Complementarity and Variational Inequalities

An Accelerated Newton Method for Equations with Semismooth Jacobians and Nonlinear Complementarity Problems: Extended Version

  • Christina Oberlin
  • Stephen Wright
    • Categories Complementarity and Variational Inequalities, Nonlinear Systems and Least-Squares Tags , ,

    We discuss local convergence of Newton’s method to a singular solution $x^*$ of the nonlinear equations $F(x) = 0$, for $F:\R^n \rightarrow \R^n$. It is shown that an existing proof of Griewank, concerning linear convergence to a singular solution $x^*$ from a starlike domain around $x^*$ for $F$ twice Lipschitz continuously differentiable and $x^*$ satisfying … Read more

    Erratum: A superlinearly convergent predictor-corrector method for degenerate LCP in a wide neighborhood of the central path with (\sqrt{n}L)hBciteration complexity

  • Florian A. Potra
    • Categories Complementarity and Variational Inequalities, Linear, Cone and Semidefinite Programming Tags , , ,

    We correct an error in Algorithm 2 from the paper with the same name that was published in Mathematical Programming, Ser. A, 100, 2(2004), 317–337. Citationsubmitted to Mathematical ProgrammingArticleDownload View PDF

    Corrector-predictor methods for sufficient linear complementarity problems in a wide neighborhood of the central path

  • Xing Liu
  • Florian A. Potra
    • Categories Complementarity and Variational Inequalities, Linear, Cone and Semidefinite Programming Tags , , , ,

    Corrector-predictor methods for sufficient linear complementarity problems in a wide neighborhood of the central path CitationTechnical Report UMBC, TR2006-22, January 2005, Revised: March 2006.ArticleDownload View PDF

    Erratum: Predictor-corrector methods for sufficient linear complementarity problems in a wide neighborhood of the central path,

  • Xing Liu
  • Florian A. Potra
    • Categories Complementarity and Variational Inequalities, Linear, Cone and Semidefinite Programming Tags , , ,

    We correct an error in Algorithms 4.1 and 4.8 from the paper with the same title that was published in Optimization Methods and Software, 20, 1 (2005), 145–168. Citationsubmitted to Optimization Methods and SoftwareArticleDownload View PDF

    Corrector-predictor methods for monotone linear complementarity problems in a wide neighborhood of the central path

  • Florian A. Potra
    • Categories Complementarity and Variational Inequalities, Linear, Cone and Semidefinite Programming Tags , , ,

    Two corrector-predictor interior point algorithms are proposed for solving mono\-tone linear complementarity problems. The algorithms produce a sequence of iterates in the $\caln_{\infty}^{-}$ neighborhood of the central path. The first algorithm uses line search schemes requiring the solution of higher order polynomial equations in one variable, while the line search procedures of the second algorithm … Read more

    Using EPECs to model bilevel games in restructured electricity markets

  • Xinmin Hu
  • Daniel Ralph
    • Categories Complementarity and Variational Inequalities, Finance and Economics Tags , , , , ,

    We study a bilevel noncooperative game-theoretic model of restructured electricity markets, with locational marginal prices. Each player in this game faces a bilevel optimization problem that we remodel as a mathematical program with equilibrium constraints, MPEC. The corresponding game is an example of an EPEC, equilibrium problem with equilibrium constraints. We establish sufficient conditions for … Read more

    A Homogeneous Model for Mixed Complementarity Problems over Symmetric Cones

  • Yedong Lin
  • Akiko Yoshise
    • Categories Complementarity and Variational Inequalities, Linear, Cone and Semidefinite Programming, Nonlinear Optimization Tags , , , , , ,

    In this paper, we propose a homogeneous model for solving monotone mixed complementarity problems over symmetric cones, by extending the results in \cite{YOSHISE04} for standard form of the problems. We show that the extended model inherits the following desirable features: (a) A path exists, is bounded and has a trivial starting point without any regularity … Read more

    A Note on Multiobjective Optimization and Complementarity Constraints

  • Sven Leyffer
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization, Multi-Criteria Optimization Tags , , ,

    We propose a new approach to convex nonlinear multiobjective optimization that captures the geometry of the Pareto set by generating a discrete set of Pareto points optimally. We show that the problem of finding an optimal representation of the Pareto surface can be formulated as a mathematical program with complementarity constraints. The complementarity constraints arise … Read more

    A PROXIMAL ALGORITHM WITH VARIABLE METRIC FOR THE P0 COMPLEMENTARITY PROBLEM

  • G. J. P. Da Silva
  • Paulo Roberto Oliveira
    • Categories Complementarity and Variational Inequalities Tags , ,

    We consider a regularization proximal method with variable metric to solve the nonlinear complementarity problem (NCP) for P0-functions. We establish global convergence properties when the solution set is non empty and bounded. Furthermore, we prove, without boundedness of the solution set, that the sequence generated by the algorithm is a minimizing sequence for the implicit … Read more

    Solving Multi-Leader-Follower Games

  • Sven Leyffer
  • Todd S. Munson
    • Categories Applications - OR and Management Sciences, Complementarity and Variational Inequalities, Constrained Nonlinear Optimization Tags , , , , , ,

    Multi-leader-follower games arise when modeling competition between two or more dominant firms and lead in a natural way to equilibrium problems with equilibrium constraints (EPECs). We examine a variety of nonlinear optimization and nonlinear complementarity formulations of EPECs. We distinguish two broad cases: problems where the leaders can cost-differentiate and problems with price-consistent followers. We … Read more