Complementarity and Variational Inequalities

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

    Design of Poisoning Attacks on Linear Regression Using Bilevel Optimization

  • Miguel F. Anjos
  • Luce Brotcorne
  • Diego Cattaruzza
  • Zeynep Suvak
    • Categories Complementarity and Variational Inequalities Tags , , ,

    Poisoning attack is one of the attack types commonly studied in the field of adversarial machine learning. The adversary generating poison attacks is assumed to have access to the training process of a machine learning algorithm and aims to prevent the algorithm from functioning properly by injecting manipulative data while the algorithm is being trained. … Read more

    On the Weak and Strong Convergence of a Conceptual Algorithm for Solving Three Operator Monotone Inclusions

  • Yunier Bello-Cruz
  • Oday Hazaimah
    • Categories Complementarity and Variational Inequalities, Convex and Nonsmooth Optimization, Infinite Dimensional Optimization Tags , , , ,

    In this paper, a conceptual algorithm modifying the forward-backward-half-forward (FBHF) splitting method for solving three operator monotone inclusion problems is investigated. The FBHF splitting method adjusts and improves Tseng’s forward-backward-forward (FBF) split- ting method when the inclusion problem has a third-part operator that is cocoercive. The FBHF method recovers the FBF iteration (when this aforementioned … Read more

    Stability Analysis of Discrete-Time Linear Complementarity Systems

  • Jeff Linderoth
  • Arvind U. Raghunathan
    • Categories Complementarity and Variational Inequalities

    A Discrete-Time Linear Complementarity System (DLCS) is a dynamical system in discrete time whose state evolution is governed by linear dynamics in states and algebraic variables that solve a Linear Complementarity Problem (LCP). A DLCS is the hybrid dynamical system that is the discrete-time counterpart of the well-known Linear Complementarity System (LCS). We derive sufficient … Read more

    Convergence Rate of an Inertial Extragradient Method for Strongly Pseudomonotone Equilibrium Problems in Hilbert Spaces

  • Viet Thong Duong
  • Phan Vuong
    • Categories Complementarity and Variational Inequalities

    In this work, we establish the $R$-linear convergence rate of the inertial extragradient method for solving strongly pseudo-monotone equilibrium problems with a new self adaptive step-size. The linear convergence rate of the proposed methods is obtained without the prior knowledge of the Lipschitz-type constants of the bifunction. We also discuss the application of the obtained … Read more

    On Linear Bilevel Optimization Problems with Complementarity-Constrained Lower Levels

  • Steven A. Gabriel
  • Martin Schmidt
  • Marina Leal
    • Categories Applications - OR and Management Sciences, Complementarity and Variational Inequalities Tags , , , , ,

    We consider a novel class of linear bilevel optimization models with a lower level that is a linear program with complementarity constraints (LPCC). We present different single-level reformulations depending on whether the linear complementarity problem (LCP) as part of the lower-level constraint set depends on the upper-level decisions or not as well as on whether … Read more

    Why there is no need to use a big-M in linear bilevel optimization: A computational study of two ready-to-use approaches

  • Thomas Kleinert
  • Martin Schmidt
    • Categories (Mixed) Integer Linear Programming, Complementarity and Variational Inequalities, Cutting Plane Approaches Tags , , , , ,

    Linear bilevel optimization problems have gained increasing attention both in theory as well as in practical applications of Operations Research (OR) during the last years and decades. The latter is mainly due to the ability of this class of problems to model hierarchical decision processes. However, this ability makes bilevel problems also very hard to … Read more

    Affinely Adjustable Robust Linear Complementarity Problems

  • Christian Biefel
  • Frauke Liers
  • Martin Schmidt
  • Jan Hendrik Rolfes
    • Categories (Mixed) Integer Linear Programming, Complementarity and Variational Inequalities, Robust Optimization Tags , , , ,

    Linear complementarity problems are a powerful tool for modeling many practically relevant situations such as market equilibria. They also connect many sub-areas of mathematics like game theory, optimization, and matrix theory. Despite their close relation to optimization, the protection of LCPs against uncertainties – especially in the sense of robust optimization – is still in … Read more

    A geodesic interior-point method for linear optimization over symmetric cones

  • Frank Permenter
    • Categories Complementarity and Variational Inequalities, Convex Optimization, Linear, Cone and Semidefinite Programming Tags , ,

    We develop a new interior-point method (IPM) for symmetric-cone optimization, a common generalization of linear, second-order-cone, and semidefinite programming. In contrast to classical IPMs, we update iterates with a geodesic of the cone instead of the kernel of the linear constraints. This approach yields a primal-dual-symmetric, scale-invariant, and line-search-free algorithm that uses just half the … Read more

    Equilibrium Oil Market Share under the COVID-19 Pandemic

  • Xiaojun Chen
  • Yun Shi
  • Xiaozhou Wang
    • Categories Applications - OR and Management Sciences, Complementarity and Variational Inequalities, Stochastic Programming Tags , , ,

    Equilibrium models for energy markets under uncertain demand and supply have attracted considerable attentions. This paper focuses on modelling crude oil market share under the COVID-19 pandemic using two-stage stochastic equilibrium. We describe the uncertainties in the demand and supply by random variables and provide two types of production decisions (here-and-now and wait-and-see). The here-and-now … Read more