2024/02/05 by R. Díaz Millán, Millán, Reinier Díaz, Julien Ugon +1
Mathematics · Business, Management and Accounting · Engineering · #Advanced Optimization Algorithms Research #Facility Location and Emergency Management #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.2402.04281
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.