Global optimization of generalized semi-infinite programs via restriction of the right hand side

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 upp...

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Bibliographic Details
Main Authors: Mitsos, Alexander (Author), Tsoukalas, Angelos (Contributor)
Other Authors: Massachusetts Institute of Technology. Department of Mechanical Engineering (Contributor)
Format: Article
Language:English
Published: Springer US, 2016-11-29T16:48:42Z.
Subjects:
Online Access:Get fulltext
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100 1 0 |a Mitsos, Alexander  |e author 
100 1 0 |a Massachusetts Institute of Technology. Department of Mechanical Engineering  |e contributor 
100 1 0 |a Tsoukalas, Angelos  |e contributor 
700 1 0 |a Tsoukalas, Angelos  |e author 
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260 |b Springer US,   |c 2016-11-29T16:48:42Z. 
856 |z Get fulltext  |u http://hdl.handle.net/1721.1/105462 
520 |a 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. 
546 |a en 
655 7 |a Article 
773 |t Journal of Global Optimization