Abstract
We study nonsmooth multiobjective fractional programming problem containing local Lipschitz exponentialB-p,r-invex functions with respect toηandb. We introduce a new concept of nonconvex functions, called exponentialB-p,r-invex functions. Base on the generalized invex functions, we establish sufficient optimality conditions for a feasible point to be an efficient solution. Furthermore, employing optimality conditions to perform Mond-Weir type duality model and prove the duality theorems including weak duality, strong duality, and strict converse duality theorem under exponentialB-p,r-invexity assumptions. Consequently, the optimal values of the primal problem and the Mond-Weir type duality problem have no duality gap under the framework of exponentialB-p,r-invexity.
Highlights
We study nonsmooth multiobjective fractional programming problem containing local Lipschitz exponential B-(p, r)-invex functions with respect to η and b
Convexity plays an important role in mathematical programming problems, some of which are sufficient optimality conditions or duality theorems
With generalized invex Lipschitz functions, optimality conditions and duality theorems were established in nonsmooth mathematical programming problems
Summary
Convexity plays an important role in mathematical programming problems, some of which are sufficient optimality conditions or duality theorems. With generalized invex Lipschitz functions, optimality conditions and duality theorems were established in nonsmooth mathematical programming problems (cf [8,9,10,11,12,13,14,15,16,17]). Extra reasonable assumptions for the necessary optimality conditions are needed in order to prove the sufficient optimality conditions These reasonable assumptions are various (e.g., generalized convexity, generalized invexity, set-value functions, and complex functions). Invexity and necessary optimality conditions to establish the sufficient optimality conditions on a nondifferentiable multiobjective fractional programming problem (P).
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