## Optimality and duality for nonsmooth multiobjective programming problems with $$V$$-$$r$$-invexity.(English)Zbl 1206.49035

Author’s abstract: “We consider a class of nonsmooth multiobjective programming problems in which involved functions are locally Lipschitz. A new concept of invexity for locally Lipschitz vector-valued functions is introduced, called $$V$$-$$r$$-invexity. The generalized Karush-Kuhn-Tuker necessary and sufficient optimality conditions are established and duality theorems are derived for nonsmooth multiobjective programming problems involving $$V$$-$$r$$-invex functions (with respect to the same function $$\eta$$).”
Consisting of five parts and of a list of references including 25 works, the article does not contain any numerical example attention of the author is concentrated on the theoretical problems of duality and optimality conditions for nonsmooth multiobjective programming problems.

### MSC:

 49N15 Duality theory (optimization) 90C29 Multi-objective and goal programming 90C26 Nonconvex programming, global optimization 90C46 Optimality conditions and duality in mathematical programming 49J52 Nonsmooth analysis 49J30 Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
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### References:

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