monotone variational inequality

Accelerating block-decomposition first-order methods for solving composite saddle-point and two-player Nash equilibrium problems

  • Yunlong He
  • Renato D.C. Monteiro
    • Categories Convex Optimization, Generalized Convexity/Monoticity, Nonsmooth Optimization Tags , , , , , ,

    This article considers the two-player composite Nash equilibrium (CNE) problem with a separable non-smooth part, which is known to include the composite saddle-point (CSP) problem as a special case. Due to its two-block structure, this problem can be solved by any algorithm belonging to the block-decomposition hybrid proximal-extragradient (BD-HPE) framework. The framework consists of a … Read more

    On the Convergence Properties of Non-Euclidean Extragradient Methods for Variational Inequalities with Generalized Monotone Operators

  • Cong D. Dang
  • Guanghui Lan
    • Categories Complementarity and Variational Inequalities, Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , , , ,

    In this paper, we study a class of generalized monotone variational inequality (GMVI) problems whose operators are not necessarily monotone (e.g., pseudo-monotone). We present non-Euclidean extragradient (N-EG) methods for computing an approximate strong solution of these problems, and demonstrate how their iteration complexities depend on the global Lipschitz or H\”{o}lder continuity properties for their operators … Read more