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Constrained incremental bundle method with partial inexact oracle for nonsmooth convex semi-infinite programming problems

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Abstract

Semi-infinite problem (SIPs) are widely used in many control systems for solving complex control problem, such as polymerase chain reaction control system or other real time control system. In this paper, we present a bundle method for solving the nonsmooth convex SIPs, with the aim of working on the basis of “improvement function”, “inexact oracle” and “incomplete knowledge” of the constraints. The proposed algorithm, whenever a new stabilized center is refreshed, requires an evaluation within some accuracy for the value of constraints. Beyond that, by using the incremental technique, it does not require all information about the constraints, but only one component function value and one subgradient needed to be estimated to update the bundle information and generate the search direction. Thus the computational cost is significantly reduced. Global convergence of this method is established based on some mild assumptions. Numerical experiments show that the algorithm is efficient for solving nonsmooth convex SIPs.

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Acknowledgments

Partially supported by the Natural Science Foundation of China, Grant 11171049 and 31271077.

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Authors and Affiliations

  1. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China

    Li-Ping Pang & Jian Lv

  2. School of Computer Engineering, Qingdao Technological University, Qingdao, 266033, China

    Jin-He Wang

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  1. Li-Ping Pang
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Pang, LP., Lv, J. & Wang, JH. Constrained incremental bundle method with partial inexact oracle for nonsmooth convex semi-infinite programming problems. Comput Optim Appl 64, 433–465 (2016). https://doi.org/10.1007/s10589-015-9810-0

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