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 up...

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Veröffentlicht in:Journal of global optimization Jg. 61; H. 1; S. 1 - 17
Hauptverfasser: Mitsos, Alexander, Tsoukalas, Angelos
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Boston Springer US 01.01.2015
Springer
Springer Nature B.V
Schlagworte:
Algorithms
Analysis
Approximation
Computational efficiency
Computer Science
Concavity
Constrictions
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinear programming
Operations Research/Decision Theory
Optimization
Optimization algorithms
Optimization techniques
Real Functions
Solvers
Studies
Slater point
Global optimization
NLP
SIP
Nonconvex
ISSN:0925-5001, 1573-2916
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Zusammenfassung: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.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-014-0146-6