Global optimization of generalized semi-infinite programs via restriction of the right hand side
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10898_2014_Article_146.pdf
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Author(s)
Mitsos, Alexander
Tsoukalas, Angelos
Date Issued
January 2014
Journal
Journal of Global Optimization
Publisher
Springer US
Citation
Mitsos, Alexander, and Angelos Tsoukalas. “Global Optimization of Generalized Semi-Infinite Programs via Restriction of the Right Hand Side.” Journal of Global Optimization 61.1 (2015): 1–17.
Version
Author's final manuscript
Abstract
The algorithm proposed in Mitsos (Optimization 60(10–11):1291–1308, 2011) for the global optimization of semi-infinite programs is extended to the global optimization of generalized semi-infinite programs. No convexity or concavity assumptions are made. The algorithm employs convergent lower and upper bounds which are based on regular (in general nonconvex) nonlinear programs (NLP) solved by a (black-box) deterministic global NLP solver. The lower bounding procedure is based on a discretization of the lower-level host set; the set is populated with Slater points of the lower-level program that result in constraint violations of prior upper-level points visited by the lower bounding procedure. The purpose of the lower bounding procedure is only to generate a certificate of optimality; in trivial cases it can also generate a global solution point. The upper bounding procedure generates candidate optimal points; it is based on an approximation of the feasible set using a discrete restriction of the lower-level feasible set and a restriction of the right-hand side constraints (both lower and upper level). Under relatively mild assumptions, the algorithm is shown to converge finitely to a truly feasible point which is approximately optimal as established from the lower bound. Test cases from the literature are solved and the algorithm is shown to be computationally efficient.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s10898-014-0146-6
