Generalized Convexity/Monoticity

On Equilibrium Problems Involving Strongly Pseudomonotone Bifunctions

  • Le Dung Muu
  • V. Quy Nguyen
    • Categories Generalized Convexity/Monoticity Tags , ,

    We study equilibrium problems with strongly pseudomonotone bifunctions in real Hilbert spaces. We show the existence of a unique solution. We then propose a generalized strongly convergent projection method for equilibrium problems with strongly pseudomonotone bifunctions. The proposed method uses only one projection without requiring Lipschitz continuity. Application to variational inequalities is discussed. Citation Institute … Read more

    A proximal technique for computing the Karcher mean of symmetric positive definite matrices

  • Ronaldo Malheiros Gregório
  • Paulo Roberto Oliveira
    • Categories Generalized Convexity/Monoticity, Global Optimization Tags , , , ,

    This paper presents a proximal point approach for computing the Riemannian or intrinsic Karcher mean of symmetric positive definite matrices. Our method derives from proximal point algorithm with Schur decomposition developed to compute minimum points of convex functions on symmetric positive definite matrices set when it is seen as a Hadamard manifold. The main idea … Read more

    BILEVEL OPTIMIZATION AS A REGULARIZATION APPROACH TO PSEUDOMONOTONE EQUILIBRIUM PROBLEMS

  • Bui Van Dinh
  • Le Dung Muu
  • Pham Gia Hung
    • Categories Convex and Nonsmooth Optimization, Generalized Convexity/Monoticity, Global Optimization Tags , , , ,

    We investigate some properties of an inexact proximal point method for pseudomonotone equilibrium problems in a real Hilbert space. Un- like monotone case, in pseudomonotone case, the regularized subprob- lems may not be strongly monotone, even not pseudomonotone. How- ever, every proximal trajectory weakly converges to the same limit, We use these properties to extend … Read more

    A Newton-Fixed Point Homotopy Algorithm for Nonlinear Complementarity Problems with Generalized Monotonicity

  • Yun-Chol Jong
    • Categories Complementarity and Variational Inequalities, Generalized Convexity/Monoticity Tags , , ,

    In this paper has been considered probability-one global convergence of NFPH (Newton-Fixed Point Homotopy) algorithm for system of nonlinear equations and has been proposed a probability-one homotopy algorithm to solve a regularized smoothing equation for NCP with generalized monotonicity. Our results provide a theoretical basis to develop a new computational method for nonlinear equation systems … Read more

    A Constructive Proof of the Existence of a Utility in Revealed Preference Theory

  • J-P Crouzeix
  • Andrew C. Eberhard
  • Daniel Ralph
    • Categories Approximation Algorithms, Finance and Economics, Generalized Convexity/Monoticity Tags , ,

    Within the context of the standard model of rationality within economic modelling we show the existence of a utility function that rationalises a demand correspondence, hence completely characterizes the associated preference structure, by taking a dense demand sample. This resolves the problem of revealed preferences under some very mild assumptions on the demand correspondence which … Read more

    Optimality conditions of set-valued optimization problem involving relative algebraic interior in ordered linear spaces

  • Peng Jian-Wen
  • Xinmin Yang
  • Zhou Zhi-Ang
    • Categories Generalized Convexity/Monoticity, Multi-Criteria Optimization Tags

    In this paper, firstly, a generalized subconvexlike set-valued map involving the relative algebraic interior is introduced in ordered linear spaces. Secondly, some properties of a generalized subconvexlike set-valued map are investigated. Finally, the optimality conditions of set-valued optimization problem are established. Citation {\bf AMS 2010 Subject Classifications:} 90C26, 90C29, 90C30 Article Download View Optimality conditions … Read more

    Identifying Active Manifolds in Regularization Problems

  • Warren Hare
    • Categories Generalized Convexity/Monoticity, Nonsmooth Optimization Tags , , , ,

    In this work we consider the problem $\min_x \{ f(x) + P(x) \}$, where $f$ is $\mathcal{C}^2$ and $P$ is nonsmooth, but contains an underlying smooth substructure. Specifically, we assume the function $P$ is prox-regular partly smooth with respect to a active manifold $\M$. Recent work by Tseng and Yun \cite{tseng-yun-2009}, showed that such a … Read more

    Further Study on Strong Lagrangian Duality Property for Invex Programs via Penalty Functions

  • X. X. Huang
  • J. Zhang
    • Categories Generalized Convexity/Monoticity, Nonlinear Optimization Tags , , , ,

    In this paper, we apply the quadratic penalization technique to derive strong Lagrangian duality property for an inequality constrained invex program. Our results extend and improve the corresponding results in the literature. Citation Bazara, M. S. and Shetty, C. M., Nonlinear Programming Theory and Algorithms, John Wiley \& Sons, New York, 1979. Ben-Israel, A. and … Read more

    A Redistributed Proximal Bundle Method for Nonconvex Optimization

  • Warren Hare
  • Claudia Sagastizábal
    • Categories Generalized Convexity/Monoticity, Nonsmooth Optimization Tags , , , , ,

    Proximal bundle methods have been shown to be highly successful optimization methods for unconstrained convex problems with discontinuous first derivatives. This naturally leads to the question of whether proximal variants of bundle methods can be extended to a nonconvex setting. This work proposes an approach based on generating cutting-planes models, not of the objective function … Read more

    Nonsmooth Optimization for Production Theory

  • Yoshihiro Tanaka
    • Categories Generalized Convexity/Monoticity

    Production theory needs generalizations so that it can incorporate broader class of production functions. A generalized Hotelling’s lemma and a generalized Shephard’s lemma in economic theory, which are established in virtue of nonsmooth analysis under the assumption of upper semicontinuity on production functions. Continuity of factor inputs with respect to a change of the factor … Read more