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Global optimization of generalized semi-infinite programs via restriction of the right hand side
- Source :
- Journal of Global Optimization. 61:1-17
- Publication Year :
- 2014
- Publisher :
- Springer Science and Business Media LLC, 2014.
-
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.
Details
- ISSN :
- 15732916 and 09255001
- Volume :
- 61
- Database :
- OpenAIRE
- Journal :
- Journal of Global Optimization
- Accession number :
- edsair.doi...........add24673ccdb2f36df3f794d8e01ad7a