asymptotic convergence

On the Trade-Off Between Distributional Belief and Ambiguity: Conservatism, Finite-Sample Guarantees, and Asymptotic Properties

  • Man Yiu Tsang
  • Karmel S. Shehadeh
    • Categories Robust Optimization, Stochastic Programming Tags , , , ,

    We propose and analyze a new data-driven trade-off (TRO) approach for modeling uncertainty that serves as a middle ground between the optimistic approach, which adopts a distributional belief, and the pessimistic distributionally robust optimization approach, which hedges against distributional ambiguity. We equip the TRO model with a TRO ambiguity set characterized by a size parameter … Read more

    A Unifying Framework for Sparsity Constrained Optimization

  • Matteo Lapucci
  • Tommaso Levato
  • Francesco Rinaldi
  • Marco Sciandrone
    • Categories Constrained Nonlinear Optimization, Global Optimization Theory, Statistics Tags , , , , ,

    In this paper, we consider the optimization problem of minimizing a continuously differentiable function subject to both convex constraints and sparsity constraints. By exploiting a mixed-integer reformulation from the literature, we define a necessary optimality condition based on a tailored neighborhood that allows to take into account potential changes of the support set. We then … Read more

    On the asymptotic convergence and acceleration of gradient methods

  • Yu-Hong Dai
  • Yakui Huang
  • Xin-Wei Liu
  • Hongchao Zhang
    • Categories Convex Optimization, Quadratic Programming, Unconstrained Optimization Tags , , , , , ,

    We consider the asymptotic behavior of a family of gradient methods, which include the steepest descent and minimal gradient methods as special instances. It is proved that each method in the family will asymptotically zigzag between two directions. Asymptotic convergence results of the objective value, gradient norm, and stepsize are presented as well. To accelerate … Read more

    On the Globally Concavized Filled Function Method

  • Wenxing Zhu
    • Categories Global Optimization, Global Optimization Theory Tags , , ,

    In this paper we present a new definition on the globally concavized filled function for the continuous global minimization problem, which was modified from that by Ge [3]. A new class of globally concavized filled functions are constructed. These functions contain two easily determinable parameters, which are not dependent on the radius of the basin … Read more

    On the globally convexized filled function method for box constrained continuous global optimization

  • Wenxing Zhu
    • Categories Global Optimization Tags , , ,

    In this paper we show that the unconstrained continuous global minimization problem can not be solved by any algorithm. So without loss of generality we consider the box constrained continuous global minimization problem. We present a new globally convexized filled function method for the problem. The definition of globally convexized filled function is adapted from … Read more