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Dynamical System Approach for Time-Varying Constrained Convex Optimization Problems
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DOI：10.1109/TAC.2023.3335004.png)
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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.
Keyword:
Optimization
TV
Trajectory
Dynamical systems
Linear programming
Prediction algorithms
Convergence
Lyapunov methods
optimization algorithms
stability of nonlinear systems
time-varying (TV) optimization
期刊
IF:
7
论文数:
1.3W
被引数:
6.7W
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