smooth nonconvex optimization

Trust-Region Newton-CG with Strong Second-Order Complexity Guarantees for Nonconvex Optimization

  • Frank E. Curtis
  • Daniel P. Robinson
  • Clément W. Royer
  • Stephen Wright
    • Categories Nonlinear Optimization, Unconstrained Optimization Tags , , , , ,

    Worst-case complexity guarantees for nonconvex optimization algorithms have been a topic of growing interest. Multiple frameworks that achieve the best known complexity bounds among a broad class of first- and second-order strategies have been proposed. These methods have often been designed primarily with complexity guarantees in mind and, as a result, represent a departure from … Read more

    A Newton-CG Algorithm with Complexity Guarantees for Smooth Unconstrained Optimization

  • Michael O'Neill
  • Clément W. Royer
  • Stephen Wright
    • Categories Unconstrained Optimization Tags , , ,

    We consider minimization of a smooth nonconvex objective function using an iterative algorithm based on Newton’s method and linear conjugate gradient, with explicit detection and use of negative curvature directions for the Hessian of the objective function. The algorithm tracks Newton-conjugate gradient procedures developed in the 1980s closely, but includes enhancements that allow worst-case complexity … Read more