A conceptual method for solving generalized semi-infinite programming problems via global optimization by exact discontinuous penalization

We consider a generalized semi-infinite programming problem (GSIP) with one semi-infinite constraint where the index set depends on the variable to be minimized. Keeping in mind the integral global optimization method of Zheng and Chew and its modifications we would like to outline theoretical consi...

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Bibliographic Details
Published in:European journal of operational research 2004-08, Vol.157 (1), p.3-15
Main Authors: Geletu, Abebe, Hoffmann, Armin
Format: Article
Language:English
Subjects:
Generalized semi-infinite programming
Global optimization
Operations research
Optimization
Penalty methods
Piecewise lower (upper) semi-continuous
Robustness and sensitivity analysis
Studies
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Summary:We consider a generalized semi-infinite programming problem (GSIP) with one semi-infinite constraint where the index set depends on the variable to be minimized. Keeping in mind the integral global optimization method of Zheng and Chew and its modifications we would like to outline theoretical considerations for determining coarse approximations of a solution of (GSIP) via global optimization of an exact discontinuous penalty approach. We consider an auxiliary parametric semi-infinite programming problem and the behavior of its marginal functional. In so doing we extend the theory of robust analysis to study robustness of marginal functions and robustness of set valued mappings with given structures.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2003.08.009