Minimax fractional programming with nondiferentiable (G,β)-invexity | Zendy

Xiaoling Liu | Zendy; Dehui Yuan | Zendy

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Minimax fractional programming with nondiferentiable (G,β)-invexity

Author(s) -

Xiaoling Liu,

Dehui Yuan

Publication year - 2014

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1410027l

Subject(s) - minimax , mathematics , duality (order theory) , lipschitz continuity , fractional programming , mathematical optimization , class (philosophy) , combinatorics , pure mathematics , nonlinear programming , computer science , artificial intelligence , physics , nonlinear system , quantum mechanics

In this paper, we consider the minimax fractional programming Problem (FP) in which the functions are locally Lipschitz $(G, \beta)$-invex. With the help of a useful auxiliary minimax programming problem, we obtain not only $G$-sufficient but also $G$-necessary optimality conditions theorems for the Problem (FP). With $G$-necessary optimality conditions and $(G, \beta)$-invexity in the hand, we further construct dual Problem (D) for the primal one (FP) and prove duality results between Problems (FP) and (D). These results extend several known results to a wider class of programs.

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