derived binary 2 d sequences with known autocorrelation properties namely the difference sets ds s are then chosen as a representative benchmark to prove that it is possible to deduce closed form synthesis formulas that a priori guarantee to fit requirements on the sidelobe level sll the directivity the half power beamwidth and the power pattern in user defined directions the selected results from a wide numerical assessment which also includes full wave simulations with realistic radiators are illustrated to validate the reliability and the accuracy of the proposed design equations and the associated performance bounds

an effective approach for the optimal focusing of array fields subject to arbitrary upper bounds a new approach to the optimal focusing of array fields subject to arbitrary upper bounds is presented the approach formulates the problem as the minimization of a linear function in a convex set unlike other approaches this one guarantees the achievement of the global optimum by using local optimization techniques and can moreover deal with any convex constraint on the unknowns such as near field constraints optimization is performed by two ad hoc developed solution algorithms which exploit the geometrical characteristics of the problem at hand thus leading to extremely effective and computationally efficient numerical codes an extensive numerical analysis has been performed in all cases of linear planar and circular arc arrays the enhanced performance of the proposed technique with respect to the solution algorithms available in the literature fully confirms the effectiveness of the approach

shape memory behaviour modelling within continuum thermomechanics abstract a phenomenological material model to represent the multiaxial material behaviour of shape memory alloys is proposed the material model is able to represent the main effects of shape memory alloys the one way shape memory effect the two way shape memory effect due to external loads the pseudoelastic and pseudoplastic behaviour as well as the transition range between pseudoelasticity and pseudoplasticity the material model is based on a free energy function and evolution equations for internal variables by means of the free energy function the energy storage during thermomechanical processes is described evolution equations for internal variables e g the inelastic strain tensor or the fraction of martensite are formulated to represent the dissipative material behaviour in order to distinguish between different deformation mechanisms case distinctions are introduced into the evolution equations thermomechanical consistency is ensured in the sense that the constitutive model satisfies the clausius duhem inequality finally some numerical solutions of the constitutive equations for isothermal and non isothermal strain and stress processes demonstrate that the various phenomena of the material behaviour are well represented this applies for uniaxial processes and for non proportional loadings as well

an algorithm twisted from generalized admm for multi block separable convex minimization models the alternating direction method with multipliers admm has been one of most powerful and successful methods for solving a two block linearly constrained convex minimization model whose objective function is the sum of two functions without coupled variables it is known that the numerical efficiency is inherited for a large number of applications but the convergence is not guaranteed if the admm is directly extended to a multiple block convex minimization model whose objective function has more than two functions this viewpoint was in fact the motivation for developing efficient algorithms that cannot only preserve the numerical advantages of the direct extension of admm but also guarantee convergence one way is to correct the output of the direct extension of admm slightly via a simple correction step and the other is to employ a simple proximal to solve inexactly each subproblem in the direct extension of admm in this paper in order to solve the multi block separable convex minimization model efficiently we present a method which is a combination of the above two ways that is we first solve each subproblem with a simple proximal then we correct the output via a simple correction step theoretically we derive global convergence results for this method and establish a worst case o 1 k iteration complexity numerically the efficiency of this method can be showed by testing the problem of recovering low rank and sparse components of matrices from incomplete and noisy observation

extrema of young s modulus for cubic and transversely isotropic solids for a homogeneous anisotropic and linearly elastic solid the general expression of youngs modulus e n embracing all classes that characterize the anisotropy is given a constrained extremum problem is then formulated for the evaluation of those directions n at which e n attains stationary values cubic and transversely isotropic symmetry classes are dealt with and explicit solutions for such directions n are provided for each case relevant properties of these directions and corresponding values of the modulus are discussed as well results are shown in terms of suitable combinations of elements of the elastic tensor that embody the discrepancy from isotropy on the basis of such material parameters for cubic symmetry two classes of behavior can be distinguished and in the case of transversely isotropic solids the classes are found to be four for both symmetries and for each class of behavior some examples for real materials are shown and graphical representations of the dependence of youngs modulus on direction n are given as well

design of subarrayed linear and planar array antennas with sll control based on an excitation matching approach in this paper the synthesis of subarrayed antennas with subarrays having different weights and dimensions is considered the problem is formulated as the definition of the element clustering into spatially contiguous subarrays and the corresponding weights to obtain a pattern with the lowest i e minimum achievable sidelobe level sll the problem is addressed with an unconstrained approach based on an excitation matching method where the synthesis of subarray weights and sizes is simultaneously carried out successively a hybrid version of such an approach is proposed to directly enforce into the optimization procedure the sll constraints a set of representative results concerned with both sum and difference patterns are shown furthermore some comparisons with state of the art hybrid evolutionary based techniques are reported as well

a proximal based decomposition method for convex minimization problems this paper presents a decomposition method for solving convex minimization problems at each iteration the algorithm computes two proximal steps in the dual variables and one proximal step in the primal variables we derive this algorithm from rockafellar s proximal method of multipliers which involves an augmented lagrangian with an additional quadratic proximal term the algorithm preserves the good features of the proximal method of multipliers with the additional advantage that it leads to a decoupling of the constraints and is thus suitable for parallel implementation we allow for computing approximately the proximal minimization steps and we prove that under mild assumptions on the problem s data the method is globally convergent and at a linear rate the method is compared with alternating direction type methods and applied to the particular case of minimizing a convex function over a finite intersection of closed convex sets

a parallel algorithm for a class of convex programs a parallel algorithm is proposed in this paper for solving the problem min q x x in c 1 cap cdots cap c m where q is an uniformly convex function and c i are closed convex sets in r n in each iteration of the method we solve in parallel m independent subproblems each minimizing a definite quadratic function over an individual set c i the method has attractive convergence properties and can be implemented as parallel algorithms for tackling definite quadratic programs linear programs systems of linear equations and systems of generalized nonlinear inequalities

on the convergence of han s method for convex programming with quadratic objective we present an iterative method for minimizing strictly convex quadratic functions over the intersection of a finite number of convex sets the method consists in computing projections onto the individual sets simultaneously and the new iterate is a convex combination of those projections we give convergence proofs even for the inconsistent case i e when the intersection of the sets is empty

a gibbs energy barrier based computational micro sphere model for the simulation of martensitic phase transformations summary we introduce a material model for the simulation of polycrystalline materials undergoing solid to solid phase transformations as a basis we present a scalar valued phase transformation model where a helmholtz free energy function depending on volumetric and deviatoric strain measures is assigned to each phase the analysis of the related overall gibbs energy density allows for the calculation of energy barriers with these quantities at hand we use a statistical physics based approach to determine the resulting evolution of volume fractions though the model facilitates to take into account an arbitrary number of solid phases of the underlying material we restrict this work to the simulation of phase transformations between an austenitic parent phase and a martensitic tension and compression phase the scalar model is embedded into a computational micro sphere formulation in view of the simulation of three dimensional boundary value problems the final modelling approach necessary for macroscopic simulations is accomplished by a finite element formulation where the local material behaviour at each integration point is governed by the response of the micro sphere model copyright 2014 john wiley sons ltd