Convergence of linesearch-based generalized conditional gradient methods without smoothness assumptions

2025/05/02 by Shotaro Yagishita, Yagishita, Shotaro · 1 citation
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2505.01092

openalex publication_date 2025/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The generalized conditional gradient method is a popular algorithm for solving composite problems whose objective function is the sum of a smooth function and a nonsmooth convex function. Many convergence analyses of the algorithm rely on smoothness assumptions, such as the Lipschitz continuity of the gradient of the smooth part. This paper provides convergence results of linesearch-based generalized conditional gradient methods without smoothness assumptions. In particular, we show that a parameter-free variant, which automatically adapts to the Hölder exponent, guarantees convergence even when the gradient of the smooth part of the objective is not Hölder continuous.

Citations

• Proximal gradient-type method with generalized distance and convergence analysis without global descent lemma
• Fast Frank--Wolfe Algorithms with Adaptive Bregman Step-Size for Weakly Convex Functions
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• Conditional Gradient Methods
• The Iterates of the Frank-Wolfe Algorithm May Not Converge
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• Conditional gradient type methods for composite nonlinear and stochastic optimization

Cited by

• Simple linesearch-free first-order methods for nonconvex optimization

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