variational inequality

Primal-dual extrapolation methods for monotone inclusions under local Lipschitz continuity with applications to variational inequality, conic constrained saddle point, and convex conic optimization problems

  • Zhaosong Lu
  • Sanyou Mei
    • Categories Convex and Nonsmooth Optimization Tags , , , , , , , ,

    In this paper we consider a class of structured monotone inclusion (MI) problems that consist of finding a zero in the sum of two monotone operators, in which one is maximal monotone while another is locally Lipschitz continuous. In particular, we first propose a primal-dual extrapolation (PDE) method for solving a structured strongly MI problem … Read more

    VARIATIONAL INEQUALITIES GOVERNED BY STRONGLY PSEUDOMONOTONE VECTOR FIELDS ON HADAMARD MANIFOLDS

  • Nguyen Thai An
  • Luong Nguyen
  • Nguyen Thu
    • Categories Complementarity and Variational Inequalities Tags , , , , ,

    We consider variational inequalities governed by strongly pseudomonotone vec- tor fields on Hadamard manifolds. The existence and uniqueness results of the solution, linear convergence, error estimates and finite convergence for sequences generated by a mod- ified projection method for solving variational inequalities are investigated. Some examples and numerical experiments are also given to illustrate our … Read more

    On Solving Elliptic Obstacle Problems by Compact Abs-Linearization

  • Olga Weiß
  • Monika Weymuth
    • Categories Infinite Dimensional Optimization, Nonsmooth Optimization Tags , , , , , ,

    We consider optimal control problems governed by an elliptic variational inequality of the first kind, namely the obstacle problem. The variational inequality is treated by penalization which leads to optimization problems governed by a nonsmooth semi- linear elliptic PDE. The CALi algorithm is then applied for the efficient solution of these nonsmooth optimization problems. The … Read more

    Openness, Holder metric regularity and Holder continuity properties of semialgebraic set-valued maps

  • Jae Hyoung Lee
  • Tiên-So'n Pham
    • Categories Complementarity and Variational Inequalities, Nonsmooth Optimization Tags , , , ,

    Given a semialgebraic set-valued map $F \colon \mathbb{R}^n \rightrightarrows \mathbb{R}^m$ with closed graph, we show that the map $F$ is Holder metrically subregular and that the following conditions are equivalent: (i) $F$ is an open map from its domain into its range and the range of $F$ is locally closed; (ii) the map $F$ is … Read more

    Equilibrium selection for multi-portfolio optimization

  • Lorenzo Lampariello
  • Christoph Neumann
  • Simone Sagratella
  • Oliver Stein
  • Jacopo Maria Ricci
    • Categories Complementarity and Variational Inequalities, Finance and Economics Tags , , , ,

    This paper studies a Nash game arising in portfolio optimization. We introduce a new general multi-portfolio model and state sufficient conditions for the monotonicity of the underlying Nash game. This property allows us to treat the problem numerically and, for the case of nonunique equilibria, to solve hierarchical problems of equilibrium selection. We also give … Read more

    A search direction inspired primal-dual method for saddle point problems

  • Shengjie Xu
    • Categories Convex and Nonsmooth Optimization, Convex Optimization Tags , , , , ,

    The primal-dual hybrid gradient algorithm (PDHG), which is indeed the Arrow-Hurwicz method, has been widely used in image processing areas. However, the convergence of PDHG was established only under some restrictive conditions in the literature, and it is still missing for the case without extra constraints. In this paper, from a perspective of the variational … Read more

    Active-set Newton methods and partial smoothness

  • Adrian Lewis
  • Calvin Wylie
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization, Nonsmooth Optimization Tags , ,

    Diverse optimization algorithms correctly identify, in finite time, intrinsic constraints that must be active at optimality. Analogous behavior extends beyond optimization to systems involving partly smooth operators, and in particular to variational inequalities over partly smooth sets. As in classical nonlinear programming, such active-set structure underlies the design of accelerated local algorithms of Newton type. … Read more

    An extragradient method for solving variational inequalities without monotonicity

  • Lei Ming
  • He Yiran
    • Categories Complementarity and Variational Inequalities Tags , , , ,

    A new extragradient projection method is devised in this paper, which does not obviously require generalized monotonicity and assumes only that the so-called dual variational inequality has a solution in order to ensure its global convergence. In particular, it applies to quasimonotone variational inequality having a nontrivial solution. ArticleDownload View PDF

    Golden Ratio Algorithms for Variational Inequalities

  • Yura Malitsky
    • Categories Complementarity and Variational Inequalities, Convex Optimization, Nonsmooth Optimization Tags , , , , ,

    The paper presents a fully explicit algorithm for monotone variational inequalities. The method uses variable stepsizes that are computed using two previous iterates as an approximation of the local Lipschitz constant without running a linesearch. Thus, each iteration of the method requires only one evaluation of a monotone operator $F$ and a proximal mapping $g$. … Read more

    Convergent Prediction-Correction-based ADMM for multi-block separable convex programming

  • Zhao Pengjun
  • Chang Xiaokai
  • Liu Sanyang
  • Li Xu
    • Categories Applications - Science and Engineering, Convex and Nonsmooth Optimization Tags , , , , ,

    The direct extension of the classic alternating direction method with multipliers (ADMMe) to the multi-block separable convex optimization problem is not necessarily convergent, though it often performs very well in practice. In order to preserve the numerical advantages of ADMMe and obtain convergence, many modified ADMM were proposed by correcting the output of ADMMe or … Read more