Hung M. Phan

Projected proximal gradient trust-region algorithm for nonsmooth optimization

  • Lindon Roberts
  • Minh N. Dao
  • Hung M. Phan
    • Categories Nonlinear Optimization, Nonsmooth Optimization Tags , , ,

    We consider trust-region methods for solving optimization problems where the objective is the sum of a smooth, nonconvex function and a nonsmooth, convex regularizer. We extend the global convergence theory of such methods to include worst-case complexity bounds in the case of unbounded model Hessian growth, and introduce a new, simple nonsmooth trust-region subproblem solver … Read more

    Conditional Extragradient Algorithms for Solving Constrained Variational Inequalities

  • Yunier Bello-Cruz
  • R. Diaz Millan
  • Hung M. Phan
    • Categories Complementarity and Variational Inequalities, Convex and Nonsmooth Optimization, Global Optimization Tags , ,

    In this paper, we generalize the classical extragradient algorithm for solving variational inequality problems by utilizing non-null normal vectors of the feasible set. In particular, conceptual algorithms are proposed with two different linesearches. We then establish convergence results for these algorithms under mild assumptions. Our study suggests that non-null normal vectors may significantly improve convergence … Read more