On Exchange Methods for Nonlinear Semi-Infinite Programs

Liping Zhang and Shouqiang Du ()
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Liping Zhang: Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P. R. China
Shouqiang Du: School of Mathematics and Statistics, Qingdao University, Qingdao 266071, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2022, vol. 39, issue 05, 1-26

Abstract: A new exchange method is presented for semi-infinite optimization problems with polyhedron constraints. The basic idea is to use an active set strategy as exchange rule to construct an approximate problem with finitely many constraints at each iteration. Under mild conditions, we prove that the proposed algorithm terminates in a finite number of iterations and guarantees that the solution of the resulting approximate problem at final iteration converges to the solution of the original problem within arbitrarily given tolerance. Numerical results indicate that the proposed algorithm is efficient and promising.

Keywords: Semi-infinite programming; finite convergence; exchange method; active set (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0217595921500433

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