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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