a test of static equilibrium models and rates of return to quasi fixed factors with an application to the bell system abstract the paper provides a statistical test to assess the adequacy of the static equilibrium framework which can be used prior to specifying a fully dynamic equilibrium model we develop and apply this test to the production structure and factor demand equations based on the theory of restricted cost functions this diagnostic test can also be used in other areas of applied economics such as consumer demand and labor supply studies where the analyst faces the choice between static and dynamic models of economic behavior the framework is used to calculate rates of return to quasi fixed factors to measure the extent of over and underinvestment in such factors to adjust measured productivity growth for departures from static equilibrium and to provide measures of marginal tobin s q for individual assets that could be used to model investment functions for those assets

generalized bundle methods we study a class of generalized bundle methods for which the stabilizing term can be any closed convex function satisfying certain properties this setting covers several algorithms from the literature that have been so far regarded as distinct under a different hypothesis on the stabilizing term and or the function to be minimized we prove finite termination asymptotic convergence and finite convergence to an optimal point with or without limits on the number of serious steps and or requiring the proximal parameter to go to infinity the convergence proofs leave a high degree of freedom in the crucial implementative features of the algorithm i e the management of the bundle of subgradients beta strategy and of the proximal parameter t strategy we extensively exploit a dual view of bundle methods which are shown to be a dual ascent approach to one nonlinear problem in an appropriate dual space where nonlinear subproblems are approximately solved at each step with an inner linearization approach this allows us to precisely characterize the changes in the subproblems during the serious steps since the dual problem is not tied to the local concept of varepsilon subdifferential for some of the proofs a generalization of inf compactness called compactness is required this concept is related to that of asymptotically well behaved functions

the proximal normal formula in banach space approximation by proximal normals to the clarke generalized subdifferential for a distance function generated by a nonempty closed set and the normal cone to the set generated by the proximal normals are important tools in nonsmooth analysis we give simple general versions of such formulae in infinite dimensional banach spaces which satisfy different geometrical conditions our first class of spaces with uniformly g teaux differentiable norm includes the hilbert space case and the formulae is attained through dense subsets our second class of reflexive kadec smooth spaces is the most general for which such formulae can be obtained for all nonempty closed sets in the space our technique also allows us to establish the existence of solutions for a class of optimization problems substantially extending similar work of ekeland and lebourg

compatibility conditions for nonlinear neumann problems abstract results we recall an abstract definition introduced in the general framework of the minimization of non coercive functionals see bbgt definition 2 1 let v a be a topological vector space and let f v co co be any mapping we call a sequential recession functional the mapping f u inf lim inf i f tnun t al u p u n m t i where t and u are sequences notice that when f is convex and a lower semicontinuous f coincides with the usual recession functional see for instance r f tu u f v lim t r r to2 where u is any point in dom f in the following we set ker f u e i f u o remark that in general ker f is not a subspace but is a possibly nonconvex set of half lines starting from the origin the following necessary condition for existence was proved in bbgt proposition 2 2 assume that the problem min f u ue v 2 1

likelihood ration test wald test and kuhn tucker test in linear models with inequality constraints on the regression parameters likelihood ratio test wald test and kuhn tucker test in linear models with inequality constraints on the regression parameters this paper considers the problem of testing statistical hypotheses in linear regression models with inequality constraints on the regression coefficients the kuhn tucker multiplier test statistic is defined and its relationships with the likelihood ratio test and the wald test are examined it is shown in particular that these relationships are the same as in the equality constrained case it is emphasized however that their common asymptotic distribution is a mixture of chi square distributions under the null hypothesis

relaxation methods for problems with strictly convex costs and linear constraints consider the problem of minimizing a strictly convex possibly nondifferentiable and nonseparable cost subject to linear constraints we propose a dual coordinate ascent method for this problem that uses inexact line search and either essentially cyclic or gauss southwell order of coordinate relaxation we show under very weak conditions that this method generates a sequence of primal vectors converging to the optimal primal solution under an additional regularity assumption and assuming that the effective domain of the cost function is polyhedral we show that a related sequence of dual vectors converges in cost to the optimal cost if the constraint set has an interior point in the effective domain of the cost function then this sequence of dual vectors is bounded and each of its limit points is an optimal dual solution when the cost function is strongly convex we show that the order of coordinate relaxation can become progressively more chaotic these results significantly improve upon those obtained previously

a bundle filter method for nonsmooth convex constrained optimization for solving nonsmooth convex constrained optimization problems we propose an algorithm which combines the ideas of the proximal bundle methods with the filter strategy for evaluating candidate points the resulting algorithm inherits some attractive features from both approaches on the one hand it allows effective control of the size of quadratic programming subproblems via the compression and aggregation techniques of proximal bundle methods on the other hand the filter criterion for accepting a candidate point as the new iterate is sometimes easier to satisfy than the usual descent condition in bundle methods some encouraging preliminary computational results are also reported

tests on the validity of static equilibrium models abstract this paper provides a framework to test the validity of static cost minimizing equilibrium assumptions that form the basis for much of the empirical literature on industrial production the point of departure in our model is to allow the observed technology to be at a short run equilibrium where firms minimize variable costs while being constrained by the utilization levels of quasi fixed factors the long run equilibrium is then inferred by minimizing total costs with the optimal adjustment of quasi fixed factor levels we use results from the optimization problem to form tests with respect to quantities and prices in the quantity space version departures between the actual and the optimal long run levels of quasi fixed factors are tested for statistical significance a significant non zero departure implies the rejection of a static equilibrium specification in the price space version the test is cast as a comparison of the market price and the long run shadow value of a quasi fixed factor although the two versions would give identical results in the non stochastic case the rejection powers of these two tests are found to depend on the particular functional form chosen to represent the production process i e cost function in an application based on aggregate u s manufacturing where capital is taken to be quasi fixed we were able to reject the static equilibrium specification these results cast doubt on the validity of a number of previous empirical studies

relaxation methods for problems with strictly convex separable costs and linear constraints we consider the minimization problem with strictly convex possibly nondifferentiable separable cost and linear constraints the dual of this problem is an unconstrained minimization problem with differentiable cost which is well suited for solution by parallel methods based on gauss seidel relaxation we show that these methods yield the optimal primal solution and under additional assumptions an optimal dual solution to do this it is necessary to extend the classical gauss seidel convergence results because the dual cost may not be strictly convex and may have unbounded level sets

generalized goal programming polynomial methods and applications in this paper we address a general goal programming problem with linear objectives convex constraints and an arbitrary componentwise nondecreasing norm to aggregate deviations with respect to targets in particular classical linear goal programming problems as well as several models in location and regression analysis are modeled within this framework

optimization of log x entropy over linear equality constraints in this paper we develop a special purpose iterative algorithm of the row action type for solving the problem of maximizing the log x entropy functional over linear equality constraints the algorithm employs projections onto hyperplanes which we call log x entropy projections a complete proof of convergence is given

how to deal with the unbounded in optimization theory and algorithms the aim of this survey is to show how the unbounded arises in optimization problems and how it leads to fundamental notions which are not only useful for proving theoretical results such as convergence of algorithms and the existence of optimal solutions but also for constructing new methods

optimality conditions in nonconvex optimization via weak subdifferentials abstract in this paper we study optimality conditions for optimization problems described by a special class of directionally differentiable functions the well known necessary and sufficient optimality condition of nonsmooth convex optimization given in the form of variational inequality is generalized to the nonconvex case by using the notion of weak subdifferentials the equivalent formulation of this condition in terms of weak subdifferentials and augmented normal cones is also presented

dynamic bundle methods lagrangian relaxation is a popular technique to solve difficult optimization problems however the applicability of this technique depends on having a relatively low number of hard constraints to dualize when there are many hard constraints it may be preferable to relax them dynamically according to some rule depending on which multipliers are active from the dual point of view this approach yields multipliers with varying dimensions and a dual objective function that changes along iterations we discuss how to apply a bundle methodology to solve this kind of dual problems our framework covers many separation procedures to generate inequalities that can be found in the literature including but not limited to the most violated inequality we analyze the resulting dynamic bundle method giving a positive answer for its primal dual convergence properties and under suitable conditions show finite termination for polyhedral problems

optimality conditions for lower semi continuous functions abstract let f be a lower semi continuous and bounded below function from a banach space x into where x is assumed to admit a lipschitz smooth bump function generalizing results of chaney we study optimality conditions for formula to be a local minimum point of f these conditions are described in terms of generalized chaney s subdifferentials and second order derivatives

coercivity conditions and variational inequalities various coercivity conditions appear in the literature in order to guarantee solutions for the variational inequality problem we show that these conditions are equivalent to each other and that they are not only sufficient but also necessary for the set of solutions to be non empty and bounded

modified barrier functions theory and methods the nonlinear rescaling principle employs monotone and sufficiently smooth functions to transform the constraints and or the objective function into an equivalent problem the classical lagrangian which has important properties on the primal and the dual spaces the application of the nonlinear rescaling principle to constrained optimization problems leads to a class of modified barrier functions mbf s and mbf methods mbfm s being classical lagrangians cl s for an equivalent problem the mbf s combine the best properties of the cl s and classical barrier functions cbf s but at the same time are free of their most essential deficiencies due to the excellent mbf properties new characteristics of the dual pair convex programming problems have been found and the duality theory for nonconvex constrained optimization has been developed the mbfm have up to a superlinear rate of convergence and are to the classical barrier functions cbf s method as the multipliers method for augmented lagrangians is to the classical penalty function method based on the dual theory associated with mbf the method for the simultaneous solution of the dual pair convex programming problems with up to quadratic rates of convergence have been developed the application of the mbf to linear lp and quadratic qp programming leads to a new type of multipliers methods which have a much better rate of convergence under lower computational complexity at each step as compared to the cbf methods the numerical realization of the mbfm leads to the newton modified barrier method nmbm the excellent mbf properties allow us to discover that for any nondegenerate constrained optimization problem there exists a hot start from which the nmbm has a better rate of convergence a better complexity bound and is more stable than the interior point methods which are based on the classical barrier functions

the palais smale condition versus coercivity possesses a convergent subsequence and cp is said to satisfy ps if ir satisfies ps for every c e ir recently among other results in critical point theory shujie i i showed that if a c functional p x k is bounded from below and satisfies the condition ps then p is coercive shujie s proof uses a gradient flow approach through the so called deformation theorem cf 3 io and for that he needs the notion of a pseudo gradient vector field tjassociated with the functional cp whose existence is guaranteed for c functionals by palais 8 in this paper we present some new results which relate the palais smale condition and the notion of coercivity and are based on the well known variational principle due to ekeland 5 61 in particular a new proof of the above mentioned result of shujie is given it should be pointed out that throughout the paper the given functional p could be assumed to be only gateaux differentiable rather than c and in addition to being conceptually simpler this approach could be used in more general situations where the functional is not even differentiable cf 4 the strong form of ekeland s variational principle to be repeatedly used is given in the following theorem

on first and second order conditions linebreak for error bounds we establish first order and second order sufficient conditions ensuring that a proper lower semicontinuous function f on a banach space x has an error bound we also consider similar problems with constraint namely that f is replaced by its restriction to a subset of x these results are employed to identify exactly when a quadratic function on x has an error bound

extended hybrid space sense for epi off resonance and eddy current corrected joint interleaved blip up down reconstruction abstract introduction geometric distortions along the phase encode direction caused by off resonant spins are still a major issue in epi based functional and diffusion imaging if the off resonance map is known it is possible to correct for distortions most correction methods operate as a post processing step on the reconstructed magnitude images theory and methods here we present an algebraic reconstruction method hybrid space sense that incorporates a physics based model of off resonances phase inconsistencies between k space segments and t2 decay during the acquisition the method can be used to perform a joint reconstruction of interleaved acquisitions with normal blip up and inverted blip down phase encode direction which results in reduced g factor penalty results a joint blip up down simultaneous multi slice sms reconstruction for sms factor 4 in combination with twofold in plane acceleration leads to a factor of two decrease in maximum g factor penalty while providing off resonance and eddy current corrected images conclusion we provide an algebraic framework for reconstructing diffusion weighted epi data that in addition to the general applicability of hybrid space sense to 2d epi sms epi and 3d epi with arbitrary k space coverage along z allows for a modeling of arbitrary spatio temporal effects during the acquisition period like off resonances phase inconsistencies and t2 decay the most immediate benefit is a reduction in g factor penalty if an interleaved blip up down acquisition strategy is chosen which facilitates eddy current estimation and ensures no loss in k space encoding in regions with strong off resonance gradients

parametric tests for static and dynamic equilibrium econometric estimates of the characteristics of production are highly sensitive to the choice of dynamic specification in this paper we propose a new approach for testing whether inputs are in static equilibrium the procedure which is based on the use of a generalized cost function tests for divergences between the actual and static equilibrium quantities of all inputs simultaneously and symmetrically we apply it to two widely used data sets one at a high level of aggregation and the other at the firm level and strongly reject static equilibrium in both cases

fast iterative image reconstruction for mri in the presence of field inhomogeneities in magnetic resonance imaging magnetic field inhomogeneities cause distortions in images that are reconstructed by conventional fast fourier transform fft methods several noniterative image reconstruction methods are used currently to compensate for field inhomogeneities but these methods assume that the field map that characterizes the off resonance frequencies is spatially smooth recently iterative methods have been proposed that can circumvent this assumption and provide improved compensation for off resonance effects however straightforward implementations of such iterative methods suffer from inconveniently long computation times this paper describes a tool for accelerating iterative reconstruction of field corrected mr images a novel time segmented approximation to the mr signal equation we use a min max formulation to derive the temporal interpolator speedups of around 60 were achieved by combining this temporal interpolator with a nonuniform fast fourier transform with normalized root mean squared approximation errors of 0 07 the proposed method provides fast accurate field corrected image reconstruction even when the field map is not smooth

the directed and rubinov subdifferentials of quasidifferentiable functions part ii calculus abstract we continue the study of the directed subdifferential for quasidifferentiable functions started in r baier e farkhi v roshchina the directed and rubinov subdifferentials of quasidifferentiable functions part i definition and examples this journal calculus rules for the directed subdifferentials of sum product quotient maximum and minimum of quasidifferentiable functions are derived the relation between the rubinov subdifferential and the subdifferentials of clarke dini michel penot and mordukhovich is discussed important properties implying the claims of ioffe s axioms as well as necessary and sufficient optimality conditions for the directed subdifferential are obtained

convex functions with unbounded level sets and applications to duality theory a class of convex functions with unbounded level sets but good behavior at infinity analyse non lineaire gauthier villars paris 1989 pp 101 122 is investigated characterizations and properties are given the results are then applied to studying sequential approximation schemes for optimization problems and to duality theory when the involved functions have unbounded level sets in particular the convergence properties of stationary sequences for the dual of a convex program are studied and methods for associating with it a primal sequence converging to a solution of the primal problem are demonstrated

imposing curvature restrictions on flexible functional forms abstract a general computational method for estimating the parameters of a flexible functional form subject to convexity quasi convexity concavity or quasi concavity at a point at several points or over a region is set forth and illustrated with an example

short cuts to dynamic factor demand modelling abstract by means of so called virtual or shadow prices short run factor demands short run marginal costs etc can be derived from any long run cost function the traditional approach short run restricted conditional variable cost functions is criticized and it is also shown that technological change scale effects etc can be added to any cost function by means of disembodied factor augmenting efficiency indexes easing the interpretations of the effects but without loss of flexibility it is shown that the trend and scale parameters of the long run translog cost function can be directly translated into trend and scale parameters of such efficiency indexes the techniques are illustrated on the well known berndt wood data set using a diewert long run generalized leontief gl cost function and assuming that capital and labour are quasi fixed

on the functions with pseudoconvex sublevel sets and optimality conditions a new class of generalized convex functions called the functions with pseudoconvex sublevel sets is defined they include quasiconvex ones a complete characterization of these functions is derived further it is shown that a continuous function admits pseudoconvex sublevel sets if and only if it is quasiconvex optimality conditions for a minimum of the nonsmooth nonlinear programming problem with inequality equality and a set constraints are obtained in terms of the lower hadamard directional derivative in particular sufficient conditions for a strict global minimum are given where the functions have pseudoconvex sublevel sets

topological properties of the approximate subdifferential abstract the approximate subdifferential introduced by mordukhovich has attracted much attention in recent works on nonsmooth optimization potential advantages over other concepts of subdifferentiability might be related to its nonconvexity this is motivation to study some topological properties more in detail as the main result it is shown that any weakly compact subset of any hilbert space may be obtained as the kuratowski painleve limit of approximate subdifferentials from a one parametric family of lipschitzian functions sharper characterizations are possible for strongly compact subsets as a consequence in any hilbert space the approximate subdifferential of a suitable lipschitzian function may be homeomorphic both in the strong and weak topology to the cantor set further results relate the approximate subdifferential to specific topological types to the one dimensional case which is extraordinary in some sense and to the value function of a c 1 optimization problem

second order necessary and sufficient conditions in nonsmooth optimization in this paper we generalize and sharpen r w chaney s results on unconstrained and constrained second order necessary and sufficient optimality conditions 5 7 for general lipschitz functions without the semismoothness assumption

comparison principles for viscosity solutions of elliptic equations via fuzzy sum rule abstract a comparison principle for viscosity sub and super solutions of second order elliptic partial differential equations is derived using the fuzzy sum rule of non smooth calculus this method allows us to weaken the assumptions made on the function f when the equation f x u d u d 2 u 0 is under consideration

testing for separable functional structure using temporary equilibrium models abstract the importance that functional structure plays in the analysis of producer behavior is well known and responsible for the empirical tests of input separability hypotheses found in the contemporary literature unfortunately to our knowledge all such tests have been conducted under the maintained assumption of full factor input equilibrium in this paper we propose and implement a method for testing functional structure hypotheses when the behavioral units are permitted to be in disequilibrium the results of this more general test provide less support for the existence of input separability in two digit manufacturing than previously reported by the authors using tests assuming full equilibrium

weak directional closedness and generalized subdifferentials abstract spingarn introduced the notion of a submonotone operator and showed that the clarke subdifferential is submonotone if and only if it is semismooth in the sense of mifflin and regular in the sense of clarke in this article a property of operators referred to as weak directional closedness wdc is introduced the wdc property is used to extend spingarn s result to a broad class of generalized subdifferentials for locally lipschitz functions two members of this class of subdifferentials are the clarke subdifferential which is always wdc and the michel penot subdifferential which may or may not be wdc a subdifferential that is wdc and is contained in the clarke subdifferential is constructed it is shown that this subdifferential coincides with the michel penot subdifferential whenever the michel penot subdifferential is wdc and submonotone

kuhn tucker likelihood ratio and wald tests for nonlinear models with inequality constraints on the parameters abstract this paper considers the problem of testing statistical hypothesis in nonlinear regression models with inequality constraints on the parameters first the kuhn tucker test procedure is defined next it is shown that the distribution of the kuhn tucker the likelihood ratio and the wald test statistics converges to the same mixture of chi square distributions under the null hypothesis to illustrate these results two examples are considered 1 the problem of testing that individual effects are missing in an error component model and 2 the problem of testing equilibrium for a model of markets in disequilibrium

epidifferentiability of the map of infima in hilbert spaces this article deals with derivatives for set valued maps that take values in ordered vector spaces in particular it concerns about the relationship between the epiderivatives of a set valued map and its associated map of infima when the image space is a real separable hilbert space ordered by an orthonormal basis by using a variational technique based on a decoupling of the ordering cone into half spaces we show that both epiderivatives coincide under certain hypothesis of compactness and stability furthermore we obtain some computation formulas for these derivatives in terms of associated scalar set valued maps

how to correct susceptibility distortions in spin echo echo planar images application to diffusion tensor imaging diffusion tensor imaging is often performed by acquiring a series of diffusion weighted spin echo echo planar images with different direction diffusion gradients a problem of echo planar images is the geometrical distortions that obtain near junctions between tissues of differing magnetic susceptibility this results in distorted diffusion tensor maps to resolve this we suggest acquiring two images for each diffusion gradient one with bottom up and one with top down traversal of k space in the phase encode direction this achieves the simultaneous goals of providing information on the underlying displacement field and intensity maps with adequate spatial sampling density even in distorted areas the resulting dt maps exhibit considerably higher geometric fidelity as assessed by comparison to an image volume acquired using a conventional 3d mr technique

a smooth variational principle with applications to hamilton jacobi equations in infinite dimensions abstract we prove that if x is a banach space which admits a smooth lipschitzian bump function then for every lower semicontinuous bounded below function there exists a lipschitzian smooth function g on x such that f g attains its strong minimum on x thus extending a result of borwein and preiss we then show how the above result can be used to obtain existence and uniqueness results of viscosity solutions of hamilton jacobi equations in infinite dimensional banach spaces a without assuming the radon nikodym property

general existence theorems for unilateral problems in continuum mechanics the problem of minimizing a possibly non convex and non coercive functional is studied either necessary or sufficient conditions for the existence of solutions are given involving a generalized recession functional whose properties are discussed thoroughly the abstract results are applied to find existence of equilibrium configurations of a deformable body subject to a system of applied forces and partially constrained to lie inside a possibly unbounded region

minimizing and stationary sequences of constrained optimization problems we study some fundamental asymptotic properties associated with the well posedness of constrained optimization problems emphasis is placed on the relation between minimizing and stationary sequences and their characterizations in terms of a set of asymptotic karush kuhn tucker kkt optimality conditions unlike the subdifferential approach used by auslender cominetti and crouzeix we use a residual function approach that is closely tied to the theory of error bounds this approach handles constraints explicitly and allows the effective treatment of infeasible stationary sequences the asymptotic kkt conditions provide an asymptotic optimality certificate for inequality constrained programs specializations of the results to convex quadratically constrained convex quadratic spline minimization problems and convex programs with holderian minima are discussed an application of the results to the convergence of a family of newton type iterative descent methods involving singular quasi newton matrices for solving a constrained minimization problem is also presented

on the equivalence of some basic principles in variational analysis the primary goal of this paper is to study relationships between certain basic principles of variational analysis and its applications to nonsmooth calculus and optimization considering a broad class of banach spaces admitting smooth renorms with respect to some bornology we establish an equivalence between useful versions of a smooth variational principle for lower semicontinuous functions an extremal principle for nonconvex sets and an enhanced fuzzy sum rule formulated in terms of viscosity normals and subgradients with controlled ranks further refinements of the equivalence result are obtained in the case of a frechet differentiable norm based on the new enhanced sum rule we provide a simplified proof for the refined sequential description of approximate normals and subgradients in smooth spaces

nonlinear rescaling and proximal like methods in convex optimization the nonlinear rescaling principle nrp consists of transforming the objective function and or the constraints of a given constrained optimization problem into another problem which is equivalent to the original one in the sense that their optimal set of solutions coincides a nonlinear transformation parameterized by a positive scalar parameter and based on a smooth sealing function is used to transform the constraints the methods based on nrp consist of sequential unconstrained minimization of the classical lagrangian for the equivalent problem followed by an explicit formula updating the lagrange multipliers we first show that the nrp leads naturally to proximal methods with an entropy like kernel which is defined by the conjugate of the scaling function and establish that the two methods are dually equivalent for convex constrained minimization problems we then study the convergence properties of the nonlinear rescaling algorithm and the corresponding entropy like proximal methods for convex constrained optimization problems special cases of the nonlinear rescaling algorithm are presented in particular a new class of exponential penalty modified barrier functions methods is introduced

a frank wolfe type theorem for nondegenerate polynomial programs in this paper we study the existence of optimal solutions to a constrained polynomial optimization problem more precisely let f 0 f 0 and f 1 ldots f p mathbb r n rightarrow mathbb r f 1 f p r n r be convenient polynomial functions and let s x in mathbb r n f i x le 0 i 1 ldots p ne emptyset s x r n f i x 0 i 1 p under the assumption that the map f 0 f 1 ldots f p mathbb r n rightarrow mathbb r p 1 f 0 f 1 f p r n r p 1 is non degenerate at infinity we show that if f 0 f 0 is bounded from below on s s then f 0 f 0 attains its infimum on s s

asymptotic analysis for penalty and barrier methods in convex and linear programming we consider a wide class of penalty and barrier methods for convex programming which includes a number of specific functions proposed in the literature we provide a systematic way to generate penalty and barrier functions in this class and we analyze the existence of primal and dual optimal paths generated by these penalty methods as well as their convergence to the primal and dual optimal sets for linear programming we prove that these optimal paths converge to single points

error bounds for lower semicontinuous functions in normed spaces without the convexity or analyticity assumption we study error bounds for an inequality system defined by a general lower semicontinuous function and establish sufficient necessary conditions on the existence of error bounds in infinite dimensional normed spaces some characterizations for a convex inequality system to possess an error bound in a reflexive banach space are also given as applications in dealing with the hoffman error bound result in normed spaces we give a computable lipschitz bound constant which is better than previous lipschitz bound constants in some examples we also consider error bounds for quadratic functions on rn

ex post tests for short and long run optimization abstract the purpose of this paper is to develop tests of long run equilibrium models where the long run is defined as the state where the observed levels of output and capital are consistent with optimizing behavior we use the implied relationship between a restricted translog cost function and derived demand equations to provide a series of nested tests which can be interpreted as ex post tests for short and long run optimization behavior a set of parameter restrictions on the translog system are specified for testing whether observable levels of capital and or output of a firm correspond to the long run optimal level our tests of the validity of long run equilibrium specifications are based on data for 28 german industries for the period 1960 1981 for most of the industries the set of restrictions implied by long run equilibrium had to be rejected

noncoercive optimization problems this paper modifies a recent sufficient condition for the existence of optimal solutions proposed by buttazzo and tomarelli to obtain a condition that is necessary and sufficient applications to mathematical programming are given and stability results established

single shot whole brain imaging using spherical stack of spirals trajectories mr encephalography allows the observation of functional signal in the brain at a frequency of 10 hz permitting filtering of physiological noise and the detection of single event activations high temporal resolution is achieved by the use of undersampled non cartesian trajectories parallel imaging and regularized image reconstruction mr encephalography is based on 3d encoding allowing undersampling in two dimensions and providing advantages in terms of signal to noise ratio long readout times which are necessary for single shot whole brain imaging up to 75 ms cause off resonance artifacts to meet this issue a spherical stack of spirals trajectory is proposed in this work by examining the trajectories in local k space it is shown that in areas of strong susceptibility gradients spatial information is fundamentally lost making a meaningful image reconstruction impossible in the affected areas it is shown that the loss of spatial information is reduced when using a stack of spirals trajectory compared to concentric shells

smoothing neural network for constrained non lipschitz optimization with applications in this paper a smoothing neural network snn is proposed for a class of constrained non lipschitz optimization problems where the objective function is the sum of a nonsmooth nonconvex function and a non lipschitz function and the feasible set is a closed convex subset of using the smoothing approximate techniques the proposed neural network is modeled by a differential equation which can be implemented easily under the level bounded condition on the objective function in the feasible set we prove the global existence and uniform boundedness of the solutions of the snn with any initial point in the feasible set the uniqueness of the solution of the snn is provided under the lipschitz property of smoothing functions we show that any accumulation point of the solutions of the snn is a stationary point of the optimization problem numerical results including image restoration blind source separation variable selection and minimizing condition number are presented to illustrate the theoretical results and show the efficiency of the snn comparisons with some existing algorithms show the advantages of the snn

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

an extended extremal principle with applications to multiobjective optimization we develop an extended version of the extremal principle in variational analysis that can be treated as a variational counterpart to the classical separation results in the case of nonconvex sets and which plays an important role in the generalized differentiation theory and its applications to optimization related problems the main difference between the conventional extremal principle and the extended version developed below is that instead of the translation of sets involved in the extremal systems we allow deformations the new version seems to be more flexible in various applications and covers in particular multiobjective optimization problems with general preference relations in this way we obtain new necessary optimality conditions for constrained problems of multiobjective optimization with nonsmooth data and also for multiplayer multiobjective games

on minimizing and critical sequences in nonsmooth optimization let f be a bounded below lower semicontinuous function from a banach space into r cup infty we study the relationships between minimizing and critical sequences of f where the criticality condition is given in terms of some subdifferential partial here the objective function f is not supposed to be convex or smooth our work extends that of auslender and crouzeix and that of chou ng and pang

smoothing methods for nonsmooth nonconvex minimization we consider a class of smoothing methods for minimization problems where the feasible set is convex but the objective function is not convex not differentiable and perhaps not even locally lipschitz at the solutions such optimization problems arise from wide applications including image restoration signal reconstruction variable selection optimal control stochastic equilibrium and spherical approximations in this paper we focus on smoothing methods for solving such optimization problems which use the structure of the minimization problems and composition of smoothing functions for the plus function x many existing optimization algorithms and codes can be used in the inner iteration of the smoothing methods we present properties of the smoothing functions and the gradient consistency of subdifferential associated with a smoothing function moreover we describe how to update the smoothing parameter in the outer iteration of the smoothing methods to guarantee convergence of the smoothing methods to a stationary point of the original minimization problem

set intersection theorems and existence of optimal solutions the question of nonemptiness of the intersection of a nested sequence of closed sets is fundamental in a number of important optimization topics including the existence of optimal solutions the validity of the minimax inequality in zero sum games and the absence of a duality gap in constrained optimization we consider asymptotic directions of a sequence of closed sets and introduce associated notions of retractive horizon and critical directions based on which we provide new conditions that guarantee the nonemptiness of the corresponding intersection we show how these conditions can be used to obtain simple and unified proofs of some known results on existence of optimal solutions and to derive some new results including a new extension of the frank wolfe theorem for nonconvex quadratic programming