A Proximal Bundle Method with Exact Penalty Technique and Bundle Modification Strategy for Nonconvex Nonsmooth Constrained Optimization

Xiaoliang Wang (), Liping Pang and Qi Wu ()
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Xiaoliang Wang: School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning 116024, P. R. China
Liping Pang: School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning 116024, P. R. China
Qi Wu: School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning 116024, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2022, vol. 39, issue 02, 1-43

Abstract: The bundle modification strategy for the convex unconstrained problems was proposed by Alexey et al. [[2007] European Journal of Operation Research, 180(1), 38–47.] whose most interesting feature was the reduction of the calls for the quadratic programming solver. In this paper, we extend the bundle modification strategy to a class of nonconvex nonsmooth constraint problems. Concretely, we adopt the convexification technique to the objective function and constraint function, take the penalty strategy to transfer the modified model into an unconstrained optimization and focus on the unconstrained problem with proximal bundle method and the bundle modification strategies. The global convergence of the corresponding algorithm is proved. The primal numerical results show that the proposed algorithms are promising and effective.

Keywords: Nonconvex and nonsmooth; bundle modification strategy; constrained optimization; penalty strategy; proximal bundle method (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0217595921500159

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