Optimality Analysis of a Class of Semi-infinite Programming Problems

Zhi Guo Feng (), Fei Chen (), Lin Chen () and Ka Fai Cedric Yiu ()
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Zhi Guo Feng: Guangdong Ocean University
Fei Chen: Chongqing Normal University
Lin Chen: Chongqing Normal University
Ka Fai Cedric Yiu: Hong Kong Polytechnic University

Journal of Optimization Theory and Applications, 2020, vol. 186, issue 2, No 3, 398-411

Abstract: Abstract In this paper, we consider a class of semi-infinite programming problems with a parameter. As the parameter increases, we prove that the optimal values decrease monotonically. Moreover, the limit of the sequence of optimal values exists as the parameter tends to infinity. In finding the limit, we decompose the original optimization problem into a series of subproblems. By calculating the maximum optimal values to the subproblems and applying a fixed-point theorem, we prove that the obtained maximum value is exactly the limit of the sequence of optimal values under certain conditions. As a result, the limit can be obtained efficiently by solving a series of simplified subproblems. Numerical examples are provided to verify the limit obtained by the proposed method.

Keywords: Semi-infinite programming; Fixed-point theorem; Filter design; Beamformer design; 90C34; 47H10; 26B10 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10957-020-01708-8

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