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

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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.

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Acknowledgements

This work was supported by the Key Research and Development Projects of Shandong Province (No. 2019GGX104089), the Natural Science Foundation of Shandong Province (No. ZR2019BA014).

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Correspondence to Qi Wu.

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Pang, LP., Wu, Q., Wang, JH. et al. A discretization algorithm for nonsmooth convex semi-infinite programming problems based on bundle methods. Comput Optim Appl 76, 125–153 (2020). https://doi.org/10.1007/s10589-020-00170-6

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