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arXiv · 2403.12738

A new framework for constrained optimization via feedback control of Lagrange multipliers

V. Cerone·S. M. Fosson·S. Pirrera·D. Regruto
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Abstract

The continuous-time analysis of existing iterative algorithms for optimization has a long history. This work proposes a novel continuous-time control-theoretic framework for equality-constrained optimization. The key idea is to design a feedback control system where the Lagrange multipliers are the control input, and the output represents the constraints. The system converges to a stationary point of the constrained optimization problem through suitable regulation. Regarding the Lagrange multipliers, we consider two control laws: proportional-integral control and feedback linearization. These choices give rise to a family of different methods. We rigorously develop the related algorithms, theoretically analyze their convergence and present several numerical experiments to support their effectiveness concerning the state-of-the-art approaches.

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V. Cerone, S. M. Fosson, S. Pirrera, D. Regruto. 2024-03-19. A new framework for constrained optimization via feedback control of Lagrange multipliers. https://doi.org/10.1109/tac.2025.3568651

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