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W. E. Schmitendorf, “Necessary Conditions and Sufficient Conditions for Static Minimax Problems,” Journal of Mathematical Analysis and Applications, Vol. 57, No. 3-4, 1977, pp. 683-693. doi:10.1016/0022-247X(77)90255-4

has been cited by the following article:

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

  AUTHORS: Caiyun Jin, Cao-Zong Cheng

  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

  JOURNAL NAME: Applied Mathematics, Vol.2 No.11, November 30, 2011

  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.