Zijian Shi

Stability analysis of parameterized models relative to nonconvex constraints

  • Zijian Shi
  • Miantao Chao
    • Categories Complementarity and Variational Inequalities, Convex and Nonsmooth Optimization Tags , , , , ,

    For solution mappings of parameterized models (such as optimization problems, variational inequalities, and generalized equations), standard stability inevitably fails as the parameter approaches the boundary of the feasible domain. One remedy is relative stability restricted to a constraint set (e.g., the feasible domain), which is our focus in this paper. We establish generalized differentiation criteria … Read more

    Newtonian Methods with Wolfe Linesearch in Nonsmooth Optimization and Machine Learning

  • Miantao Chao
  • Boris S. Mordukhovich
  • Zijian Shi
  • Jin Zhang
    • Categories Nonlinear Optimization Tags , , , , , ,

    This paper introduces and develops coderivative-based Newton methods with Wolfe linesearch conditions to solve various classes of problems in nonsmooth optimization and machine learning. We first propose a generalized regularized Newton method with Wolfe linesearch (GRNM-W) for unconstrained $C^{1,1}$ minimization problems (which are second-order nonsmooth) and establish global as well as local superlinear convergence of … Read more