strict saddle

Shadow splitting methods for nonconvex optimisation: epi-approximation, convergence and saddle point avoidance

  • Felipe Atenas
    • Categories Generalized Convexity/Monoticity, Nonsmooth Optimization Tags , , , , , ,

    We propose the shadow Davis-Yin three-operator splitting method to solve nonconvex optimisation problems. Its convergence analysis is based on a merit function resembling the Moreau envelope. We explore variational analysis properties behind the merit function and the iteration operators associated with the shadow method. By capitalising on these results, we establish convergence of a damped … Read more

    A Line-Search Descent Algorithm for Strict Saddle Functions with Complexity Guarantees

  • Michael J. O'Neill
  • Stephen Wright
    • Categories Unconstrained Optimization Tags , ,

    We describe a line-search algorithm which achieves the best-known worst-case complexity results for problems with a certain “strict saddle” property that has been observed to hold in low-rank matrix optimization problems. Our algorithm is adaptive, in the sense that it makes use of backtracking line searches and does not require prior knowledge of the parameters … Read more