nonlinear complementarity problems

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 barrier-based smoothing proximal point algorithm for NCPs over closed convex cones

  • Chek Beng Chua
  • Zhen Li
    • Categories Complementarity and Variational Inequalities, Convex Optimization Tags , , ,

    We present a new barrier-based method of constructing smoothing approximations for the Euclidean projector onto closed convex cones. These smoothing approximations are used in a smoothing proximal point algorithm to solve monotone nonlinear complementarity problems (NCPs) over a convex cones via the normal map equation. The smoothing approximations allow for the solution of the smoothed … Read more

    ON REGULARITY CONDITIONS FOR COMPLEMENTARITY PROBLEMS

  • Alexey F. Izmailov
  • A. S. Kurennoy
    • Categories Complementarity and Variational Inequalities Tags , , , , , , , , , ,

    In the context of mixed complementarity problems, various concepts of solution regularity are known, each of them playing a certain role in related theoretical and algorithmic developments. In this note, we provide the complete picture of relations between the most important regularity conditions for mixed complementarity problems. A special attention is paid to the particular … Read more

    Local path-following property of inexact interior methods in nonlinear programming

  • Paul Armand
  • Jean-Pierre Dussault
  • Joël Benoist
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , , ,

    We study the local behavior of a primal-dual inexact interior point methods for solving nonlinear systems arising from the solution of nonlinear optimization problems or more generally from nonlinear complementarity problems. The algorithm is based on the Newton method applied to a sequence of perturbed systems that follows by perturbation of the complementarity equations of … 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

    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

    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

    A new class of proximal algorithms for the nonlinear complementarity problem

  • Paulo Roberto Oliveira
  • Geci Silva
    • Categories Complementarity and Variational Inequalities Tags , ,

    In this paper, we consider a variable proximal regularization method for solving the nonlinear complementarity problem for P0 functions. CitationApplied Optimization Series, 96, Optimization and Control With Applications, L. Qi, K. Teo and X. Yang (Eds.), pp 549-561, Springer, 2005.

    Global Newton-type methods and semismooth reformulations for NCP

  • Maria Grazia Gasparo
  • Sandra Pieraccini
  • Aldo Pasquali
    • Categories Complementarity and Variational Inequalities Tags , , ,

    It is known that a nonlinear complementarity problem (NCP) can be reformulated as a semismooth system of nonlinear equations by using a so called NCP-function. Global Newton-type methods for solving NCP via semismooth reformulation need to use a merit function, which is usually required to be continuously differentiable. In this paper we present a global … Read more