Complementarity and Variational Inequalities

A New Relaxation Scheme for Mathematical Programs with Equilibrium Constraints

  • Michael Ulbrich
  • Sonja Veelken
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization Tags , , ,

    We present a new relaxation scheme for mathematical programs with equilibrium constraints (MPEC), where the complementarity constraints are replaced by a reformulation that is exact for the complementarity conditions corresponding to sufficiently non-degenerate complementarity components and relaxes only the remaining complementarity conditions. A positive parameter determines to what extent the complementarity conditions are relaxed. The … Read more

    Proximal-like contraction methods for monotone variational inequalities in a unified framework

  • Bingsheng He
  • Lizhi Liao
  • Xiang Wang
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization, Convex Optimization Tags , ,

    Approximate proximal point algorithms (abbreviated as APPAs) are classical approaches for convex optimization problems and monotone variational inequalities. To solve the subproblems of these algorithms, the projection method takes the iteration in form of $u^{k+1} = P_{\Omega}[u^k-\alpha_k d^k]$. Interestingly, many of them can be paired such that $%\exists \tilde{u}^k, \tilde{u}^k = P_{\Omega}[u^k – \beta_kF(v^k)] = … Read more

    Impulsive Optimal Control of Hybrid Finite-Dimensional Lagrangian Systems

  • Kerim Yunt
    • Categories Complementarity and Variational Inequalities, Control Applications, Nonsmooth Optimization Tags , ,

    The scope of this dissertation addresses numerical and theoretical issues in the impulsive control of hybrid finite-dimensional Lagrangian systems. In order to treat these aspects, a modeling framework is presented based on the measure-differential inclusion representation of the Lagrangian dynamics. The main advantage of this representation is that it enables the incorporation of set-valued force … Read more

    Necessary Conditions for the Impulsive Optimal Control of Multibody Mechanical Systems

  • Kerim Yunt
    • Categories Complementarity and Variational Inequalities, Nonsmooth Optimization Tags , , , ,

    In this work, necessary conditions for the impulsive optimal control of multibody mechanical systems are stated. The conditions are obtained by the application subdifferential calculus techniques to extended-valued lower semi-continuous generalized Bolza functional that is evaluated on multiple intervals. Contrary to the approach in literature so far, the instant of possibly impulsive transition is considered … Read more

    Projections Onto Super-Half-Spaces for Monotone Variational Inequality Problems in Finite-Dimensional Spaces

  • Yair Censor
  • Aviv Gibali
    • Categories Complementarity and Variational Inequalities Tags , ,

    The variational inequality problem (VIP) is considered here. We present a general algorithmic scheme which employs projections onto hyperplanes that separate balls from the feasible set of the VIP instead of projections onto the feasible set itself. Our algorithmic scheme includes the classical projection method and Fukushima’s subgradient projection method as special cases. CitationTechnical report: … Read more

    An LPCC Approach to Nonconvex Quadratic Programs

  • Jing Hu
  • John E. Mitchell
  • Jong-Shi Pang
    • Categories Complementarity and Variational Inequalities, Quadratic Programming Tags , , ,

    Filling a gap in nonconvex quadratic programming, this paper shows that the global resolution of a feasible quadratic program (QP), which is not known a priori to be bounded or unbounded below, can be accomplished in finite time by solving a linear program with linear complementarity constraints, i.e., an LPCC. Alternatively, this task can be … Read more

    Large-Scale Parallel Multibody Dynamics with Frictional Contact on the Graphical Processing Unit

  • Mihai Anitescu
  • Dan Negrut
  • Alessandro Tasora
    • Categories Complementarity and Variational Inequalities, Mechanical Engineering, Second-Order Cone Programming Tags , ,

    In the context of simulating the frictional contact dynamics of large systems of rigid bodies, this paper reviews a novel method for solving large cone complementarity problems by means of a fixed-point iteration algorithm. The method is an extension of the Gauss-Seidel and Gauss-Jacobimethods with overrelaxation for symmetric convex linear complementarity problems. Convergent under fairly … Read more

    On a class of superlinearly convergent polynomial time interior point methods for sufficient LCP

  • Florian A. Potra
  • Josef Stoer
    • Categories Complementarity and Variational Inequalities Tags , , , ,

    A new class of infeasible interior point methods for solving sufficient linear complementarity problems requiring one matrix factorization and $m$ backsolves at each iteration is proposed and analyzed. The algorithms from this class use a large $(\caln_\infty^-$) neighborhood of an infeasible central path associated with the complementarity problem and an initial positive, but not necessarily … Read more

    A Two Stage Stochastic Equilibrium Model for Electricity Markets with Two Way Contracts

  • Yue Wu
  • Huifu Xu
  • Dali Zhang
    • Categories Applications - OR and Management Sciences, Complementarity and Variational Inequalities

    This paper investigates generators’ strategic behaviors in contract signing in the forward market and power transaction in the electricity spot market. A stochastic equilibrium program with equilibrium constraints (SEPEC) model is proposed to characterize the interaction of generators’ competition in the two markets. The model is an extension of a similar model proposed by Gans, … Read more

    Fischer-Burmeister Complementarity Function on Euclidean Jordan Algebras

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

    Recently, Gowda et al. [10] established the Fischer-Burmeister (FB) complementarity function (C-function) on Euclidean Jordan algebras. In this paper, we prove that FB C-function as well as the derivatives of the squared norm of FB C-function are Lipschitz continuous. CitationResearch Report CORR 2007-17, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, November … Read more