saddle point problems

An Inexact Trust-Region Method for Structured Nonsmooth Optimization with Application to Risk-Averse Stochastic Programming

  • Drew P. Kouri
    • Categories Nonsmooth Optimization, Optimization of Systems modeled by PDEs, Stochastic Programming Tags , , , , ,

    We develop a trust-region method for efficiently minimizing the sum of a smooth function, a nonsmooth convex function, and the composition of a finite-valued support function with a smooth function. Optimization problems with this structure arise in numerous applications including risk-averse stochastic programming and subproblems for nonsmooth penalty nonlinear programming methods. Our method permits the … Read more

    A Stochastic Bregman Primal-Dual Splitting Algorithm for Composite Optimization

  • Antonio Silveti-Falls
  • Cesare Molinari
  • Jalal Fadili
    • Categories Convex and Nonsmooth Optimization, Infinite Dimensional Optimization, Stochastic Programming Tags , , , , , , , ,

    We study a stochastic first order primal-dual method for solving convex-concave saddle point problems over real reflexive Banach spaces using Bregman divergences and relative smoothness assumptions, in which we allow for stochastic error in the computation of gradient terms within the algorithm. We show ergodic convergence in expectation of the Lagrangian optimality gap with a … Read more