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

N. V. Thoai ()
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N. V. Thoai: University of Trier

Journal of Optimization Theory and Applications, 2010, vol. 147, issue 2, No 4, 263-277

Abstract: Abstract 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.

Keywords: Reverse convex programs; Global optimization; Multiple criteria optimization; Optimization over the efficient set; Space of extreme criteria; Branch and bound methods (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-010-9721-2

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