Nondifferentiable mathematical programming and convex-concave functions |
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Authors: | S. Tanimoto |
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Affiliation: | (1) Department of Applied Mathematics, Faculty of Engineering Science, Osaka University, Toyonaka, Osaka, Japan |
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Abstract: | For a convex-concave functionL(x, y), we define the functionf(x) which is obtained by maximizingL with respect toy over a specified set. The minimization problem with objective functionf is considered. We derive necessary conditions of optimality for this problem. Based upon these necessary conditions, we define its dual problem. Furthermore, a duality theorem and a converse duality theorem are obtained. It is made clear that these results are extensions of those derived in studies on a class of nondifferentiable mathematical programming problems.This work was supported by the Japan Society for the Promotion of Sciences. |
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Keywords: | Minimax theorems Kuhn-Tucker optimality conditions duality theorem converse duality theorem constraint qualifications |
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