using sampling and simplex derivatives in pattern search methods in this paper we introduce ways of making a pattern search more efficient by reusing previous evaluations of the objective function based on the computation of simplex derivatives e g simplex gradients at each iteration one can attempt to compute an accurate simplex gradient by identifying a sampling set of previously evaluated points with good geometrical properties this can be done using only past successful iterates or by considering all past function evaluations the simplex gradient can then be used to reorder the evaluations of the objective function associated with the directions used in the poll step or to update the mesh size parameter according to a sufficient decrease criterion neither of which requires new function evaluations we present these procedures in detail and apply them to a set of problems from the cuter collection numerical results show that these procedures can enhance significantly the practical performance of pattern search methods

model selection in the presence of nonstationarity abstract this paper studies model selection methods in the presence of nonstationarity we focus on the bayesian model selection rule and compare it with other criteria that are frequently used in econometric practice first we derive each of these criteria in the presence of nonstationarity in particular we study the bayesian model selection rule in detail and derive three alternative forms of it in the presence of nonstationarity one important feature of the bayesian model selection criterion bmsc is that bmsc gives different weights to the stationary and nonstationary components of a model while the other criteria do not this feature of bmsc is a desirable property for a model selection rule in the presence of possible nonstationarity second we compare these criteria with regard to parsimony and power we have found that bmsc shows the highest parsimony aic is the second and c p and r 2 having the same level of parsimony are the third with regard to power the order is not clearly established however for the size adjusted power bmsc becomes dominant as the sample size increases without size adjustment the order in the power is exactly the opposite to that in parsimony also we find that bmsc is a consistent selection rule while the other criteria are not third we consider four different cases of practical interest for which bmsc with some of the other criteria is applicable we discuss how our bmsc can be used in these cases of practical interest results of an extensive monte carlo simulation for models in these four cases show that overall the bmsc outperforms other criteria

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

orthomads a deterministic mads instance with orthogonal directions the purpose of this paper is to introduce a new way of choosing directions for the mesh adaptive direct search mads class of algorithms the advantages of this new orthomads instantiation of mads are that the polling directions are chosen deterministically ensuring that the results of a given run are repeatable and that they are orthogonal to each other which yields convex cones of missed directions at each iteration that are minimal in a reasonable measure convergence results for orthomads follow directly from those already published for mads and they hold deterministically rather than with probability one as is the case for ltmads the first mads instance the initial numerical results are quite good for both smooth and nonsmooth and constrained and unconstrained problems considered here

review of options for structural design sensitivity analysis part 1 linear systems the paper reviews options for structural design sensitivity analysis including global finite differences continuum derivatives discrete derivatives and computational or automated differentiation the objective is to put these different approaches to design sensitivity analysis in the context of accuracy and consistency computational cost and implementation options and effort linear static analysis and transient dynamic analysis are reviewed in a separate appendix special attention is paid to the semi analytical method a future paper will address design sensitivity analysis in nonlinear structural problems

constrained integration of rigid body dynamics in the present paper rigid body dynamics is formulated as mechanical system with holonomic constraints this approach offers the appealing possibility to deal with finite rotations without employing any specific rotational parameterization the numerical discretization of the underlying system of differential algebraic equations is treated in detail the proposed algorithm obeys major conservation laws of the underlying continuous system such as conservation of energy and angular momentum in addition to that the constraints on the configuration and momentum level are fulfilled exactly two numerical examples are dealt with to assess the performance of the constrained algorithm

an alternative quasi likelihood approach bayesian analysis and data based inference for model specification abstract this paper studies an alternative quasi likelihood approach under possible model misspecification we derive a filtered likelihood from a given quasi likelihood ql called a limited information quasi likelihood li ql that contains relevant but limited information on the data generation process our li ql approach in one hand extends robustness of the ql approach to inference problems for which the existing approach does not apply our study in this paper on the other hand builds a bridge between the classical and bayesian approaches for statistical inference under possible model misspecification we can establish a large sample correspondence between the classical ql approach and our li ql based bayesian approach an interesting finding is that the asymptotic distribution of an li ql based posterior and that of the corresponding quasi maximum likelihood estimator share the same sandwich type second moment based on the li ql we can develop inference methods that are useful for practical applications under possible model misspecification in particular we can develop the bayesian counterparts of classical ql methods that carry all the nice features of the latter studied in white 1982 in addition we can develop a bayesian method for analyzing model specification based on an li ql

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

new results on a continuously differentiable exact penalty function the main motivation of this paper is to weaken the conditions that imply the correspondence between the solution of a constrained problem and the unconstrained minimization of a continuously differentiable function in particular a new continuously differentiable exact penalty function is proposed for the solution of nonlinear programming problems under mild assumptions a complete equivalence can be established between the solution of the original constrained problem and the unconstrained minimization of this penalty function on a perturbation of the feasible set this new penalty function and its exactness properties allow us to define globally and superlinearly convergent algorithms to solve nonlinear programming problems as an example a newton type algorithm is described which converges locally in one iteration in case of quadratic programming problems

on asymptotic normality of limiting density functions with bayesian implications walker 1969 presented a straightforward approach to asymptotic normality of posterior distributions based on independent and identically distributed i i d observations dawid 1970 extended this work by providing a weaker set of conditions to cover some distributions whose ranges depend on the parameters of interest more recently heyde and johnstone 1979 simplified walker s conditions for stochastic processes in this paper we introduce three basic normality conditions for limiting density functions in the bayesian context our approach is data determined and is nonprobabilistic in nature nevertheless the results thus obtained can be easily converted to probabilistic ones when compared with those given by other investigators it is shown that our conditions as a whole have a greater generality and flexibility than those previously assumed either by dawid or heyde and johnstone in particular for the i i d case the commonly assumed wald type uniform boundedness condition for tail behaviours is shown to be unnecessary for asymptotic normality section 3 3 the advantage of our approach is further exemplified by a simple proof of the asymptotic normality of distributions conjugate to the exponential family

on the global convergence of derivative free methods for unconstrained optimization in this paper starting from the study of the common elements that some globally convergent direct search methods share a general convergence theory is established for unconstrained minimization methods employing only function values the introduced convergence conditions are useful for developing and analyzing new derivative free algorithms with guaranteed global convergence as examples we describe three new algorithms which combine pattern and line search approaches

integrating finite rotations abstract we study the integration of problems of evolution in the rotation group instead of attacking the problem in the nonlinear differential manifold so 3 pure rotational dynamics as is usually done we derive equations for the complete problem of motion translational and rotational dynamics on an extended manifold we develop a generalization of runge kutta methods that by design ensures that the solution will remain on the manifold for any choice of the tableau this is obtained through configuration updates performed via the exponential map we show how certain terms can be approximated while retaining the order of accuracy of the scheme and how the method conserves the total momentum of the system within this framework we develop two nonlinearly unconditionally stable time integration schemes that are associated with discrete laws of conservation dissipation of the total energy the dissipating algorithm generalizes to the nonlinear case the high frequency damping characteristics provided by some well known conventional methods we present numerical results to support our analysis and we develop a complete application of this methodology to the nonlinear dynamics of three dimensional rods undergoing large displacements and finite rotations under the assumption of small strains

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

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

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

a new sequential optimality condition for constrained nonsmooth optimization we introduce a sequential optimality condition for locally lipschitz constrained nonsmooth optimization verifiable just using derivative information and which holds even in the absence of any con

energy conserving decaying implicit time stepping scheme for nonlinear dynamics of three dimensional beams undergoing finite rotations in this work we present an extension of time integration energy conserving scheme which introduces desirable properties of controllable energy decay as well as numerical dissipation of high frequency contribution to total response finite element implementation details are given for the chosen model problem of geometrically exact beam undergoing finite rotations several numerical simulations illustrate a very satisfying performance of the proposed time stepping scheme

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

erratum mesh adaptive direct search algorithms for constrained optimization in siam j optim 17 2006 pp 188 217 audet and dennis proposed the class of mesh adaptive direct search mads algorithms for minimization of a nonsmooth function under general nonsmooth constraints the notation used in the paper evolved since the preliminary versions and unfortunately even though the statement of proposition 4 2 is correct it is not compatible with the final notation the purpose of this note is to show that the proposition is valid

a derivative free approach to constrained multiobjective nonsmooth optimization in this work we consider multiobjective optimization problems with both bound constraints on the variables and general nonlinear constraints where objective and constraint function values can only be obtained by querying a black box we define a linesearch based solution method and we show that it converges to a set of pareto stationary points to this aim we carry out a theoretical analysis of the problem by only assuming lipschitz continuity of the functions more specifically we give new optimality conditions that take explicitly into account the bound constraints and prove that the original problem is equivalent to a bound constrained problem obtained by penalizing the nonlinear constraints with an exact merit function finally we present the results of some numerical experiments on bound constrained and nonlinearly constrained problems showing that our approach is promising when compared to a state of the art method from the literature

global convergence of general derivative free trust region algorithms to first and second order critical points in this paper we prove global convergence for first and second order stationary points of a class of derivative free trust region methods for unconstrained optimization these methods are based on the sequential minimization of quadratic or linear models built from evaluating the objective function at sample sets the derivative free models are required to satisfy taylor type bounds but apart from that the analysis is independent of the sampling techniques a number of new issues are addressed including global convergence when acceptance of iterates is based on simple decrease of the objective function trust region radius maintenance at the criticality step and global convergence for second order critical points

stationarity results for generating set search for linearly constrained optimization we present a new generating set search gss approach for minimizing functions subject to linear constraints gss is a class of direct search optimization methods that includes generalized pattern search one of our main contributions in this paper is a new condition to define the set of conforming search directions that admits several computational advantages for continuously differentiable functions we also derive a bound relating a measure of stationarity which is equivalent to the norm of the gradient of the objective in the unconstrained case and a parameter used by gss algorithms to control the lengths of the steps with the additional assumption that the derivative is lipschitz we obtain a big o bound as a consequence of this relationship we obtain subsequence convergence to a kkt point even though gss algorithms lack explicit gradient information numerical results indicate that the bound provides a reasonable estimate of stationarity

automatic differentiation of numerical integration algorithms automatic differentiation ad is a technique for automatically augmenting computer programs with statements for the computation of derivatives this article discusses the application of automatic differentiation to numerical integration algorithms for ordinary differential equations odes in particular the ramifications of the fact that ad is applied not only to the solution of such an algorithm but to the solution procedure itself this subtle issue can lead to surprising results when ad tools are applied to variable stepsize variable order ode integrators the computation of the final time step plays a special role in determining the computed derivatives we investigate these issues using various integrators and suggest constructive approaches for obtaining the desired derivatives

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

reduction method for finite element nonlinear dynamic analysis of shells doi 10 2514 1 j051003theprojectionoftheequationsofmotiononasuitablemodalbasiscandrasticallyreducethenumberofdegreesoffreedom of a nonlinear dynamic nite element analysis a reduction method based on enriching a set of vibrationmodeswithsecond ordermodescalculatedviaaperturbationtechniqueispresented thesesecond ordermodesarereadily calculated via the solution of corresponding linear problems the results indicate that the second ordermodes are displacement elds that are essential for an appropriate representation of the nonlinear behavior of thestructure problems exhibiting strong geometrical nonlinearities under relatively high dynamic loads aresuccessfully handled by forming the reduction basis with vibration modes and their corresponding second ordermodes calculated at two different static equilibrium con gurations

a progressive barrier for derivative free nonlinear programming we propose a new constraint handling approach for general constraints that is applicable to a widely used class of constrained derivative free optimization methods as in many methods that allow infeasible iterates constraint violations are aggregated into a single constraint violation function as in filter methods a threshold or barrier is imposed on the constraint violation function and any trial point whose constraint violation function value exceeds this threshold is discarded from consideration in the new algorithm unlike the filter method the amount of constraint violation subject to the barrier is progressively decreased adaptively as the iteration evolves we test this progressive barrier pb approach versus the extreme barrier eb with the generalized pattern search gps and the lower triangular mesh adaptive direct search ltmads methods for nonlinear derivative free optimization tests are also conducted using the gps filter which uses a version of the fletcher leyffer filter approach we know that gps cannot be shown to yield kkt points with this strategy or the filter but we use the clarke nonsmooth calculus to prove clarke stationarity of the sequences of feasible and infeasible trial points for ltmads pb numerical experiments are conducted on three academic test problems with up to 50 variables and on a chemical engineering problem the new ltmads pb method generally outperforms our ltmads eb in the case where no feasible initial points are known and it does as well when feasible points are known which leads us to recommend ltmads pb thus the ltmads pb is a useful practical extension of our earlier ltmads eb algorithm particularly in the common case for real problems where no feasible point is known the same conclusions hold for gps pb versus gps eb

parameter based asymptotics in certain cases statistical methods based on standard maximum likelihood asymptotics become valid as the true parameter value approaches a boundary of the parameter space examples are given which motivate a general parameter based asymptotic theory and a result is obtained which covers such situations of particular interest are applications to stochastic process models

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

on the differentiation of the rodrigues formula and its significance for the vector like parameterization of reissner simo beam theory in this paper we present a systematic way of differentiating up to the second directional derivative i the rodrigues formula and ii the spin rotation vector variation relationship to achieve this goal several trigonometric functions are grouped into a family of scalar quantities which can be expressed in terms of a single power series these results are then applied to the vector like parameterization of reissner simo beam theory enabling a straightforward derivation and leading to a clearer formulation in particular and in contrast with previous formulations a relatively compact and obviously symmetric form of the tangent operator is obtained the paper also discusses several relevant issues concerning a beam finite element implementation and concludes with the presentation of a few selected illustrative examples copyright 2002 john wiley sons ltd

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

large sample properties of posterior densities bayesian information criterion and the likelihood principle in nonstationary time series models asymptotic normality of the posterior is a well understood result for dynamic as well as nondynamic models based on sets of abstract conditions whose actual applicability is hardly known especially for the case of nonstationarity in this paper we provide a set of conditions by which we can relatively easily prove the asymptotic posterior normality under quite general situations of possible nonstationarity this result reinforces and generalizes the point of sims and uhlig 1991 that inference based on the likelihood principle explained by berger and wolpert 1988 will be unchanged regardless of whether the data are generated by a stationary process or by a unit root process on the other hand our conditions allow us to generalize the bayesian information criterion known as the schwarz criterion to the case of possible nonstationarity in addition we have shown that consistency of the maximum likelihood estimator not the asymptotic normality of the estimator with some minor additional assumptions is sufficient for asymptotic posterior normality

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

design sensitivity analysis in large deformation elasto plastic and elasto viscoplastic problems implicit time integration algorithm derived by simo for his large deformation elasto plastic constitutive model is generalized for the case of isotropy and associative flow rule towards viscoplastic material behaviour and consistently differentiated with respect to its input parameters combining it with the general formulation of design sensitivity analysis dsa for non linear finite element transient equilibrium problem we come at a numerically efficient closed form finite element formulation of dsa for large deformation elasto plastic and elasto viscoplastic problems with various types of design variables material constants shape parameters the paper handles several specific issues like the use of a non algorithmic coefficient matrix or sensitivity discontinuities at points of instantaneous structural stiffness change computational examples demonstrate abilities of the formulation and quality of results copyright 2005 john wiley sons ltd

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

an augmented lagrangian function with improved exactness properties in this paper we introduce a new exact augmented lagrangian function for the solution of general nonlinear programming problems for this lagrangian function a complete equivalence between its unconstrained minimization on an open set and the solution of the original constrained problem can be established under mild assumptions and without requiring the boundedness of the feasible set of the constrained problem moreover we describe an unconstrained algorithmic model which is globally convergent toward kkt pairs of the original constrained problem the algorithmic model can be endowed with a superlinear rate of convergence by a proper choice of the search direction in the unconstrained minimization without requiring strict complementarity

asymptotic posterior normality for stochastic processes revisited the problem of demonstrating the limiting normality of a posterior distribution arising from some stochastic process is revisited it is shown that certain processes of practical interest are not covered by conditions currently available in the literature in this paper we present a fairly general set of conditions for asymptotic posterior normality which cover a wide class of problems the theory is applied to a nonhomogeneous poisson process and birth process case of independent and identically distributed i i d observations we mention le cam 1953 1958 freedman 1963 lindley 1965 bickel and yahav 1969 walker 1969 johnson 1970 dawid 1970 strasser 1976 and hartigan 1983 markov processes and stochastic processes more generally are discussed in borwanker et al 1971 moore 1976 heyde and johnstone 1979 basawa and rao 1980 and chen 1985 the present paper is in the spirit of heyde and johnstone 1979 hereafter referred to as h j where asymptotic posterior normality is obtained for general stochastic processes under certain conditions these conditions however do not cover some cases of practical interest they fail for example for certain nonhomogeneous poisson processes which are of interest in reliability we prove here a general result on asymptotic posterior normality which covers a wide class of problems in particular the type of nonhomogeneous process not covered in the literature in section 2 we state our regularity conditions and the main result we have specialized to the case of a single parameter for reasons of clarity and comparison with existing results under the regularity conditions imposed by h j it appears that asymptotic posterior normality holds under weaker conditions than those needed for asymptotic normality of the maximum likelihood ml estimator however a weakening of h j s conditions in order to cover a broader range of applications necessitates the introduction of other conditions which also guarantee the asymptotic normality of the ml estimator from this point of view then it appears that further conditions are needed for posterior normality since nonlocal as well as

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

direct multisearch for multiobjective optimization in practical applications of optimization it is common to have several conflicting objective functions to optimize frequently these functions are subject to noise or can be of black box type preventing the use of derivative based techniques we propose a novel multiobjective derivative free methodology calling it direct multisearch dms which does not aggregate any of the objective functions our framework is inspired by the search poll paradigm of direct search methods of directional type and uses the concept of pareto dominance to maintain a list of nondominated points from which the new iterates or poll centers are chosen the aim of our method is to generate as many points in the pareto front as possible from the polling procedure itself while keeping the whole framework general enough to accommodate other disseminating strategies in particular when using the here also optional search step dms generalizes to multiobjective optimization moo all direct search methods of directional type

sensitivity analysis for dynamic mechanical systems with finite rotations this paper presents a sensitivity analysis for dynamic systems with large rotations using a semi analytical direct differentiation technique the choice of a suitable time integration strategy for the rotation group appears to be critical for the development of an efficient sensitivity analysis three versions of the generalized time integration scheme are considered a residual form a linear form and a geometric form their consistency is discussed and we show that the residual form which is the most direct extension of the generalized algorithm defined in structural dynamics should not be used for problems with large rotations the sensitivity analysis is performed and close connections are highlighted between the structure of the sensitivity equations and of the linearized dynamic equations hence algorithms developed for the original problem can be directly reused for the sensitivities finally a numerical example is analysed in detail copyright 2007 john wiley sons ltd

energy conserving and decaying algorithms in non linear structural dynamics a generalized formulation of the energy momentum methodwill be developed within the framework of the generalizedmethodwhich allows at the same time guaranteed conservation or decay of total energy and controllable numerical dissipation of unwanted high frequency response furthermore the latter algorithm will be extended by the consistently integrated constraints of energy and momentum conservation originally derived for the constraint energy momentum algorithm the goal of this general approach of implicit energyconserving and decaying time integration schemes is to compare these algorithms on the basis of an equivalent notation by the means of an overall algorithmic design and hence to investigate their numerical properties numerical stability and controllable numerical dissipation of high frequencies will be studied in application to non linear structural dynamics among the methods considered will be the newmark method the classical methods the energy momentum methodwith and without numerical dissipation the constraint energymomentum algorithm and the constraint energy method copyright 1999 john wiley sons ltd

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

sensitivity analysis for non linear constrained elastostatic systems adjoint and direct differentiation methods are used to formulate design sensitivities for non linear constrained elastostatic systems variations of a general response functional are expressed in explicit form with respect to all design field variations including shape the response functional is expressed over the undeformed configuration however the displacement gradient is included so that field quantities that are defined over the deformed configuration such as cauchy stress may be modelled the finite element method is used to evaluate the sensitivities in an example problem

numerical methods and parallel algorithms for computation of periodic responses of plates numerical methods that compute the nonlinear frequency response curves of plates are presented the equation of motion of the plate is derived by assuming first order shear deformation theory and considering geometrical type of nonlinearity it is discretized by the finite element method using bilinear quadrilateral elements the frequency response curve is computed by shooting and continuation methods parallel implementation of the shooting method is presented and its scalability is investigated

benchmarking derivative free optimization algorithms we propose data profiles as a tool for analyzing the performance of derivative free optimization solvers when there are constraints on the computational budget we use performance and data profiles together with a convergence test that measures the decrease in function value to analyze the performance of three solvers on sets of smooth noisy and piecewise smooth problems our results provide estimates for the performance difference between these solvers and show that on these problems the model based solver tested performs better than the two direct search solvers tested

limited information likelihood and bayesian analysis in this paper we study how to embed the optimal generalized method of moments gmm estimate in a likelihood based inference framework and the bayesian framework first we derive a limited information likelihood lil under some moment based limited information available in gmm based on entropy theory of i projection theory second we study a limited information bayesian framework in which the posterior is derived from the lil and a prior as the lil enables us to incorporate gmm or related inference methods in the likelihood based inference framework it allows us a rich set of practical applications in the bayesian framework in which the posterior is obtained from a likelihood and a prior our results are primarily large sample results as inference in the underlying gmm framework is usually justified in asymptotics investigation of large sample properties of the posterior derived from the lil reveals an interesting relation between the bayesian and the classical distribution theories

an excursion into large rotations the present discourse develops an enlarged exploration of the matrix formulation of finite rotations in space initiated in 1 it is shown how a consistent but subtle matrix calculus inevitably leads to a number of elegant expressions for the transformation or rotation matrix t appertaining to a rotation about an arbitrary axis also analysed is the case of multiple rotations about fixed or follower axes particular attention is paid to an explicit derivation of a single compound rotation vector equivalent to two consecutive arbitrary rotations this theme is discussed in some detail for a number of cases semitangential rotations for which commutativity holds first proposed in 2 3 are also considered furthermore an elementary geometrical analysis of large rotations is also given finally we deduce in an appendix using a judicious reformulation of quarternions the compound pseudovector representing the combined effect of n rotations in the author s opinion the present approach appears preferable to a pure vectorial scheme and even more so to an indicial formulation and is computationally more convenient

tangent operators and design sensitivity formulations for transient non linear coupled problems with applications to elastoplasticity tangent operators and design sensitivities are derived for transient non linear coupled problems the solution process and the formation of tangent operators are presented in a systematic manner and sensitivities for a generalized response functional are formulated via both the direct differentiation and adjoint methods the derived formulations are suitable for finite element implementations analyses of systems with materials that exhibit history dependent response may be obtained directly by applying the analyses of transient non linear coupled systems rate independent elastoplasticity is investigated as a case study and a problem with an analytical solution is analysed for demonstration purposes

a derivative free algorithm for linearly constrained finite minimax problems in this paper we propose a new derivative free algorithm for linearly constrained finite minimax problems due to the nonsmoothness of this class of problems standard derivative free algorithms can locate only points which satisfy weak necessary optimality conditions in this work we define a new derivative free algorithm which is globally convergent toward standard stationary points of the finite minimax problem to this end we convert the original problem into a smooth one by using a smoothing technique based on the exponential penalty function of kort and bertsekas this technique depends on a smoothing parameter which controls the approximation to the finite minimax problem the proposed method is based on a sampling of the smooth function along a suitable search direction and on a particular updating rule for the smoothing parameter that depends on the sampling stepsize numerical results on a set of standard minimax test problems are reported

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

on the design of energy preserving and decaying schemes for flexible nonlinear multi body systems abstract energy preserving schemes achieve unconditional stability for nonlinear systems by establishing discrete energy preservation statements several schemes have been presented by various authors within drastically different frameworks finite difference schemes based on a mid point approximation galerkin and time discontinuous galerkin approximations of the equations of motion written in the symmetric hyperbolic form finite elements in time and 2 stage fsal runge kutta methods furthermore different types of parameterization of finite rotations were used in the various formulations this paper presents a unified finite difference framework which readily allows comparing the various schemes and their respective properties numerical examples are presented and show that the predictions of two of these schemes are in very close agreement with each other

lie group methods for rigid body dynamics and time integration on manifolds recently there has been an increasing interest in time integrators for ordinary differential equations which use lie group actions as a primitive in the design of the methods these methods are usually phrased in an abstract sense for arbitrary lie groups and actions we show here how the methods look when applied to the rigid body equations in particular and indicate how the methods work in general an important part of the lie group methods involves the computation of a coordinate map and its derivative various options are available and they vary in cost accuracy and ability to approximately conserve invariants we discuss how the computation of these maps can be optimized for the rigid body case and we provide numerical experiments which give an idea of the performance of lie group methods compared to other known integration schemes

unconditionally stable algorithms for rigid body dynamics that exactly preserve energy and momentum we show that for rigid body dynamics the mid point rule formulated in body co ordinates exactly conserves energy and the norm of the angular momentum for incremental force free motions but fails to conserve the direction of the angular momentum vector further we show that the mid point rule formulated in the spatial representation is in general physically and geometrically meaningless an alternative algorithm is developed which exactly preserves energy and the total spatial angular momentum in incremental force free motions the implicit version of this algorithm is unconditionally stable and second order accurate the explicit version conserves exactly angular momentum in incremental force free motions numerical simulations are presented which illustrate the excellent performance of the proposed procedure even for incremental rotations over 65 degrees the procedure is directly applicable to transient dynamic calculations of geometrically exact rods and shells

trust region methods for the derivative free optimization of nonsmooth black box functions in this paper we study the minimization of a nonsmooth black box type function without assuming any access to derivatives or generalized derivatives and without any knowledge about the analytical