An Adaptive Forward-Backward-Forward Splitting Algorithm for Solving Pseudo-Monotone Inclusions

• 成果类型: Article; Early Access
• 署名作者: Chorobura, Flavia; Necoara, Ion; Pesquet, lean-Christophe
• 署名单位: National University of Science & Technology POLITEHNICA Bucharest; Romanian Academy; Universite Paris Saclay; Inria
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X; 1526-5471
• DOI: 10.1287/moor.2025.0931
• 发表日期: 2026-03-31
• 关键词: pseudo-monotone operators; forward-backward-forward splitting; adaptive step size; convergence analysis; Nonconvex Optimization; convex; PSEUDOCONVEXITY; Operators; QCQP; SUM

摘要

In this paper, we propose an adaptive forward-backward-forward splitting algorithm for finding a zero of a pseudo-monotone operator that is split as a sum of three operators: the first is continuous single-valued, the second is Lipschitzian, and the third is maximally monotone. This setting covers, in particular, constrained minimization scenarios, such as problems having smooth and convex functional constraints (e.g., quadratically constrained quadratic programs) or problems with a pseudo-convex objective function minimized over a simple closed convex set (e.g., quadratic over linear fractional programs). For the general problem, we design a forward-backward-forward splitting type method based on novel adaptive step-size strategies. Under an additional generalized Lipschitz property of the first operator, sublinear convergence rate is derived for the sequence generated by our adaptive algorithm. Moreover, if the sum is uniformly pseudo-monotone, linear/sublinear rates are derived depending on the parameter of uniform pseudomonotonicity. Preliminary numerical experiments demonstrate the good performance of our method when compared with some existing optimization methods and software.