On Efficiency and Duality for Multiobjective Variational Control Problems with (F−ρ)-Convexity

Arana‐Jiménez

2014

OpMath

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.

Section: Introductionmentioning

confidence: 99%

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

Arana‐Jiménez

2014

OpMath

“…Bhatia and Mehra [3] extended the concepts of B-type I and generalized B-type I functions to the continuous case and they used these concepts to establish sufficient optimality conditions and duality results for multiobjective variational programming problems. Nahak and Nanda [17] discussed duality theorems and related efficient solutions of the primal and dual problems for multiobjective variational control problems with (F, ρ)-convexity. Reddy and Mukherjee [18] studied duality theorems and related efficient solutions of the primal and dual problems for multiobjective fractional control problems under (F, ρ)-convexity.…”

Section: Introductionmentioning

confidence: 99%

On efficiency and mixed duality for a new class of nonconvex multiobjective variational control problems

2013

J Glob Optim

In this paper, we extend the notions of ( , ρ)-invexity and generalized ( , ρ)-invexity to the continuous case and we use these concepts to establish sufficient optimality conditions for the considered class of nonconvex multiobjective variational control problems. Further, multiobjective variational control mixed dual problem is given for the considered multiobjective variational control problem and several mixed duality results are established under ( , ρ)-invexity. Keywords Multiobjective variational problems · Efficient solution · ( , ρ)-invexity · ( , ρ)-pseudo-invexity · ( , ρ)-quasi-invexity · Mixed dualityMathematics Subject Classification 65K10 · 90C29 · 26B25

“…Mishra and Mukherjee [10] generalized (F, ρ)-convexity introduced by Preda [20], and established duality results for a class of multiobjective variational control problems with (F, ρ)-convex functions. Nahak and Nanda [18] used the concept of efficiency to formulate Wolfe and Mond-Weir type duals for multiobjective variational control problems and established weak and strong duality theorems under generalized (F, ρ)-convexity assumptions. Also Reddy and Mukherjee [21] have studied duality theorems under (F, ρ)-convexity assumptions and related efficient solutions of the primal and dual problems for multiobjective fractional control problems.…”

Section: Introductionmentioning

confidence: 99%

Duality for multiobjective variational control problems with $$(\Phi , \rho )$$ ( Φ , ρ ) -invexity

2013

Calcolo

In this paper, Mond-Weir and Wolfe type duals for multiobjective variational control problems are formulated. Several duality theorems are established relating efficient solutions of the primal and dual multiobjective variational control problems under ( , ρ)-invexity. The results generalize a number of duality results previously established for multiobjective variational control problems under other generalized convexity assumptions.