## Optimality and duality for nonsmooth multiobjective fractional programming problems involving exponential $$V$$-$$r$$-invexity.(English)Zbl 1235.90179

Summary: We study a subdifferentiable multiobjective fractional programming problem under exponential $$V$$-$$r$$-invexity. We establish sufficient optimality conditions for multiobjective fractional programming problems involving exponential $$V$$-$$r$$-invex Lipschitz functions. By optimality conditions, the parametric dual model is formulated. Consequently, the duality theorems are proved so that the optimal values of the duality problems are equal to the primary problem under the framework of exponential $$V$$-$$r$$-invexity for the Lipschitz function.

### MSC:

 90C46 Optimality conditions and duality in mathematical programming 90C32 Fractional programming 90C30 Nonlinear programming
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### References:

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