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1

On efficiency and duality for a class of nonconvex nondifferentiable multiobjective fractional variational control problems

Antczak Tadeusz, Arana-Jimenéz Manuel, Treanţă Savin

Opuscula Mathematica

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2023

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Vol. 43, no. 3

335--391

EN

In this paper, we consider the class of nondifferentiable multiobjective fractional variational control problems involving the nondifferentiable terms in the numerators and in the denominators. Under univexity and generalized univexity hypotheses, we prove optimality conditions and various duality results for such nondifferentiable multiobjective fractional variational control problems. The results established in the paper generalize many similar results established earlier in the literature for such nondifferentiable multiobjective fractional variational control problems.

2

Necessary optimality conditions for robust nonsmooth multiobjective optimization problems

Gadhi Nazih Abderrazzak, Ohda Mohamed

Control and Cybernetics

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2022

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Vol. 51, No. 3

289--302

EN

This paper deals with a robust multiobjective optimization problem involving nonsmooth/nonconvex real-valued functions. Under an appropriate constraint qualification, we establish necessary optimality conditions for weakly robust efficient solutions of the considered problem. These optimality conditions are presented in terms of Karush-Kuhn-Tucker multipliers and convexificators of the related functions. Examples illustrating our findings are also given.

3

Sufficient optimality criteria and duality for multiobjective variational control problems with B-(p,r)-invex function

Antczak T., Jimenez M. A.

Opuscula Mathematica

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2014

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Vol. 34, no. 4

665--682

EN

In this paper, we generalize the notion of B-(p, r)-invexity introduced by Antczak in [A class of B-(p; r)-invex functions and mathematical programming, J. Math. Anal. Appl. 286 (2003), 187–206] for scalar optimization problems to the case of a multiobjective variational programming control problem. For such nonconvex vector optimization problems, we prove sufficient optimality conditions under the assumptions that the functions constituting them are B-(p, r)-invex. Further, for the considered multiobjective variational control problem, its dual multiobjective variational control problem in the sense of Mond-Weir is given and several duality results are established under B-(p, r)-invexity.

4

Multiobjective variational programming under generalized (V, p)-B-type I functions

Khazafi K., Rueda N., Enflo P.

Control and Cybernetics

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2009

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Vol. 38, no 2

555-572

EN

In this paper, we generalize the (V, p)-invexity denned for nonsmooth multiobjective fractional programming by Mishra, Rueda and Giorgi (2003) to variational programming problems by defining new classes of vector- valued functions called (V, p)-B-type I and generalized (V, p)-B-type I. Then we use these new classes to derive various sufficient optimality conditions and mixed type duality results.

5

Second order duality in multiobjective programming

Ahmad I., Husain Z.

Journal of Applied Analysis

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2008

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Vol. 14, nr 1

131-148

EN

A nonlinear multiobjective programming problem is considered. Weak, strong and strict converse duality theorems are established under generalized second order (F, α, ρ, d)-convexity for second order Mangasarian type and general Mond-Weir type vector duals.

6

Sufficient conditions and duality for multiobjective variational problems with generalized B-invexity

Aghezzaf B., Khazafi K.

Control and Cybernetics

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2004

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Vol. 33, no 1

113-126

EN

In this paper, we consider the multiobjective variational problem. We propose a class of generalized B-type I vector-valued functions and use this concept to establish sufficient optimality conditions and mixed type duality results