A note on the Douglas–Rachford splitting method for optimization problems involving hypoconvex functions

Ke Guo () and Deren Han ()
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Ke Guo: China West Normal University
Deren Han: Nanjing Normal University

Journal of Global Optimization, 2018, vol. 72, issue 3, No 3, 441 pages

Abstract: Abstract Recently, the convergence of the Douglas–Rachford splitting method (DRSM) was established for minimizing the sum of a nonsmooth strongly convex function and a nonsmooth hypoconvex function under the assumption that the strong convexity constant $$\beta $$ β is larger than the hypoconvexity constant $$\omega $$ ω . Such an assumption, implying the strong convexity of the objective function, precludes many interesting applications. In this paper, we prove the convergence of the DRSM for the case $$\beta =\omega $$ β = ω , under relatively mild assumptions compared with some existing work in the literature.

Keywords: Douglas–Rachford splitting method; Hypoconvex; Convergence; Nonexpansive operators (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10898-018-0660-z

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