strict saddle

Weakly convex Douglas-Rachford splitting avoids strict saddle points

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

    We prove that the Douglas-Rachford splitting method converges, almost surely, to local minimizers of semialgebraic weakly convex optimization problems, under the assumption of the strict saddle property. The approach consists of two steps: first, we prove a manifold identification result, and local smoothness of the involved iteration operator. Then, we proceed to show that strict … Read more

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

  • Michael 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