Barrier Algorithms for Constrained Non-Convex Optimization

Published: 02 May 2024, Last Modified: 25 Jun 2024ICML 2024 PosterEveryoneRevisionsBibTeXCC BY 4.0
Abstract: In this paper we theoretically show that interior-point methods based on self-concordant barriers possess favorable global complexity beyond their standard application area of convex optimization. To do that we propose first- and second-order methods for non-convex optimization problems with general convex set constraints and linear constraints. Our methods attain a suitably defined class of approximate first- or second-order KKT points with the worst-case iteration complexity similar to unconstrained problems, namely $O(\varepsilon^{-2})$ (first-order) and $O(\varepsilon^{-3/2})$ (second-order), respectively.
Submission Number: 7008
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