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

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.

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 )

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

Higher-Order (F, α, p, d, b, φ )

Cite this paper

nullC. Jin and C. Cheng, "Higher-Order Duality for Minimax Fractional Type Programming Involving Symmetric Matrices,"*Applied Mathematics*, Vol. 2 No. 11, 2011, pp. 1387-1392. doi: 10.4236/am.2011.211196.

nullC. Jin and C. Cheng, "Higher-Order Duality for Minimax Fractional Type Programming Involving Symmetric Matrices,"

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