THE NOTION OF V -r-INVEXITY IN DIFFERENTIABLE MULTIOBJECTIVE PROGRAMMING
نویسنده
چکیده
In this paper, a generalization of convexity, namely V -rinvexity, is considered in the case of nonlinear multiobjective programming problems where the functions involved are differentiable. The assumptions on Pareto solutions are relaxed by means of V -r-invex functions. Also some duality results are obtained for such optimization problems.
منابع مشابه
Duality for the class of a multiobjective problem with support functions under $K$-$G_f$-invexity assumptions
In this article, we formulate two dual models Wolfe and Mond-Weir related to symmetric nondifferentiable multiobjective programming problems. Furthermore, weak, strong and converse duality results are established under $K$-$G_f$-invexity assumptions. Nontrivial examples have also been depicted to illustrate the theorems obtained in the paper. Results established in this paper unify...
متن کاملOptimality Conditions and Duality in Multiobjective Programming with Invexity*
( , ) ρ Φ − invexity has recently been introduced with the intent of generalizing invex functions in mathematical programming. Using such conditions we obtain new sufficiency results for optimality in multiobjective programming and extend some classical duality properties.
متن کاملResearch Article Continuous-Time Multiobjective Optimization Problems via Invexity
We introduce some concepts of generalized invexity for the continuous-time multiobjective programming problems, namely, the concepts of Karush-Kuhn-Tucker invexity and Karush-Kuhn-Tucker pseudoinvexity. Using the concept of Karush-Kuhn-Tucker invexity, we study the relationship of the multiobjective problems with some related scalar problems. Further, we show that Karush-Kuhn-Tucker pseudoinvex...
متن کاملOptimality conditions and duality results of the nonlinear programming problems under (p, r)-invexity on differentiable manifolds
The main purpose of this paper is to study a pair of optimization problems on differentiable manifolds under (p, r)-invexity assumptions. By using the (p, r)-invexity assumptions on the functions involved, optimality conditions and duality results (Mond-Weir, Wolfe and mixed type) are established on differentiable manifolds. We construct counterexample to justify that our investigations are mor...
متن کاملNew optimality conditions for multiobjective fuzzy programming problems
In this paper we study fuzzy multiobjective optimization problems defined for $n$ variables. Based on a new $p$-dimensional fuzzy stationary-point definition, necessary efficiency conditions are obtained. And we prove that these conditions are also sufficient under new fuzzy generalized convexity notions. Furthermore, the results are obtained under general differentiability hypothesis.
متن کامل