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Minimax fractional programming problem with \((p,r)-\rho-(\eta,\theta)\)-invex functions. (English) Zbl 1413.90283
Summary: In this paper, new classes of generalized \((p,r)-\rho-(\eta, \theta)\)-invex functions are introduced i.e., \((p,r)-\rho-(\eta,\theta)\)-quasi-invex and (strictly) \((p,r)-\rho-(\eta,\theta)\)-pseudo-invex functions. We focus on minimax fractional programming problem and establish sufficient optimality conditions under the assumption of generalized \((p,r)-\rho-(\eta,\theta)\)-invexity. Weak, strong and strict converse duality theorems are also derived for two type of dual models related to minimax fractional programming problem involving aforesaid generalized invex functions.

MSC:
90C32 Fractional programming
90C46 Optimality conditions and duality in mathematical programming
49N15 Duality theory (optimization)
90C47 Minimax problems in mathematical programming
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