convex and nonconvex optimization – Optimization Online

Tuning-Free Bilevel Optimization: New Algorithms and Convergence Analysis

Published: 2024/10/10

Convex and Nonsmooth Optimization, Convex Optimization, Other Topics adaptive algorithms, automatic tuning of parameters, bilevel optimization, convex and nonconvex optimization, machine learning

Bilevel optimization has recently attracted considerable attention due to its abundant applications in machine learning problems. However, existing methods rely on prior knowledge of problem parameters to determine stepsizes, resulting in significant effort in tuning stepsizes when these parameters are unknown. In this paper, we propose two novel tuning-free algorithms, D-TFBO and S-TFBO. D-TFBO employs … Read more

Convergence of the Chambolle–Pock Algorithm in the Absence of Monotonicity

Published: 2023/12/21

Brecht Evens

Generalized Convexity/Monoticity, Nonsmooth Optimization Chambolle–Pock, convex and nonconvex optimization, inclusion problems, monotone and nonmonotone variational inequalities, primal-dual hybrid gradient, semimonotone operators

The Chambolle-Pock algorithm (CPA), also known as the primal-dual hybrid gradient method (PDHG), has surged in popularity in the last decade due to its success in solving convex/monotone structured problems. This work provides convergence results for problems with varying degrees of (non)monotonicity, quantified through a so-called oblique weak Minty condition on the associated primal-dual operator. … Read more