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arXiv · 2402.04281

Global minimisation of nonconvex functions by generalising the mirror descent method

Reinier Díaz Millán·Julien Ugon
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Abstract

In this paper we introduce two conceptual algorithms for minimising abstract convex functions. Both algorithms rely on solving a proximal-type subproblem with an abstract Bregman distance based proximal term. We prove their convergence when the set of abstract linear functions forms a linear space. This latter assumption can be relaxed to only require the set of abstract linear functions to be closed under the sum, which is a classical assumption in abstract convexity. We provide numerical examples on the minimisation of nonconvex functions with the presented algorithms.

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Reinier Díaz Millán, Julien Ugon. 2024-02-05. Global minimisation of nonconvex functions by generalising the mirror descent method. https://arxiv.org/abs/2402.04281

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