An indefinite proximal subgradient-based algorithm for nonsmooth composite optimization

Rui Liu (), Deren Han () and Yong Xia ()
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Rui Liu: Beihang University
Deren Han: Beihang University
Yong Xia: Beihang University

Journal of Global Optimization, 2023, vol. 87, issue 2, No 10, 533-550

Abstract: Abstract We propose an indefinite proximal subgradient-based algorithm (IPSB) for solving nonsmooth composite optimization problems. IPSB is a generalization of the Nesterov’s dual algorithm, where an indefinite proximal term is added to the subproblems, which can make the subproblem easier and the algorithm efficient when an appropriate proximal operator is judiciously setting down. Under mild assumptions, we establish sublinear convergence of IPSB to a region of the optimal value. We also report some numerical results, demonstrating the efficiency of IPSB in comparing with the classical dual averaging-type algorithms.

Keywords: Nonsmooth optimization; Composite convex optimization; Nesterov’s dual averaging; Subgradient (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10898-022-01173-9

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