stochastic convex feasibility

Nonexpansive Markov Operators and Random Function Iterations for Stochastic Fixed Point Problems

  • Russell Luke
    • Categories Global Optimization Theory, Stochastic Approaches, Stochastic Programming Tags , ,

    We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant mea- sure the stochastic fixed point problem. This generalizes earlier work studying the stochastic feasibility problem, namely, to find points that are, with probability 1, fixed points of … Read more

    A Different Perspective on the Stochastic Convex Feasibility Problem

  • James Renegar
  • Song Zhou
    • Categories Convex and Nonsmooth Optimization, Stochastic Programming Tags , , , ,

    We analyze a simple randomized subgradient method for approximating solutions to stochastic systems of convex functional constraints, the only input to the algorithm being the size of minibatches. By introducing a new notion of what is meant for a point to approximately solve the constraints, determining bounds on the expected number of iterations reduces to … Read more