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Safety-critical control as a design paradigm of anytime solvers of variational inequalities
A. Allibhoy, J. Cortés
Proceedings of the IEEE Conference on Decision and Control, Cancun, Mexico, 2022, pp. 6211-6216

Abstract

This paper shows that safety-critical control methods for the synthesis of safeguarding controllers also have an important role to play in optimization theory. We are chiefly concerned with two problems: (i) minimization of a convex function subject to constraints and (ii) finding saddle points of convex-concave functions. We design algorithms to solve these problems by blending techniques from safety-critical control with tools from monotone operator theory. These algorithms are anytime, meaning that they are guaranteed to return a feasible solution to the optimization problem regardless of when they are terminated, which makes them particularly suitable for real-time applications. In some cases, our approach leads to reinterpretations of well-known algorithms from the lens of control theory, and in other cases we derive entirely novel algorithms. Our results demonstrate the promising potential of safety-critical control for both the analysis and design of optimization algorithms.

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