Complexity Guarantees

Riemannian trust-region methods for strict saddle functions with complexity guarantees

  • Florentin Goyens
  • ClĂ©ment W. Royer
    • Categories Nonlinear Optimization Tags , , ,

    The difficulty of minimizing a nonconvex function is in part explained by the presence of saddle points. This slows down optimization algorithms and impacts worst-case complexity guarantees. However, many nonconvex problems of interest possess a favorable structure for optimization, in the sense that saddle points can be escaped efficiently by appropriate algorithms. This strict saddle … Read more

    Complexity of a Projected Newton-CG Method for Optimization with Bounds

  • Yue Xie
  • Stephen Wright
    • Categories Bound-constrained Optimization Tags , , , ,

    This paper describes a method for solving smooth nonconvex minimization problems subject to bound constraints with good worst-case complexity and practical performance. The method contains elements of two existing methods: the classical gradient projection approach for bound-constrained optimization and a recently proposed Newton-conjugate gradient algorithm for unconstrained nonconvex optimization. Using a new definition of approximate … Read more