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Higher-Order Duality for Minimax Fractional Type Programming Involving Symmetric Matrices
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Applied Mathematics·Volume 02 (2011)·Pages 1387–1392·Published 30 November 2011·DOI10.4236/am.2011.211196
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Abstract
Convexity and generalized convexity play important roles in optimization theory. With the development of programming problem, there has been a growing interest in the higher-order dual problem and a lot of related generalized convexities are given. In this paper, we give the convexity of (F, α ,p ,d ,b , φ )<sub>β</sub> vector-pseudo- quasi-Type I and formulate a higher-order duality for minimax fractional type programming involving symmetric matrices, and give the weak, strong and strict converse duality theorems under the condition of higher-order (F, α ,p ,d ,b , φ )<sub>β</sub> vector-pseudoquasi-Type I.
KeywordsHigher-Order (Fαpdbφ )<sub>β</sub>Vector-Pseudoquasi-Type IHigher-Order DualityMinimax Fractional Type ProgrammingPositive Semidefinite Symmetric Matrix
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