Hanyang Li

Subgradient Regularization: A Descent-Oriented Subgradient Method for Nonsmooth Optimization

  • Hanyang Li
  • Ying Cui
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization, Nonsmooth Optimization Tags , , ,

    In nonsmooth optimization, a negative subgradient is not necessarily a descent direction, making the design of convergent descent methods based on zeroth-order and first-order information a challenging task. The well-studied bundle methods and gradient sampling algorithms construct descent directions by aggregating subgradients at nearby points in seemingly different ways, and are often complicated or lack … Read more

    Variational Theory and Algorithms for a Class of Asymptotically Approachable Nonconvex Problems

  • Hanyang Li
  • Ying Cui
    • Categories Nonlinear Optimization, Nonsmooth Optimization Tags , , ,

    We investigate a class of composite nonconvex functions, where the outer function is the sum of univariate extended-real-valued convex functions and the inner function is the limit of difference-of-convex functions. A notable feature of this class is that the inner function may fail to be locally Lipschitz continuous. It covers a range of important yet … Read more

    A Decomposition Algorithm for Two-Stage Stochastic Programs with Nonconvex Recourse

  • Hanyang Li
  • Ying Cui
    • Categories Nonsmooth Optimization, Stochastic Programming Tags , ,

    In this paper, we have studied a decomposition method for solving a class of nonconvex two-stage stochastic programs, where both the objective and constraints of the second-stage problem are nonlinearly parameterized by the first-stage variable. Due to the failure of the Clarke regularity of the resulting nonconvex recourse function, classical decomposition approaches such as Benders … Read more