Reverse Convex Programming Approach in the Space of Extreme Criteria for Optimization over Efficient Sets

The problem of minimizing a convex function over the difference of two convex sets is called ‘reverse convex program’. This is a typical problem in global optimization, in which local optima are in general different from global optima. Another typical example in global optimization is the optimizati...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 147; no. 2; pp. 263 - 277
Main Author: Thoai, N. V.
Format: Journal Article
Language:English
Published: Boston Springer US 01.11.2010
Springer
Subjects:
Applications of Mathematics
Applied sciences
Calculus of Variations and Optimal Control; Optimization
Engineering
Exact sciences and technology
Mathematical programming
Mathematics
Mathematics and Statistics
Operational research and scientific management
Operational research. Management science
Operations Research/Decision Theory
Optimization
Theory of Computation
Global optimization
Optimization over the efficient set
Reverse convex programs
Multiple criteria optimization
Space of extreme criteria
Branch and bound methods
Convex set
Multicriteria analysis
Branch and bound method
Local optimum
Minimization
Global optimum
Global Optimization
Difference set
Convex programming
Optimization
Problem solving
Convex function
Mathematical programming
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary:The problem of minimizing a convex function over the difference of two convex sets is called ‘reverse convex program’. This is a typical problem in global optimization, in which local optima are in general different from global optima. Another typical example in global optimization is the optimization problem over the efficient set of a multiple criteria programming problem. In this article, we investigate some special cases of optimization problems over the efficient set, which can be transformed equivalently into reverse convex programs in the space of so-called extreme criteria of multiple criteria programming problems under consideration. A suitable algorithm of branch and bound type is then established for globally solving resulting problems. Preliminary computational results with the proposed algorithm are reported.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-010-9721-2