complementary slackness

Stochastic nested primal-dual method for nonconvex constrained composition optimization

  • Ling-Zi Jin
  • Xiao Wang
    • Categories Constrained Nonlinear Optimization, Data Science Algorithms, Stochastic Programming Tags , , , , , , ,

    In this paper we study the nonconvex constrained composition optimization, in which the objective contains a composition of two expected-value functions whose accurate information is normally expensive to calculate. We propose a STochastic nEsted Primal-dual (STEP) method for such problems. In each iteration, with an auxiliary variable introduced to track the inner layer function values … Read more

    On Blocking and Anti-Blocking Polyhedra in Infinite Dimensions

  • Luis Rademacher
  • Alejandro Toriello
  • Juan Pablo Vielma
    • Categories Graphs and Matroids, Infinite Dimensional Optimization, Polyhedra Tags , , ,

    We consider the natural generalizations of blocking and anti-blocking polyhedra in infinite dimensions, and study issues related to duality and integrality of extreme points for these sets. Using appropriate finite truncations, we give conditions under which complementary slackness holds for primal-dual pairs of the infi nite linear programming problems associated with infi nite blocking and anti-blocking polyhedra. … Read more