Dynamical System Approach for Time-Varying Constrained Convex Optimization Problems

• 成果类型: Article
• 署名作者: Raveendran, Rejitha; Mahindrakar, Arun D.; Vaidya, Umesh
• 署名单位: Tata Sons; Tata Consultancy Services Limited (TCS); Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Madras; Clemson University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3335004
• 发表日期: 2024
• 页码: 3822-3834
• 关键词: Optimization; tv; trajectory; dynamical systems; linear programming; Prediction algorithms; CONVERGENCE; Lyapunov methods; optimization algorithms; stability of nonlinear systems; time-varying (TV) optimization

摘要

Optimization problems emerging in most of the real-world applications are dynamic, where either the objective function or the constraints change continuously over time. This article proposes projected primal-dual dynamical system approaches to track the primal and dual optimizer trajectories of an inequality constrained time-varying (TV) convex optimization problem with a strongly convex objective function. First, we present a dynamical system that asymptotically tracks the optimizer trajectory of an inequality constrained TV optimization problem. Later, we modify the proposed dynamics to achieve the convergence to the optimizer trajectory within a fixed time. The asymptotic and fixed-time convergence of the proposed dynamical systems to the optimizer trajectory is shown via the Lyapunov-based analysis. Finally, we consider the TV extended Fermat-Torricelli problem of minimizing the sum-of-squared distances to a finite number of nonempty, closed, and convex TV sets, to illustrate the applicability of the projected dynamical systems proposed in this article.