Online Interior-Point Methods for Time-Varying Equality-Constrained Optimization

• 成果类型: Article
• 署名作者: Lupien, Jean-Luc; Shames, Iman; Lesage-Landry, Antoine
• 署名单位: Universite de Montreal; Polytechnique Montreal; Mila Quebec Artificial Intelligence Institute; Universite de Montreal; Australian National University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3491819
• 发表日期: 2025
• 页码: 2636-2643
• 关键词: Heuristic algorithms; optimization; vectors; measurement; Approximation algorithms; Convex functions; Linear matrix inequalities; Renewable energy sources; Machine learning algorithms; Load flow; Machine Learning; online convex optimization (OCO); optimization algorithms; Time-varying systems

摘要

An important challenge in the online convex optimization (OCO) setting is to incorporate generalized inequalities and time-varying constraints. The inclusion of constraints in OCO widens the applicability of such algorithms to dynamic and safety-critical settings such as the online optimal power flow (OPF) problem. In this work, we propose the first projection-free OCO algorithm admitting time-varying linear constraints and convex generalized inequalities: the online interior-point method for time-varying equality constraints (OIPM-TEC). We derive simultaneous sublinear dynamic regret and constraint violation bounds for OIPM-TEC under standard assumptions. For applications where a given tolerance around optima is accepted, we employ an alternative OCO performance metric-the epsilon-regret-and a more computationally efficient algorithm, the epsilon-OIPM-TEC that possesses sublinear bounds under this metric. Finally, we showcase the performance of these two algorithms on an online OPF problem and compare them to another OCO algorithm from the literature.