A discretization algorithm for nonsmooth convex semi-infinite programming problems based on bundle methods

Li-Ping Pang (), Qi Wu (), Jin-He Wang () and Qiong Wu ()
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Li-Ping Pang: Dalian University of Technology
Qi Wu: Dalian University of Technology
Jin-He Wang: Huzhou University
Qiong Wu: Dalian University of Technology

Computational Optimization and Applications, 2020, vol. 76, issue 1, No 4, 125-153

Abstract: Abstract We propose a discretization algorithm for solving a class of nonsmooth convex semi-infinite programming problems that is based on a bundle method. Instead of employing the inexact calculation to evaluate the lower level problem, we shall carry out a discretization scheme. The discretization method is used to get a number of discretized problems which are solved by the bundle method. In particular, the subproblem used to generate a new point is independent of the number of constraints of the discretized problem. We apply a refinement-step which can be used to guarantee the convergence of the bundle method for the discretized problems as well as reduce the cost of the evaluations for the constraint functions during iteration. In addition we adopt an aggregation technique to manage the bundle information coming from previous steps. Both theoretical convergence analysis and preliminary computational results are reported. The results obtained have shown the good performance of the new algorithm.

Keywords: Nonsmooth convex optimization; Semi-infinite programming; Bundle methods; Discretization methods (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10589-020-00170-6

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