Nonsmooth and Nonconvex Optimization via Approximate Difference-of-Convex Decompositions

Wim Ackooij () and Welington Oliveira ()
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Wim Ackooij: Électricité de France
Welington Oliveira: MINES ParisTech, PSL – Research University, CMA – Centre de Mathématiques Appliquées

Journal of Optimization Theory and Applications, 2019, vol. 182, issue 1, No 4, 49-80

Abstract: Abstract We propose an optimization technique for computing stationary points of a broad class of nonsmooth and nonconvex programming problems. The proposed approach (approximately) decomposes the objective function as the difference of two convex functions and performs inexact optimization of the resulting (convex) subproblems. We prove global convergence of our method in the sense that, for an arbitrary starting point, every accumulation point of the sequence of iterates is a Clarke-stationary solution. The given approach is validated by encouraging numerical results on several nonsmooth and nonconvex distributionally robust optimization problems.

Keywords: Nonconvex programming; Nonsmooth optimization; Lower- $$C^2$$ C 2 functions; DC decomposition; 49J52; 49J53; 49K99; 90C26 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10957-019-01500-3

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