MELMO provably matches the best known convergence rates for weakly convex composite optimization while allowing non-Euclidean update directions.
An Affine Invariant Linear Convergence Analysis for Frank-Wolfe Algorithms
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abstract
We study the linear convergence of variants of the Frank-Wolfe algorithms for some classes of strongly convex problems, using only affine-invariant quantities. As in Guelat & Marcotte (1986), we show the linear convergence of the standard Frank-Wolfe algorithm when the solution is in the interior of the domain, but with affine invariant constants. We also show the linear convergence of the away-steps variant of the Frank-Wolfe algorithm, but with constants which only depend on the geometry of the domain, and not any property of the location of the optimal solution. Running these algorithms does not require knowing any problem specific parameters.
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2026 1verdicts
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Variable Smoothing for Weakly Convex Problems with Non-Euclidean Directions
MELMO provably matches the best known convergence rates for weakly convex composite optimization while allowing non-Euclidean update directions.