stationary fuzzy fokker planck learning for derivative free optimization stationary fuzzy fokker planck learning sffpl is a recently introduced computational method that applies fuzzy modeling to solve optimization problems this study develops a concept of applying sffpl based computations for nonlinear constrained optimization we consider the development of sffpl based optimization algorithms which do not require derivatives of the objective function and of the constraints the sequential penalty approach was used to handle the inequality constraints it was proved under some standard assumptions that the carefully designed sffpl based algorithms converge asymptotically to the stationary points the convergence proofs follow a simple mathematical approach and invoke mean value theorem the algorithms were evaluated on the test problems with the number of variables up to 50 the performance comparison of the proposed algorithms with some of the standard optimization algorithms further justifies our approach the sffpl based optimization approach due to its novelty could possibly be extended to several research directions

kriging sparse polynomial dimensional decomposition surrogate model with adaptive refinement uncertainty quantification and global sensitivity analysis problems are made more difficult in the case of applications which involve expensive computer simulations this because a limited amount of simulations is available to build a sufficiently accurate metamodel of the quantities of interest in this work a numerical technique for the construction of a low cost and accurate metamodel is proposed having in mind applications with expensive computer codes two main points are intro duced firstly a technique which couples universal kriging with sparse polynomial dimensional decomposition pdd to build a metamodel with improved accuracy the polynomials selected by the adaptive pdd representation are used as a sparse basis to build an universal kriging surrogate model the second is a strategy derived from anisotropic mesh adaptation to adaptively add a fixed number of new training points to an existing design of experiments the convergence of the proposed algorithm is analyzed and assessed on different test functions with an increasing size of the input space finally the algorithm is used to propagate uncertainties in two high dimensional real problems related to the atmospheric reentry

convergence of the restricted nelder mead algorithm in two dimensions the nelder mead algorithm a longstanding direct search method for unconstrained optimization published in 1965 is designed to minimize a scalar valued function f of n real variables using only function values without any derivative information each nelder mead iteration is asso ciated with a nondegenerate simplex defined by n 1 vertices and their function values a typical iteration produces a new simplex by replacing the worst vertex by a new point despite the method s widespread use theoretical results have been limited for strictly convex objective functions of one variable with bounded level sets the algorithm always converges to the minimizer for such func tions of two variables the diameter of the simplex converges to zero but examples constructed by mckinnon show that the algorithm may converge to a nonminimizing point this paper considers the restricted nelder mead algorithm a variant that does not allow expansion steps in two dimen sions we show that for any nondegenerate starting simplex and any twice continuously differentiable function with positive definite hessian and bounded level sets the algorithm always converges to the minimizer the proof is based on treating the method as a discrete dynamical system and relies on several techniques that are nonstandard in convergence proofs for unconstrained optimization

mesh adaptive direct search algorithms for constrained optimization this paper addresses the problem of minimization of a nonsmooth function under general nonsmooth constraints when no derivatives of the objective or constraint functions are available we introduce the mesh adaptive direct search mads class of algorithms which extends the generalized pattern search gps class by allowing local exploration called polling in an asymptotically dense set of directions in the space of optimization variables this means that under certain hypotheses including a weak constraint qualification due to rockafellar mads can treat constraints by the extreme barrier approach of setting the objective to infinity for infeasible points and treating the problem as unconstrained the main gps convergence result is to identify limit points hat x where the clarke generalized derivatives are nonnegative in a finite set of directions called refining directions although in the unconstrained case nonnegative combinations of these directions span the whole space the fact that there can only be finitely many gps refining directions limits rigorous justification of the barrier approach to finitely many linear constraints for gps the main result of this paper is that the general mads framework is flexible enough to allow the generation of an asymptotically dense set of refining directions along which the clarke derivatives are nonnegative we propose an instance of mads for which the refining directions are dense in the hypertangent cone at hat x with probability 1 whenever the iterates associated with the refining directions converge to a single hat x the instance of mads is compared to versions of gps on some test problems we also illustrate the limitation of our results with examples

superlinear convergence and implicit filtering in this paper we show how the implicit filtering algorithm can be coupled with the bfgs quasi newton update to obtain a superlinearly convergent iteration if the noise in the objective function decays sufficiently rapidly as the optimal point is approached in this way we give insight into the observations of good performance in practice of quasi newton methods when they are coupled with implicit filtering we also report on numerical experiments that show how an implementation of implicit filtering that exploits these new results can improve the performance of the algorithm

classes of nonseparable spatio temporal stationary covariance functions abstract suppose that a random process z s t indexed in space and time has spatio temporal stationary covariance c h u where h d d 1 is a spatial lag and u is a temporal lag separable spatio temporal covariances have the property that they can be written as a product of a purely spatial covariance and a purely temporal covariance their ease of definition is counterbalanced by the rather limited class of random processes to which they correspond in this article we derive a new approach that allows one to obtain many classes of nonseparable spatio temporal stationary covariance functions and fit several such classes to spatio temporal data on wind speed over a region in the tropical western pacific ocean

modeling an augmented lagrangian for blackbox constrained optimization constrained blackbox optimization is a difficult problem with most approaches coming from the mathematical programming literature the statistical literature is sparse especially in addressing problems with nontrivial constraints this situation is unfortunate because statistical methods have many attractive properties global scope handling noisy objectives sensitivity analysis and so forth to narrow that gap we propose a combination of response surface modeling expected improvement and the augmented lagrangian numerical optimization framework this hybrid approach allows the statistical model to think globally and the augmented lagrangian to act locally we focus on problems where the constraints are the primary bottleneck requiring expensive simulation to evaluate and substantial modeling effort to map out in that context our hybridization presents a simple yet effective solution that allows existing objective oriented statistical approaches like those based on gaussian process surrogates

general framework for the identification of constitutive parameters from full field measurements in linear elasticity in this paper several approaches available in the literature for identifying the constitutive parameters of linear elastic materials from full field measurements are presented and their sensitivity to a white noise added to the data is compared the first investigated approach is the virtual fields method vfm it is shown that the uncertainty of the parameters identified with the vfm when a white noise is added to the data depends on the choice of a relevant set of virtual fields optimal virtual fields exist thus minimizing the uncertainty and providing the maximum likelihood solution the other approaches investigated in this paper are based on finite element model updating femu it is proved that femu approaches actually yield equations similar to the ones derived from the vfm but with nonoptimal sets of virtual fields therefore the femu approaches do not provide the maximum likelihood solution however the uncertainty of femu approaches varies dramatically with the cost function to minimize on one hand the femu approach based on the displacement gap minimization yields equations which are very close to the ones of the vfm approach and therefore its uncertainty is almost the same as the vfm one on the other hand it is shown that other approaches based on the constitutive equation gap minimization or the equilibrium gap minimization provide biased solutions for all the approaches very fast algorithms converging in only two iterations have been devised they are finally applied to real experimental data obtained on an orthotropic composite material results confirm the success of two methods the vfm approach which provides the maximum likelihood solution and the femu approach based on the displacement gap minimization

parallel space decomposition of the mesh adaptive direct search algorithm this paper describes a parallel space decomposition psd technique for the mesh adaptive direct search mads algorithm mads extends a generalized pattern search for constrained nonsmooth optimization problems the objective of the present work is to obtain good solutions to larger problems than the ones typically solved by mads the new method psd mads is an asynchronous parallel algorithm in which the processes solve problems over subsets of variables the convergence analysis based on the clarke calculus is essentially the same as for the mads algorithm a practical implementation is described and some numerical results on problems with up to 500 variables illustrate the advantages and limitations of psd mads

adjoint weighted equation for inverse problems of incompressible plane stress elasticity the adjoint weighted equation awe formulation is applied to incompressible isotropic plane stress elasticity for the solution of inverse problems for the strong form of the problem to have a solution a restrictive strain compatibility condition must hold in the awe variational formulation on the other hand a much milder sufficient condition is that uniaxial stress states be precluded making the method more robust to noisy data we prove that the formulation leads to a stable converging numerical method and show through computations that the method performs well

simulation of the entire range of daily precipitation using a hybrid probability distribution 1 underestimation of extreme values is a widely acknowledged issue in daily precipitation simulation nonparametric precipitation generators have inherent limitations in representing extremes parametric generators can realistically model the full spectrum of precipitation amount through compound distributions nevertheless fitting these distributions suffers from numerical instability supervised learning and computational demand this study presents an easy to implement hybrid probability distribution to model the full spectrum of precipitation amount the basic idea for the hybrid distribution lies in synthesizing low to moderate precipitation by an exponential distribution and extreme precipitation by a generalized pareto distribution by forcing the two distributions to be continuous at the junction point the threshold of the generalized pareto distribution can be implicitly learned in an unsupervised manner monte carlo simulation shows that the hybrid distribution is capable of modeling heavy tailed data performance of the distribution is further evaluated using 49 daily precipitation records across texas results show that the model is able to capture both the bulk and the tail of daily precipitation amount the maximum goodness of fit and penalized maximum likelihood methods are found to be reliable complements to the maximum likelihood method in that generally they can provide adequate goodness of fit the proposed distribution can be incorporated into precipitation generators and downscaling models in order to realistically simulate the entire range of precipitation without losing extreme values

on the convergence of pattern search algorithms we introduce an abstract definition of pattern search methods for solving nonlinear unconstrained optimization problems our definition unifies an important collection of optimization methods that neither compute nor explicitly approximate derivatives we exploit our characterization of pattern search methods to establish a global convergence theory that does not enforce a notion of sufficient decrease our analysis is possible because the iterates of a pattern search method lie on a scaled translated integer lattice this allows us to relax the classical requirements on the acceptance of the step at the expense of stronger conditions on the form of the step and still guarantee global convergence

on the convergence of grid based methods for unconstrained optimization the convergence of direct search methods for unconstrained minimization is examined in the case where the underlying method can be interpreted as a grid or pattern search over successively refined meshes an important aspect of the main convergence result is that translation rotation scaling and shearing of the successive grids are allowed

unconstrained derivative free optimization by successive approximation we present an algorithmic framework for unconstrained derivative free optimization based on dividing the search space in regions partitions every partition is assigned a representative point the representative points form a grid a piecewise constant approximation to the function subject to optimization is constructed using a partitioning and its corresponding grid the convergence of the framework to a stationary point of a continuously differentiable function is guaranteed under mild assumptions the proposed framework is appropriate for upgrading heuristics that lack mathematical analysis into algorithms that guarantee convergence to a local minimizer a convergent variant of the nelder mead algorithm that conforms to the given framework is constructed the algorithm is compared to two previously published convergent variants of the nm algorithm the comparison is conducted on the more garbow hillstrom set of test problems and on four variably dimensional functions with dimension up to 100 the results of the comparison show that the proposed algorithm outperforms both previously published algorithms

pattern search ranking and selection algorithms for mixed variable simulation based optimization the class of generalized pattern search gps algorithms for mixed variable optimization is extended to problems with stochastic objective functions because random noise in the objective function makes it more difficult to compare trial points and ascertain which points are truly better than others replications are needed to generate sufficient statistical power to draw conclusions rather than comparing pairs of points the approach taken here augments pattern search with a ranking and selection r s procedure which allows for comparing many function values simultaneously asymptotic convergence for the algorithm is established numerical issues are discussed and performance of the algorithm is studied on a set of test problems

estimation of layerwise elastic parameters of stiffened composite plates for the first time an investigation of stiffened and unstiffened multilayered composite plates has been conducted to determine the material property parameters of the plate as well as the stiffener from numerically simulated experimental modal data and finite element predictions using model updating techniques the problem is formulated as a global minimization of the error function defined by the difference in undamped eigenvalues as well as mode shapes as predicted from the finite element modeling compared to that obtained experimentally the parameter estimation problem is solved using an iterative gradient based minimization algorithm which can start from any randomly selected set of initial parameters the position physical properties and orientation of stiffeners create considerable variations in the modal properties as compared to the bare plates of similar construction this makes each of the stiffened plate problems rather unique a few simulated examples are presented and the methodology is found to be robust even in the presence of random noise

accelerated random search for constrained global optimization assisted by radial basis function surrogates abstract the accelerated random search ars algorithm appel et al 2004 is a stochastic algorithm for the global optimization of black box functions subject only to bound constraints ars iteratively samples uniformly within a box centered at the current best point if the sample point is worse than the current best point then the size of the box is reduced thereby making it more likely to generate an improving solution if the current best point is not yet a local minimum otherwise if the sample point is an improvement over the current best point then the size of the box is reset to the initial value so that the box covers the entire search space ars has been shown theoretically and numerically to converge to the global minimum faster than the pure random search prs algorithm on bound constrained problems this article develops the constrained ars cars algorithm which is an extension of ars for optimization problems with black box inequality constraints under some mild conditions on the constrained optimization problem we prove the convergence to the global minimum in a probabilistic sense of a class of stochastic search algorithms called scattered uniform random search scat urs algorithms which includes cars as a special case to improve performance of cars on computationally expensive simulation based problems we incorporate radial basis function rbf surrogate models to approximate the objective and constrained functions and refer to the resulting algorithm as cars rbf numerical experiments show that cars consistently and substantially outperforms both the pure random search prs and accelerated particle swarm optimization apso algorithms yang 2010 on 31 test problems with dimensions ranging from 2 to 20 moreover cars rbf is an improvement over cars outperforms a sequential penalty derivative algorithm and competes with constrlmsrbf regis 2011 on the same test problems finally sensitivity analysis of cars rbf to the type of rbf model used shows that the cubic rbf model generally yields the best results on the test problems among six types of rbf models considered including the thin plate spline gaussian and multiquadric models

a pattern search filter method for nonlinear programming without derivatives this paper formulates and analyzes a pattern search method for general constrained optimization based on filter methods for step acceptance roughly a filter method accepts a step that improves either the objective function value or the value of some function that measures the constraint violation the new algorithm does not compute or approximate any derivatives penalty constants or lagrange multipliers a key feature of the new algorithm is that it preserves the division into search and local poll steps which allows the explicit use of inexpensive surrogates or random search heuristics in the search step it is shown here that the algorithm identifies limit points at which optimality conditions depend on local smoothness of the functions and to a greater extent on the choice of a certain set of directions stronger optimality conditions are guaranteed for smoother functions and in the constrained case for a fortunate choice of the directions on which the algorithm depends these directional conditions generalize those given previously for linear constraints but they do not require a feasible starting point in the absence of general constraints the proposed algorithm and its convergence analysis generalize previous work on unconstrained bound constrained and linearly constrained generalized pattern search the algorithm is illustrated on some test examples and on an industrial wing planform engineering design application

a naive multi scale search algorithm for global optimization problems this paper proposes a multi scale search algorithm for solving global optimization problems given a finite number of function evaluations we refer to this algorithm as the naive multi scale search optimization nmso nmso looks for the optimal solution by optimistically partitioning the search space over multiple scales in a hierarchical fashion based on a weak assumption about the function smoothness we present a theoretical analysis on its finite time and asymptotic convergence an empirical assessment of the algorithm has been conducted on the noiseless black box optimization benchmarking bbob testbed and compared with the state of the art optimistic as well as stochastic algorithms moreover the efficacy of nmso has been validated on the black box optimization competition within the gecco 15 conference where it has secured the third place out of twenty eight participating algorithms overall nmso is suitable for problems with limited function evaluations low dimensionality search space and objective functions that are separable or multi modal otherwise it is comparable with the top performing algorithms

identification of orthotropic elastic constants using the eigenfunction virtual fields method abstract the virtual fields method vfm pierron and grediac 2012 an inverse method based on the principle of virtual work pvw is being increasingly used to estimate mechanical properties of materials from full field deformations obtained from techniques such as digital image correlation moire and speckle interferometry and grid methods by making specific choices for virtual fields vfs in pvw one obtains a system of algebraic equations which is then solved for the unknown material constants recently a new variant of vfm known as the eigenfunction virtual fields method evfm has been proposed subramanian 2013 in evfm principal components of the measured i e true strain fields are used to systematically generate vfs we extend evfm to orthotropic elastic materials in this work and estimate the relevant material parameters from full field strain data generated from a finite element model of an unnotched iosipescu test varying levels of gaussian white noise are added to the synthetic strain data to evaluate the sensitivity of evfm to input noise it is observed that for low to moderate noise the material properties estimated by the proposed method are relatively insensitive to noise however when noise levels are high the proposed method yields large variance in some of the computed properties when compared to the state of the art optimized piecewise continuous vfm toussaint et al 2006 pierron and grediac 2012 some of the large variance in properties estimated from noisy data using evfm is traced to the sensitivity of the third dominant eigenfunction and modifications to the proposed method to address this issue are suggested

algebraic cycles and homotopy theory examine its homotopy groups which after a certain idealization of the space turn out to be astonishingly simple in fact for complex projective space pn the structure can be understood completely this yields new information about the topology of the classical chow varieties and establishes an explicit relationship with universal cohomology operations in the general case complete computations are difficult but we shall establish a complex suspension theorem and lay the foundations for a theory based on the homotopy groups of chow varieties to state the results we must give precise meaning to the space of subvarieties we begin with the fundamental case of subvarieties in complex projective n space pln for each pair of integers p and d with d 1 and 0 p n consider the set wp d pn of all finite formal sums

a stochastic daily weather generator for skewed data 1 to simulate multivariate daily time series minimum and maximum temperatures global radiation wind speed and precipitation intensity we propose a weather state approach with a multivariate closed skew normal generator wacs gen that is able to accurately reproduce the statistical properties of these five variables our weather generator construction takes advantage of two elements we first extend the classical wet and dry days dichotomy used in most past weather generators to the definition of multiple weather states using clustering techniques the transitions among weather states are modeled by a first order markov chain second the vector of our five daily variables of interest is sampled conditionally on these weather states from a closed skew normal distribution this class of distribution allows us to handle nonsymmetric behaviors our method is applied to the 20 years of daily weather measurements from colmar france this example illustrates the advantages of our approach especially improving the simulation of radiation and wind distributions

determination of the size of the representative volume element for random composites statistical and numerical approach the representative volume element rve plays a central role in the mechanics and physics of random heterogeneous materials with a view to predicting their effective properties a quantitative definition of its size is proposed in this work a rve size can be associated with a given precision of the estimation of the wanted overall property and the number of realizations of a given volume v of microstructure that one is able to consider it is shown to depend on the investigated morphological or physical property the contrast in the properties of the constituents and their volume fractions the methodology is applied to a specific random microstructure namely a two phase three dimensional voronoi mosaic finite element simulations of volumes of different sizes are performed in the case of linear elasticity and thermal conductivity the volumes are subjected to homogeneous strain stress or periodic boundary conditions the effective properties can be determined for large volumes and a small number of realizations conversely smaller volumes can be used providing that a sufficient number of realizations are considered a bias in the estimation of the effective properties is observed for too small volumes for all types of boundary conditions the variance of computed apparent properties for each volume size is used to define the precision of the estimation the key notion of integral range is introduced to relate this error estimation and the definition of the rve size for given wanted precision and number of realizations one is able to provide a minimal volume size for the computation of effective properties the results can also be used to predict the minimal number of realizations that must be considered for a given volume size in order to estimate the effective property for a given precision the rve sizes found for elastic and thermal properties but also for a geometrical property like volume fraction are compared

a fully integrated noise robust strategy for the identification of constitutive laws from digital images constitutive parameter identification has been greatly improved by the achievement of full field measurements in this context noise sensitivity has been shown to be of great importance it is crucial to incorporate noise sensitivity minimization in the design of robust identification procedures in this paper we investigate noise sensitivity reduction techniques for constitutive parameter identification based on finite element model updating after examining the existing strategies we propose a single step algorithm based on a mixed optical mechanical cost function the key point of this novel procedure is that no boundary conditions are needed a first example on a real case illustrates the advantages of the proposed methodology in terms of noise sensitivity a second example shows its capabilities to identify a non linear consitutive law copyright 2010 john wiley sons ltd

simple full field method for the elastic characterization of orthotropic composite plates a speckle shearing interferometer with a simple setup is designed and tested for full field characterization of the elastic properties of isotropic and orthotropic composite plates the technique is straightforward and provides comparable results obtained by standard methods the proposed method has the advantages of being noncontact and full field in nature beam specimens cut from the plate were loaded under the standard four point bending configuration gradients of bending deformation are measured by the speckle shearing interferometer directly curvature of each bended beam is calculated from the slope of the fitted line of the gradient data the elastic moduli and poisson s ratios of the plate material are determined from the curvature of the beam specimens comparing the present approach to other full field techniques reported in literature that are mostly based on deformation measurement of a specimen subjected to a complicated load field the present method is much easier to apply and the image analysis procedure is much simpler

special virtual fields for the direct determination of material parameters with the virtual fields method 2 application to in plane properties this paper deals with the direct identification of mechanical parameters that govern the in plane constitutive law of orthotropic materials those parameters are extracted from heterogeneous strain fields that occur in a short beam specimen tested in a iosipescu fixture the procedure used is the virtual fields method with special virtual fields the case of linear elasticity is first addressed it is shown that the parameters are directly extracted with this method no iterative calculations are required the stability is also discussed in different cases a non linear shear response is then considered the parameter that governs this non linearity is also directly identified with the special virtual fields

generalized pattern searches with derivative information a common question asked by users of direct search algorithms is how to use derivative information at iterates where it is available this paper addresses that question with respect to generalized pattern search gps methods for unconstrained and linearly constrained optimization specifically this paper concentrates on the gps pollstep polling is done to certify the need to refine the current mesh and it requires o n function evaluations in the worst case we show that the use of derivative information significantly reduces the maximum number of function evaluations necessary for pollsteps even to a worst case of a single function evaluation with certain algorithmic choices given here furthermore we show that rather rough approximations to the gradient are sufficient to reduce the pollstep to a single function evaluation we prove that using these less expensive pollsteps does not weaken the known convergence properties of the method all of which depend only on the pollstep

spatial temporal rainfall simulation using generalized linear models 1 we consider the problem of simulating sequences of daily rainfall at a network of sites in such a way as to reproduce a variety of properties realistically over a range of spatial scales the properties of interest will vary between applications but typically will include some measures of extreme rainfall in addition to means variances proportions of wet days and autocorrelation structure our approach is to fit a generalized linear model glm to rain gauge data and with appropriate incorporation of intersite dependence structure to use the glm to generate simulated sequences we illustrate the methodology using a data set from southern england and show that the glm is able to reproduce many properties at spatial scales ranging from a single site to 2000 km2 the limit of the available data

optimization by direct search new perspectives on some classical and modern methods direct search methods are best known as unconstrained optimization techniques that do not explicitly use derivatives direct search methods were formally proposed and widely applied in the 1960s but fell out of favor with the mathematical optimization community by the early 1970s because they lacked coherent mathematical analysis nonetheless users remained loyal to these methods most of which were easy to program some of which were reliable in the past fifteen years these methods have seen a revival due in part to the appearance of mathematical analysis as well as to interest in parallel and distributed com puting this review begins by briefly summarizing the history of direct search methods and considering the special properties of problems for which they are well suited our focus then turns to a broad class of methods for which we provide a unifying framework that lends itself to a variety of convergence results the underlying principles allow general ization to handle bound constraints and linear constraints we also discuss extensions to problems with nonlinear constraints

a comparison of three methods for selecting values of input variables in the analysis of output from a computer code two types of sampling plans are examined as alternatives to simple random sampling in monte carlo studies these plans are shown to be improvements over simple random sampling with respect to variance for a class of estimators which includes the sample mean and the empirical distribution function

spherical mesh adaptive direct search for separating quasi uncorrelated sources by range based independent component analysis it is seemingly paradoxical to the classical definition of the independent component analysis ica that in reality the true sources are often not strictly uncorrelated with this in mind this letter concerns a framework to extract quasi uncorrelated sources with finite supports by optimizing a range based contrast function under unit norm constraints to handle the inherent scaling indeterminacy of ica but without orthogonality constraints albeit the appealing contrast properties of the range based function e g the absence of mixing local optima the function is not differentiable everywhere unfortunately there is a dearth of literature on derivative free optimizers that effectively handle such a nonsmooth yet promising contrast function this is the compelling reason for the design of a nonsmooth optimization algorithm on a manifold of matrices having unit norm columns with the following objectives to ascertain convergence to a clarke stationary point of the contrast function and adhere to the necessary unit norm constraints more naturally the proposed nonsmooth optimization algorithm crucially relies on the design and analysis of an extension of the mesh adaptive direct search mads method to handle locally lipschitz objective functions defined on the sphere the applicability of the algorithm in the ica domain is demonstrated with simulations involving natural face aerial and texture images

sequential penalty derivative free methods for nonlinear constrained optimization we consider the problem of minimizing a continuously differentiable function of several variables subject to smooth nonlinear constraints we assume that the first order derivatives of the objective function and of the constraints can be neither calculated nor explicitly approximated hence every minimization procedure must use only a suitable sampling of the problem functions these problems arise in many industrial and scientific applications and this motivates the increasing interest in studying derivative free methods for their solution the aim of the paper is to extend to a derivative free context a sequential penalty approach for nonlinear programming this approach consists in solving the original problem by a sequence of approximate minimizations of a merit function where penalization of constraint violation is progressively increased in particular under some standard assumptions we introduce a general theoretical result regarding the connections between the sampling technique and the updating of the penalization which are able to guarantee convergence to stationary points of the constrained problem on the basis of the general theoretical result we propose a new method and prove its convergence to stationary points of the constrained problem the computational behavior of the method has been evaluated both on a set of test problems and on a real application the obtained results and the comparison with other well known derivative free software show the viability of the proposed sequential penalty approach

inexact restoration method for derivative free optimization with smooth constraints a new method is introduced for solving constrained optimization problems in which the derivatives of the constraints are available but the derivatives of the objective function are not the method is based on the inexact restoration framework by means of which each iteration is divided in two phases in the first phase one considers only the constraints in order to improve feasibility in the second phase one minimizes a suitable objective function subject to a linear approximation of the constraints the second phase must be solved using derivative free methods an algorithm introduced recently by kolda lewis and torczon for linearly constrained derivative free optimization is employed for this purpose under usual assumptions convergence to stationary points is proved a computer implementation is described and numerical experiments are presented

estimation of in plane elastic parameters and stiffener geometry of stiffened plates abstract an investigation on stiffened plates has been conducted for the first time to determine the elastic parameters as well as the cross sectional dimensions of rectangular stiffeners from experimental modal data and finite element predictions using model updating technique the problem is formulated as a global minimization of the error function defined by the difference in modal properties as predicted from the finite element modelling to that obtained experimentally the parameter estimation problem is solved using an iterative gradient based minimization algorithm and can start from different randomly selected set of initial parameters the levenberg marquardt algorithm has been implemented to minimize the error function proper bounds are realistically chosen for the selection of the initial values of the parameters the position physical properties and orientation of stiffeners create considerable variations in the modal properties as compared with the bare plates of similar construction this makes each of the stiffened plate identification problem rather unique the position of stiffeners as well as its orientation makes certain measurement points more suitable for comparing analytical and experimental mode shapes the optimum measurement set of co ordinates which can be used for the purpose of identification is thus case specific the geometrical properties of stiffener cross section also affect the modes inclusion of different sets of modes in noisy environment and the differences in the estimated parameters are studied a few simulated examples are presented to investigate the uniqueness and convergence of results the methodology is found to be very accurate and robust

a nonderivative version of the gradient sampling algorithm for nonsmooth nonconvex optimization we give a nonderivative version of the gradient sampling algorithm of burke lewis and overton for minimizing a locally lipschitz function f on mathbb r n that is continuously differentiable on an open dense subset instead of gradients of f we use estimates of gradients of the steklov averages of f obtained by convolution with mollifiers which require f values only we show that the nonderivative version retains the convergence properties of the gradient sampling algorithm in particular with probability 1 it either drives the f values to infty or each of its cluster points is clarke stationary for f

a linesearch based derivative free approach for nonsmooth constrained optimization in this paper we propose new linesearch based methods for nonsmooth constrained optimization problems when first order information on the problem functions is not available in the first part we describe a general framework for bound constrained problems and analyze its convergence toward stationary points using the clarke jahn directional derivative in the second part we consider inequality constrained optimization problems where both objective function and constraints can possibly be nonsmooth in this case we first split the constraints into two subsets difficult general nonlinear constraints and simple bound constraints on the variables then we use an exact penalty function to tackle the difficult constraints and we prove that the original problem can be reformulated as the bound constrained minimization of the proposed exact penalty function finally we use the framework developed for the bound constrained case to solve the penalized problem moreover we prove that every accumulation poin

finding optimal algorithmic parameters using derivative free optimization the objectives of this paper are twofold we devise a general framework for identifying locally optimal algorithmic parameters algorithmic parameters are treated as decision variables in a problem for which no derivative knowledge or existence is assumed a derivative free method for optimization seeks to minimize some measure of performance of the algorithm being fine tuned this measure is treated as a black box and may be chosen by the user examples are given in the text the second objective is to illustrate this framework by specializing it to the identification of locally optimal trust region parameters in unconstrained optimization the derivative free method chosen to guide the process is the mesh adaptive direct search a generalization of pattern search methods we illustrate the flexibility of the latter and in particular make provision for surrogate objectives locally optimal parameters with respect to overall computational time on a set of test problems are identified each function call may take several hours and may not always return a predictable result a tailored surrogate function is used to guide the search towards a local solution the parameters thus identified differ from traditionally used values and allow one to solve a problem that remained otherwise unsolved in a reasonable time using traditional values

completions and fibrations for topological monoids we show that for a certain class of topological monoids there is a homotopy equivalence between the homotopy theoretic group completion m of a monoid m in that class and the topologized grothendieck group m associated to m the class under study is broad enough to include the chow monoids effective cycles associated to a projective algebraic variety and also the infinite symmetric products of finite cw complexes we associate principal fibrations to the completions of pairs of monoids showing the existence of long exact sequences for the naive approach to lawson homology fri91 lf91 a another proof of the eilenberg steenrod axioms for the functors x sp x in the category of finite cw complexes dold thom theorem dt56 is obtained

analysis of direct searches for discontinuous functions it is known that the clarke generalized directional derivative is nonnegative along the limit directions generated by directional direct search methods at a limit point of certain subsequences of unsuccessful iterates if the function being minimized is lipschitz continuous near the limit point in this paper we generalize this result for discontinuous functions using rockafellar generalized directional derivatives upper subderivatives we show that rockafellar derivatives are also nonnegative along the limit directions of those subsequences of unsuccessful iterates when the function values converge to the function value at the limit point this result is obtained assuming that the function is directionally lipschitz with respect to the limit direction it is also possible under appropriate conditions to establish more insightful results by showing that the sequence of points generated by these methods eventually approaches the limit point along the locally best branch or step function when the number of steps is equal to two the results of this paper are presented for constrained optimization and illustrated numerically

the constitutive compatibility method for identification of material parameters based on full field measurements abstract we revisit here the concept of the constitutive relation error for the identification of elastic material parameters based on image correlation an additional concept so called constitutive compatibility of stress is introduced defining a subspace of the classical space of statically admissible stresses the key idea is to define stresses as compatible with the observed deformation field through the chosen class of constitutive equation this makes possible the uncoupling of the identification of stress from the identification of the material parameters as a result the global cost of the identification is strongly reduced this uncoupling also leads to parametrized solutions in cases where the solution is non unique as demonstrated on 2d numerical examples

anisotropic linear elastic parameter estimation using error in the constitutive equation functional a modified error in the constitutive equation based approach for identification of heterogeneous and linear anisotropic elastic parameters involving static measurements is proposed and explored following an alternating minimization procedure associated with the underlying optimization problem the new strategy results in an explicit material parameter update formula for general anisotropic material this immediately allows us to derive the necessary constraints on measured data and thus restrictions on physical experimentation to achieve the desired reconstruction we consider a few common materials to derive such conditions then we exploit the invariant relationships of the anisotropic constitutive tensor to propose an identification procedure for space dependent material orientations finally we assess the numerical efficacy of the developed tools against a few parameter identification problems of engineering interest

daily spatiotemporal precipitation simulation using latent and transformed gaussian processes 1 a daily stochastic spatiotemporal precipitation generator that yields spatially consistent gridded quantitative precipitation realizations is described the methodology relies on a latent gaussian process to drive precipitation occurrence and a probability integral transformed gaussian process for intensity at individual locations the model reduces to a markov chain for precipitation occurrence and a gamma distribution for precipitation intensity allowing statistical parameters to be included in a generalized linear model framework statistical parameters are modeled as spatial gaussian processes which allows for interpolation to locations where there are no direct observations via kriging one advantage of such a model for the statistical parameters is that stochastic generator parameters are immediately available at any location with the ability to adapt to spatially varying precipitation characteristics a second advantage is that parameter uncertainty generally unavailable with deterministic interpolators can be immediately quantified at all locations the methodology is illustrated on two data sets the first in iowa and the second over the pampas region of argentina in both examples the method is able to capture the local and domain aggregated precipitation behavior fairly well at a wide range of time scales including daily monthly and annually

analysis of generalized pattern searches this paper contains a new convergence analysis for the lewis and torczon generalized pattern search gps class of methods for unconstrained and linearly constrained optimization this analysis is motivated by a desire to understand the successful behavior of the algorithm under hypotheses that are satisfied by many practical problems specifically even if the objective function is discontinuous or extended valued the methods find a limit point with some minimizing properties simple examples show that the strength of the optimality conditions at a limit point depends not only on the algorithm but also on the directions it uses and on the smoothness of the objective at the limit point in question the contribution of this paper is to provide a simple convergence analysis that supplies detail about the relation of optimality conditions to objective smoothness properties and to the defining directions for the algorithm and it gives previous results as corollaries

on the inverse problem of identifying lame coefficients in linear elasticity an output least squares type functional is employed to identify the lame parameters in linear elasticity to be able to identify even the discontinuous lame parameters the regularization is performed by the bv seminorm finite element discretization is used and convergence analysis is given numerical examples are given to show the feasibility of the approach

space time covariance functions this work considers a number of properties of space time covariance functions and how these relate to the spatial temporal interactions of the process first it examines how the smoothness away from the origin of a space time covariance function affects for example temporal correlations of spatial differences models that are not smoother away from the origin than they are at the origin such as separable models have a kind of discontinuity to certain correlations that one might wish to avoid in some circumstances smoothness away from the origin of a covariance function is shown to follow from the corresponding spectral density having derivatives with finite moments these results are used to obtain a parametric class of spectral densities whose corresponding space time covariance functions are infinitely differentiable away from the origin and that allows for essentially arbitrary and possibly different degrees of smoothness for the process in space and time second this work considers models that

a mesh adaptive direct search algorithm for multiobjective optimization abstract this work studies multiobjective optimization mop of nonsmooth functions subject to general constraints we first present definitions and optimality conditions as well as some single objective formulations of mop parameterized with respect to some reference point in the space of objective functions next we propose a new algorithm called m ulti m ads multiobjective mesh adaptive direct search for mop m ulti m ads generates an approximation of the pareto front by solving a series of single objective formulations of mop generated using the nbi natural boundary intersection framework these single objective problems are solved using the m ads mesh adaptive direct search algorithm for constrained nonsmooth optimization the pareto front approximation is shown to satisfy some first order necessary optimality conditions based on the clarke calculus m ulti m ads is then tested on problems from the literature with different pareto front landscapes and on a styrene production process simulation problem from chemical engineering

globally convergent evolution strategies in this paper we show how to modify a large class of evolution strategies es s for unconstrained optimization to rigorously achieve a form of global convergence meaning convergence to stationary points independently of the starting point the type of es under consideration recombines the parent points by means of a weighted sum around which the offspring points are computed by random generation one relevant instance of such an es is covariance matrix adaptation es cma es the modifications consist essentially of the reduction of the size of the steps whenever a sufficient decrease condition on the function values is not verified when such a condition is satisfied the step size can be reset to the step size maintained by the es s themselves as long as this latter one is sufficiently large we suggest a number of ways of imposing sufficient decrease for which global convergence holds under reasonable assumptions in particular density of certain limit directions in the unit sphere given a limited budget of function evaluations our numerical experiments have shown that the modified cma es is capable of further progress in function values moreover we have observed that such an improvement in efficiency comes without weakening significantly the performance of the underlying method in the presence of several local minimizers

moving algebraic cycles of bounded degree the chow moving lemma is a theorem which asserts that a given algebraic s cycle on a smooth algebraic variety x can be moved within its rational equivalence class to intersect properly a given r cycle on x provided that r s dim x cf chow s2 in the past few years there has been considerable interest in studying spaces of algebraic cycles rather than simply cycles modulo an equivalence relation with this in mind it is natural to ask whether one can move a given bounded family of s cycles on the smooth variety x to intersect properly a given bounded family of r cycles the main point of this paper is to formulate and prove just such a result in theorem 3 1 we demonstrate that for any integer e and any smooth projective variety x one can simultaniously and algebraically move all effective s cycles of degree e on x so that each such cycle meets every effective r cycle of degree e on x in proper dimension the primary motivation for this moving lemma for cycles of bounded degree was the possibility of a duality theorem between cohomology and homology theories defined in terms of homotopy groups of cycle spaces using theorem 3 1 we have proved such a duality theorem for complex quasi projective varieties in f l2 we prove our moving lemma for varieties over an arbitary infinite field permitting a proof in f v of a duality theorem for motivic cohomology and homology the reader will find that our moving lemma has numerous good properties first of all the move is given as an algebraic move parametrized by a punctured projective line on chow varietes although this move is good only for s cycles of bounded degree it is defined on all effective s cycles moreover the move starts at time 0 by expressing an effective s cycle z as a difference of effective s cycles both of which have intersection properties no worse than z finally our moving lemma is applicable to smooth quasiprojective varieties for it is stated for a possibly singular projective variety x resulting in a conclusion of proper intersection off the singular locus of x the classical motivation for the moving lemma was to define an intersection product on algebraic cycles modulo rational equivalence thereby establishing the chow ring a x some of the classical literature overlooked the question of whether or not intersection of cycles defined via a moving lemma is independent of the move e g chow r s2 on the other hand cf chev s3 one direct consequence of our moving lemma is a proof for smooth quasi projective varieties that the intersection product is indeed well defined independent of the choice of move theorem 3 4 of course the intersection product now has an intrinsic formulation for all smooth algebraic varieties due to fulton

on the elastic characterization of composite plates with vibration data this paper takes a global look at a method of obtaining the elastic constants of the material of a rectangular plate sample by explicitly inputting the geometrical shapes and frequencies of a sufficient number of experimental vibration modes into a computational procedure that essentially compares experimental frequencies with analytical predictions there are many aspects of this method that have important bearing on accuracy ease of use and computational economy the issues that arise include vibration representation functions selection of experimental mode shapes and frequencies for analysis goodness of experimental data frequency sensitivity of the elastic constants influence of diagonal modes where relevant plate thickness plate aspect ratio material orthotropy ratio and orientation of reinforcing fibers in laminate composites whereas some of these factors have been discussed separately in other works this paper attempts bring the method completely into focus in one place with an examination of all the factors believed to influence the efficiency of the method

regularized virtual fields method for mechanical properties identification of composite materials abstract this paper presents a new material parameters identification method based on the virtual fields method vfm where a regularization term coming from a micromechanical model has been added in this regularized virtual fields method rvfm the system of equations associated to the vfm is solved within a constrained optimization framework the method was applied to virtual scanning electron microscope in situ tests aiming at determining the local properties of uni directional composites loaded in the transverse direction and for which the strain fields were obtained through digital image correlation dic the method was tested for composites with various volume fractions and properties contrasts and under different boundary conditions the potentials and limitations of the algorithm in the presence of noisy images were investigated and compared to that of the vfm and the other finite element based methods the corresponding results indicate that the proposed rvfm is more efficient than the other identification techniques in terms of both accuracy and computational time an optimum size of region of interest was also determined by taking into account dic magnification requirements and based on the accuracy of the identified parameters this kind of study can be very useful for determining a priori the level of resolution in the imaging system required for a favorable accuracy of the identified parameters

a globally convergent augmented lagrangian pattern search algorithm for optimization with general constraints and simple bounds we give a pattern search method for nonlinearly constrained optimization that is an adaption of a bound constrained augmented lagrangian method first proposed by conn gould and toint siam j numer anal 28 1991 pp 545 572 in the pattern search adaptation we solve the bound constrained subproblem approximately using a pattern search method the stopping criterion proposed by conn gould and toint for the solution of the subproblem requires explicit knowledge of derivatives such information is presumed absent in pattern search methods however we show how we can replace this with a stopping criterion based on the pattern size in a way that preserves the convergence properties of the original algorithm in this way we proceed by successive inexact bound constrained minimization without knowing exactly how inexact the minimization is as far as we know this is the first provably convergent direct search method for general nonlinear programming

a spatiotemporal precipitation generator based on a censored latent gaussian field a daily stochastic spatiotemporal precipitation generator that yields precipitation realizations that are quantitatively consistent is described the methodology relies on a latent gaussian field that drives both the occurrence and intensity of the precipitation process for the precipitation intensity the marginal distributions which are space and time dependent are described by a composite model of a gamma distribution for observations below some threshold with a generalized pareto distribution modeling the excesses above the threshold model parameters are estimated from data and extrapolated to locations and times with no direct observations using linear regression of position covariates one advantage of such a model is that stochastic generator parameters are readily available at any location and time of the year inside the stationarity regions the methodology is illustrated for a network of 12 locations in sweden performance of the model is judged through its ability to accurately reproduce a series of spatial dependence measures and weather indices 2015 american geophysical union all rights reserved

direct identification of elastic constants of anisotropic plates by modal analysis experimental results abstract the determination of the six elastic stiffnesses of thin anisotropic plates from vibration tests is usually performed with numerical procedures based on the finite element or the rayleigh ritz method which both require assumptions concerning the studied mode shapes the present paper describes a method based on the measurement and the processing of natural frequencies as well as mode shapes of the vibrating tested plate as a result the unknown stiffnesses are determined directly without any iterative calculations the experimental aspects of the method are presently described and several results illustrate the relevance of the approach