optimality conditions for multiobjective programming with generalized i ρ θ convex set functions abstract necessary conditions for pareto optimality in multiobjective programming with subdifferentiable set functions are established in theorem 12 of h c lai and l j lin j math anal appl 132 1988 558 571 in this paper we establish some sufficient conditions under which a feasible solution of such a problem will be pareto optimal provided that a weaker convexity requirement is satisfied for instance i convexity is assumed for both objective and constraint set functions some duality models are also discussed wolfe type and mond weir type duality theorems are proved

controlled differential equations as young integrals a simple approach the theory of rough paths allows one to define controlled differential equations driven by a path which is irregular the most simple case is the one where the driving path has finite p variations with 1 p 2 in which case the integrals are interpreted as young integrals the prototypal example is given by stochastic differential equations driven by fractional brownian motion with hurst index greater than 1 2 using simple computations we give the main results regarding this theory existence uniqueness convergence of the euler scheme flow property which are spread out among several articles

a stabilized mixed finite element method for finite elasticity formulation for linear displacement and pressure interpolation abstract a stabilized mixed finite element method for finite elasticity is presented the method circumvents the fulfillment of the ladyzenskaya babuska brezzi condition by adding mesh dependent terms which are functions of the residuals of the euler lagrange equations to the usual galerkin method the weak form and the linearized weak form are presented in terms of the reference and current configuration numerical experiments using a tetrahedral element with linear shape functions for the displacements and for the pressure show that the method successfully yields a stabilized element

on minimax fractional optimality conditions with invexity abstract under different forms of invexity conditions sufficient kuhn tucker conditions and three dual models are presented for the minimax fractional programming

variational solutions for partial differential equations driven by a fractional noise abstract in this article we develop an existence and uniqueness theory of variational solutions for a class of nonautonomous stochastic partial differential equations of parabolic type defined on a bounded open subset d r d and driven by an infinite dimensional multiplicative fractional noise we introduce two notions of such solutions for them and prove their existence and their indistinguishability by assuming that the noise is derived from an l 2 d valued fractional wiener process w h with hurst parameter h 1 1 1 whose covariance operator satisfies appropriate integrability conditions and where 0 1 denotes the holder exponent of the derivative of the nonlinearity in the stochastic term of the equations we also prove the uniqueness of solutions when the stochastic term is an affine function of the unknown random field our existence and uniqueness proofs rest upon the construction and the convergence of a suitable sequence of faedo galerkin approximations while our proof of indistinguishability is based on certain density arguments as well as on new continuity properties of the stochastic integral we define with respect to w h

a return mapping algorithm for plane stress elastoplasticity an unconditionally stable algorithm for plane stress elastoplasticity is developed based upon the notion of elastic predictor return mapping plastic corrector enforcement of the consistency condition is shown to reduce to the solution of a simple nonlinear equation consistent elastoplastic tangent moduli are obtained by exact linearization of the algorithm use of these moduli is essential in order to preserve the asymptotic rate of quadratic convergence of newton methods the accuracy of the algorithm is assessed by means of iso error maps the excellent performance of the algorithm for large time steps is illustrated in numerical experiments

duality for a minimax programming problem containingn set functions abstract parameter necessary and sufficient optimality conditions for the discrete minimax programming problem with differentiable n set functions are established in zalmai optimization 20 1989 377 395 in this paper we establish nonparameter necessary and sufficient optimality conditions the nonparameter necessary optimality conditions suggest the establishment of two parameter free duality models for the discrete minimax programming problem with differentiable n set functions and the weak strong and strict converse duality theorems have been derived

a return map algorithm for general isotropic elasto visco plastic materials in principal space we describe a methodology for solving the constitutive problem and evaluating the consistent tangent operator for isotropic elasto visco plastic models whose yield function incorporates the third stress invariant the developments presented are based upon original results proved in the paper concerning the derivatives of eigenvalues and eigenprojectors of symmetric second order tensors with respect to the tensor itself and upon an original algebra of fourth order tensors obtained as second derivatives of isotropic scalar functions of a symmetric tensor argument the analysis initially referred to the small strain case is then extended to a formulation for the large deformation regime for both cases we provide a derivation of the consistent tangent tensor which shows the analogy between the two formulations and the close relationship with the tangent tensors of the lagrangian description of large strain elastoplasticity copyright 2004 john wiley sons ltd

controlling rough paths abstract we formulate indefinite integration with respect to an irregular function as an algebraic problem which has a unique solution under some analytic constraints this allows us to define a good notion of integral with respect to irregular paths with holder exponent greater than 1 3 e g samples of brownian motion and study the problem of the existence uniqueness and continuity of solution of differential equations driven by such paths we recover young s theory of integration and the main results of lyons theory of rough paths in holder topology

on minimax fractional optimality conditions with f ρ convexity abstract we establish the sufficient conditions for generalized fractional programming in the framework of f convex functions when the sufficient conditions are utilized one parametric dual problem and two parametric free dual problems may be formulated and duality results are derived

generalized fractional minimax programming with b p r invexity optimality conditions are proved for a class of generalized fractional minimax programming problems involving b p r invexity functions subsequently these optimality conditions are utilized as a basis for constructing various duality models for this type of fractional programming problems and proving appropriate duality theorems

rough differential equations driven by signals in besov spaces rough differential equations are solved for signals in general besov spaces unifying in particular the known results in holder and p variation topology to this end the paracontrolled distribution approach which has been introduced by gubinelli imkeller and perkowski 24 to analyze singular stochastic pdes is extended from holder to besov spaces as an application we solve stochastic differential equations driven by random functions in besov spaces and gaussian processes in a pathwise sense

optimality and duality for complex nondifferentiable fractional programming abstract both parametric and nonparametric necessary and sufficient optimality conditions are established for a class of complex nondifferentiable fractional programming problems containing generalized convex functions subsequently these optimality criteria are utilized as a basis for constructing one parametric and two other parameter free dual models with appropriate duality theorems

optimality and duality for generalized fractional programming involving nonsmooth f ρ convex functions using a parametric approach we establish necessary and sufficient conditions and derive duality theorems for a class of nonsmooth generalized minimax fractional programming problems containing f r convex functions

finite element implementation of non linear elastoplastic constitutive laws using local and global explicit algorithms with automatic error control implicit stress integration algorithms have been demonstrated to provide a robust formulation for finite element analyses in computational mechanics but are difficult and impractical to apply to increasingly complex non linear constitutive laws this paper discusses the performance of fully explicit local and global algorithms with automatic error control used to integrate general non linear constitutive laws into a non linear finite element computer code the local explicit stress integration procedure falls under the category of return mapping algorithm with standard operator split and does not require the determination of initial yield or the use of any form of stress adjustment to prevent drift from the yield surface the global equations are solved using an explicit load stepping with automatic error control algorithm in which the convergence criterion is used to compute automatically the coarse load increment size the proposed numerical procedure is illustrated here through the implementation of a set of elastoplastic constitutive relations including isotropic and kinematic hardening as well as small strain hysteretic non linearity a series of numerical simulations confirm the robustness accuracy and efficiency of the algorithms at the local and global level published in 2001 by john wiley sons ltd

necessary and sufficient conditions for minimax fractional programming we establish the necessary and sufficient optimality conditions for a class of nondifferentiable minimax fractional programming problems solving generalized convex functions subsequently we apply the optimality conditions to formulate one parametric dual problem and we prove weak duality strong duality and strict converse duality theorems

a version of hormander s theorem for the fractional brownian motion it is shown that the law of an sde driven by fractional brownian motion with hurst parameter greater than 1 2 has a smooth density with respect to lebesgue measure provided that the driving vector fields satisfy hormander s condition the main new ingredient of the proof is an extension of norris lemma to this situation

optimality and duality for generalized fractional programming involving nonsmooth pseudoinvex functions using a parametric approach we establish necessary and sufficient conditions and derive duality theorems for a class of nonsmooth generalized minimax fractional programming problems containing pseudoinvex functions

optimality conditions and duality for a minimax fractional programming with generalized convexity we establish the sufficient conditions for generalized fractional programming from a viewpoint of the generalized convexity when the sufficient conditions are utilized the corresponding duality theorems are derived for two types of duals of the generalized fractional programming we extend the corresponding results of several authors

general solution procedures in elasto viscoplasticity constitutive relations and numerical integration algorithms for elasto viscoplastic problems are investigated a fully implicit integration scheme is adopted and the relevant expression of the consistent tangent operator for yield criteria and flow functions of arbitrary type is derived by suitably generalizing the approach exploited for rate independent plasticity this is achieved by replacing the consistency condition of plasticity with a relation between the viscoplastic consistency parameter and the flow function of the constitutive model in use the methodology adopted simplifies alternative procedures for the evaluation of consistent tangent operators which necessitate the inversion of a viscoplastic compliance operator the general expression of the consistent tangent operator is then specialized to the von mises yield criterion endowed with commonly adopted viscoplastic constitutive models numerical examples are finally presented

an implicit integration algorithm for the finite element implementation of a nonlinear anisotropic material model including hysteretic nonlinearity abstract fully implicit integration schemes have been demonstrated to be very robust and efficient for nonlinear elastoplastic and elastic viscoplastic models and enjoy widespread use in finite element formulations the paper introduces a new form of fully implicit local and global algorithms for the integration of nonlinear elastoplastic constitutive laws including anisotropic plasticity and hysteretic small strain elastic nonlinearity the local stress integration algorithm is based on a single step backward differentiation method with iterative solution for the predictor as well as the corrector steps the global system of implicit nonlinear equations is solved with a quasi newton technique using a numerical tangent computed every load step by finite difference and optimized with iterative updating using the broyden fletcher goldfarb shano bfgs procedure the proposed numerical procedure is illustrated here through the implementation of a set of nonlinear constitutive equations describing the response of lightly overconsolidated cohesive materials numerical simulations of single element tests as well as a boundary value problem confirm the robustness accuracy and efficiency of the proposed algorithm at the local and global level

sensitivity of rough differential equations an approach through the omega lemma the ito map assigns the solution of a rough differential equation a generalization of an ordinary differential equation driven by an irregular path when existence and uniqueness hold by studying how a path is transformed through the vector field which is integrated we prove that the ito map is holder or lipschitz continuous with respect to all its parameters this result unifies and weaken the hypotheses of the regularity results already established in the literature

three types dual model for minimax fractional programming abstract we establish necessary and sufficient optimality conditions for minimax fractional programming involving nonsmooth generalized t convex functions three types dual model of 1 are considered and certain duality results have been derived in the framework of generalized t convex functions