Revisiting Projection-Free Optimization for Strongly Convex Constraint Sets

  • Jarrid Rector-Brooks University of Michigan
  • Jun-Kun Wang Georgia Institute of Technology
  • Barzan Mozafari University of Michigan

Abstract

We revisit the Frank-Wolfe (FW) optimization under strongly convex constraint sets. We provide a faster convergence rate for FW without line search, showing that a previously overlooked variant of FW is indeed faster than the standard variant. With line search, we show that FW can converge to the global optimum, even for smooth functions that are not convex, but are quasi-convex and locally-Lipschitz. We also show that, for the general case of (smooth) non-convex functions, FW with line search converges with high probability to a stationary point at a rate of O(1/t), as long as the constraint set is strongly convex—one of the fastest convergence rates in non-convex optimization.

Published
2019-07-17
Section
AAAI Technical Track: Constraint Satisfaction and Optimization