A new framework for constrained optimization via feedback control of Lagrange multipliers
CoRR(2024)
摘要
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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