Complementarity and Variational Inequalities

Necessary Optimality Conditions for two-stage Stochastic Programs with Equilibrium Constraints

  • Huifu Xu
  • Jane J. Ye
    • Categories Complementarity and Variational Inequalities, Nonsmooth Optimization, Stochastic Programming Tags , , , , ,

    Developing first order optimality conditions for a two-stage stochastic mathematical program with equilibrium constraints (SMPEC) whose second stage problem has multiple equilibria/solutions is a challenging undone work. In this paper we take this challenge by considering a general class of two-stage whose equilibrium constraints are represented by a parametric variational inequality (where the first stage … Read more

    On the Solution of Complementarity Problems Arising in American Options Pricing

  • Liming Feng
  • V. Linetsky
  • Jose Luis Morales
  • Jorge Nocedal
    • Categories Applications - OR and Management Sciences, Complementarity and Variational Inequalities, Finance and Economics Tags , ,

    In the Black-Scholes-Merton model, as well as in more general stochastic models in finance, the price of an American option solves a system of partial differential variational inequalities. When these inequalities are discretized, one obtains a linear complementarity problem that must be solved at each time step. This paper presents an algorithm for the solution … Read more

    Uniform nonsingularity and complementarity problems over symmetric cones

  • Chek Beng Chua
  • Huiling Lin
  • Peng Yi
    • Categories Complementarity and Variational Inequalities Tags , , , ,

    We study the uniform nonsingularity property recently proposed by the authors and present its applications to nonlinear complementarity problems over a symmetric cone. In particular, by addressing theoretical issues such as the existence of Newton directions, the boundedness of iterates and the nonsingularity of B-subdifferentials, we show that the non-interior continuation method proposed by Xin … Read more

    Real-Time Optimization as a Generalized Equation

  • Mihai Anitescu
  • Victor M. Zavala
    • Categories Complementarity and Variational Inequalities, Control Applications, Nonlinear Optimization Tags , , , ,

    We establish results for the problem of tracking a time-dependent manifold arising in online nonlinear programming by casting this as a generalized equation. We demonstrate that if points along a solution manifold are consistently strongly regular, it is possible to track the manifold approximately by solving a linear complementarity problem (LCP) at each time step. … Read more

    Stability for solution of Differential Variational Inequalitiy

  • Jianxun Zhao
    • Categories Complementarity and Variational Inequalities

    In this paper we study the class of differential variational inequality(DVI) in a finite-dimension Euclidean space. We study stability and perturbation of the DVI under the OSL condition. Besides, we establish a Prior Bound Theorem, which is a useful tool to prove stability of DVI. In this paper, we replace the classical Lipshitz continuity by … Read more

    An inexact parallel splitting augmented Lagrangian method for large system of linear equations

  • Donghua Wu
  • Peng Zheng
    • Categories Complementarity and Variational Inequalities, Convex Optimization, Nonlinear Systems and Least-Squares

    Parallel iterative methods are power tool for solving large system of linear equations (LQs). The existing parallel computing research results are all most concentred to sparse system or others particular structure, and all most based on parallel implementing the classical relaxation methods such as Gauss-Seidel, SOR, and AOR methods e±ciently on multiprcessor systems. In this … Read more

    An novel ADM for finding Cournot equilibria of bargaining problem with alternating offers

  • Zheng Peng
    • Categories Complementarity and Variational Inequalities, Game Theory

    Bargaining is a basic game in economic practice. Cournot duopoly game is an important model in bargaining theory. Recently, asymmetry information [20] and incomplete information [19], limited individual rationality [2] and slightly altruistic equilibrium [10] are introduced into bargaining theory. And computational game theory come into being a new research field. In this paper, we … Read more

    Homogeneous Cone Complementarity Problems and $ Properties

  • Lingchen Kong
  • Levent Tunçel
  • Naihua Xiu
    • Categories Complementarity and Variational Inequalities Tags , , , ,

    We consider existence and uniqueness properties of a solution to homogeneous cone complementarity problem (HCCP). Employing the $T$-algebraic characterization of homogeneous cones, we generalize the $P, P_0, R_0$ properties for a nonlinear function associated with the standard nonlinear complementarity problem to the setting of HCCP. We prove that if a continuous function has either the … Read more

    A continuation method for nonlinear complementarity problems over symmetric cone

  • Chek Beng Chua
  • Peng Yi
    • Categories Complementarity and Variational Inequalities Tags , , , ,

    In this paper, we introduce a new P-type condition for nonlinear functions defined over Euclidean Jordan algebras, and study a continuation method for nonlinear complementarity problems over symmetric cones. This new P-type condition represents a new class of nonmonotone nonlinear complementarity problems that can be solved numerically. CitationResearch Report, Division of Mathematical Sciences, School of … Read more

    On the complexity of the hybrid proximal extragradient method for the iterates and the ergodic mean

  • Renato D.C. Monteiro
  • Benar Fux Svaiter
    • Categories Complementarity and Variational Inequalities, Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming Tags , , , ,

    In this paper we analyze the iteration-complexity of the hybrid proximal extragradient (HPE) method for finding a zero of a maximal monotone operator recently proposed by Solodov and Svaiter. One of the key points of our analysis is the use of new termination criteria based on the $\varepsilon$-enlargement of a maximal monotone operator. The advantage … Read more