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

In: Journal of Optimization Theory and Applications   ;  147 ,  2  ;  263-277  ;  2010

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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.

Table of contents – Volume 147, Issue 2

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The tables of contents are generated automatically and are based on the data records of the individual contributions available in the index of the TIB portal. The display of the Tables of Contents may therefore be incomplete.

205
Optimal Control of Second Order Systems with Infinite Time Horizon: Existence of Solutions
Idczak, D. / Walczak, S. | 2010
223
Pseudotransient Continuation for Solving Systems of Nonsmooth Equations with Inequality Constraints
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243
Minimizing Sequences for a Family of Functional Optimal Estimation Problems
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263
Reverse Convex Programming Approach in the Space of Extreme Criteria for Optimization over Efficient Sets
Thoai, N. V. | 2010
278
Optimal Motion of a Two-Body System in a Resistive Medium
Chernousko, F. L. | 2010
298
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318
Decentralized Reliable Control of Interconnected Time-Delay Systems Against Sensor Failures
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337
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358
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378
Uniform Approximation by the Highest Defect Continuous Polynomial Splines: Necessary and Sufficient Optimality Conditions and Their Generalisations
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395
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411
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