A proximal bundle method for a class of nonconvex nonsmooth composite optimization problems

Liping Pang, Xiaoliang Wang () and Fanyun Meng
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Liping Pang: Dalian University of Technology, Key Laboratory for Computational Mathematics and Data Intelligence of Liaoning Province
Xiaoliang Wang: Zhejiang Sci-Tech University
Fanyun Meng: Qingdao University of Technology

Journal of Global Optimization, 2023, vol. 86, issue 3, No 3, 589-620

Abstract: Abstract In this paper, a proximal bundle method is proposed for a class of nonconvex nonsmooth composite optimization problems. The composite problem considered here is the sum of two functions: one is convex and the other is nonconvex. Local convexification strategy is adopted for the nonconvex function and the corresponding convexification parameter varies along iterations. Then the sum of the convex function and the extended function is dynamically constructed to approximate the primal problem. To choose a suitable cutting plane model for the approximation function, here we consider the sum of two cutting planes, which are designed respectively for the convex function and the extended function. By choosing appropriate descent condition, our method can keep track of the relationship between primal problem and approximate models. Under mild conditions, the convergence is proved and the accumulation point of iterations is a stationary point of the primal problem. Two polynomial problems and twelve DC (difference of convex) problems are referred in numerical experiments. The preliminary numerical results show that the proposed method is effective for solving these testing problems.

Keywords: Proximal bundle method; Nonconvex and nonsmooth; Redistributed strategy; DC problems; 65K05; 90C26 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10898-023-01279-8

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