Higher-Order Duality for Minimax Fractional Type Programming Involving Symmetric Matrices

Caiyun Jin, Cao-Zong Cheng

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DOI: 10.4236/am.2011.211196                

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 )_β 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 )_β vector-pseudoquasi-Type I.

Keywords

Higher-Order (F, α , p , d , b , φ )_β Vector-Pseudoquasi-Type I, Higher-Order Duality, Minimax Fractional Type Programming, Positive Semidefinite Symmetric Matrix

Conflicts of Interest

The authors declare no conflicts of interest.

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