Barrier Algorithms for Constrained Non-Convex Optimization

Pavel Dvurechensky; Mathias Staudigl

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arXiv · 2404.18724

Barrier Algorithms for Constrained Non-Convex Optimization

Pavel Dvurechensky·Mathias Staudigl

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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.

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BibTeX RIS

Pavel Dvurechensky, Mathias Staudigl. 2024-04-29. Barrier Algorithms for Constrained Non-Convex Optimization. https://arxiv.org/abs/2404.18724

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