sufficient optimality conditions

Optimality Conditions for Constrained Minimax Optimization

  • Yu-Hong Dai
  • Liwei Zhang
    • Categories Constrained Nonlinear Optimization Tags , , , , ,

    Minimax optimization problems arises from both modern machine learning including generative adversarial networks, adversarial training and multi-agent reinforcement learning, as well as from tradition research areas such as saddle point problems, numerical partial differential equations and optimality conditions of equality constrained optimization. For the unconstrained continuous nonconvex-nonconcave situation, Jin, Netrapalli and Jordan (2019) carefully considered … Read more

    Optimality conditions for various efficient solutions involving coderivatives: from set-valued optimization problems to set-valued equilibrium problems

  • Xuan Duc Ha Truong
    • Categories Complementarity and Variational Inequalities, Multi-Criteria Optimization, Nonsmooth Optimization Tags , , , , , , , , , , , , ,

    We present a new approach to the study of a set-valued equilibrium problem (for short, SEP) through the study of a set-valued optimization problem with a geometric constraint (for short, SOP) based on an equivalence between solutions of these problems. As illustrations, we adapt to SEP enhanced notions of relative Pareto efficient solutions introduced in … Read more

    Necessary and Sufficient Optimality Conditions for Mathematical Programs with Equilibrium Constraints

  • Jane J. Ye
    • Categories Complementarity and Variational Inequalities, Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , ,

    In this paper we consider a mathematical program with equilibrium constraints (MPEC) formulated as a mathematical program with complementarity constraints. Various stationary conditions for MPECs exist in literature due to different reformulations. We give a simple proof to the M-stationary condition and show that it is sufficient or locally sufficient for optimality under some MPEC … Read more