A necessary and sufficient condition for duality in multiobjective variational problems

Arana‐Jiménez, Manuel; Garzón, Gabriel Ruiz; Rufián-Lizana, A.; Osuna-Gómez, R.

doi:10.1016/j.ejor.2009.03.047

Cited by 13 publications

(8 citation statements)

References 21 publications

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“…Craven [17], remarkably established KT-type necessary conditions for multiobjective variational problems under pseudo and quasi convexity assumptions. In [13], Arana-Jimenez et al studied various duality results for multiobjective variational problems by using pseudoinvexity concept.…”

Section: Introductionmentioning

confidence: 99%

Multitime multiobjective variational problems via η-approximation method

Jha

Das

Bandhyopadhyay

2022

YUGOSLAV J OPERATION

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The present article is devoted to multitime multiobjective variational problems via ?-approximation method. In this method, an ?-approximation approach is applied to the considered problem, and a new problem is constructed, called as ?-approximated multitime multiobjective variational problem that contains the change in objective and both constraints functions. The equivalence between an efficient (Pareto optimal) solution to the main multitime multiobjective variational problem is derived along with its associated ?-approximated problem under invexity defined for a multi- time functional. Furthermore, we have also discussed the saddle-point criteria for the problem considered and its associated ?-approximated problems via generalized invexity assumptions.

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Section: Introductionmentioning

confidence: 99%

Multitime multiobjective variational problems via η-approximation method

Jha

Das

Bandhyopadhyay

2022

YUGOSLAV J OPERATION

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“…In order to prove sufficient optimality conditions for the considered multiobjective variational programming problem (MVP), we give the Karush-Kuhn-Tucker necessary optimality conditions for such vector optimization problems (see, for instance, [5,6,12,19,26]). …”

Section: Definition 21 If There Exist Functionsmentioning

confidence: 99%

“…Multiobjective variational programming problems with equality and inequality restrictions were considered by many authors (see, for example, [1,2,[4][5][6][8][9][10][11][12][13][14][15][16][17][18][20][21][22][23][24][25][26][27][28][29], and others).…”

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confidence: 99%

The Modified Objective Function Method for Univex Multiobjective Variational Problems

Antczak

Jayswal

Jha

2018

Bull. Iran. Math. Soc.

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In this paper, we use the modified objective function method for a class of nonconvex multiobjective variational problems involving univex functions. Under univexity hypotheses, we prove the equivalence between an (weakly) efficient solution of the considered multiobjective variational problem and an (weakly) efficient solution of the associated modified multiobjective variational problem constructed in the modified objective function method.

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“…In [6], Arana-Jiménez et al defined the V -KT -pseudoinvex multiobjective control problem and proved that a V -KT -pseudoinvex multiobjective control problem is characterized so that a Kuhn-Tucker point is an efficient solution. Recently, Arana-Jiménez et al [7] introduced new classes of pseudoinvex functions and established a necessary and sufficient condition for duality results in the considered multiobjective control problem.…”

Section: Introductionmentioning

confidence: 99%

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

Antczak

Arana‐Jiménez

2014

OpMath

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Abstract. 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.

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A necessary and sufficient condition for duality in multiobjective variational problems

Cited by 13 publications

References 21 publications

Multitime multiobjective variational problems via η-approximation method

Multitime multiobjective variational problems via η-approximation method

The Modified Objective Function Method for Univex Multiobjective Variational Problems

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

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