Symmetric Dual Problems Research Articles

Duality for a class of second order symmetric nondifferentiable fractional variational problems

The present work frames a pair of symmetric dual problems for second order nondifferentiable fractional variational problems over cone constraints with the help of support functions. Weak, strong and converse duality theorems are derived under second order F-convexity assumptions. By removing time dependency, static case of the problem is obtained. Suitable numerical example is constructed.

Second-order symmetric duality in multiobjective variational problems

In this work, we introduce a pair of multiobjective second-order symmetric dual variational problems. Weak, strong, and converse duality theorems for this pair are established under the assumption of ?-bonvexity/?-pseudobonvexity. At the end, the static case of our problems has also been discussed.

Wolfe Type Higher Order Multiple Objective Nondifferentiable Symmetric Dual Programming with Generalized Invex Function

In this paper, a new class of higher order (ϕ, ρ)-invex function is introduced with an example, in which the sublinearity and convexity assumption on ϕ with respect to third argument is relaxed. A pair of higher order Wolfe type multiobjective symmetric dual for a class of nondifferentiable multiobjective programming involving square root term is presented and the weak duality, strong duality and converse duality theorems are established with their proofs under higher order (ϕ, ρ)-invexity and (ϕ, ρ)-incavity assumption. Self duality theorem is proved for the proposed dual program. These results are used to discuss Wolfe type higher-order symmetric minimax mixed integer dual problems. A numerical example is developed where the results of weak and strong duality theorems can be applied. Discussion on some particular cases shows that our results generalize earlier results in related domain.

Symmetric duality for nondifferentiable multiobjective fractional variational problems involving cones

Abstract We introduce a pair of symmetric dual problems for nondifferentiable multiobjective fractional variational problems with cone constraints over arbitrary cones. On the basis of weak efficiency, we obtain symmetric duality relations for Mond-Weir-type problems under invexity and pseudoinvexity assumptions. Our symmetric duality results extend and improve some known results in Mishra et al. (J. Math. Anal. Appl. 333:1093-1110, 2007) to the cone constraints. MSC:90C29, 90C32, 90C26.

Higher-order symmetric duality under cone-invexity and other related concepts

In this paper we establish weak, strong and converse duality results for a pair of Wolfe type higher-order symmetric dual problems over cones under the assumption of higher-order cone-invexity. We also introduce the concepts of higher-order strictly and strongly cone-pseudoinvexity and use them to obtain weak, strong and converse duality results for the pair of Mond–Weir type higher-order symmetric dual problems.

Mond-Weir type second order minimax mixed integer programming involving generalised (φ, δ)-univex functions

: In this paper, we presented a pair of Mond-Weir type non-differentiable second order symmetric minimax mixed integer primal and dual problem containing quadratic form. The duality theorems are established under second order (ϕ, δ)-pseudounivexity assumption. Also self-duality theorem is proved with an example. At the end, several known results are obtained as special cases and a numerical example is developed which validates the model and weak duality theorem.

Duality for a class of symmetric nondifferentiable multiobjective fractional variational problems with generalized [formula omitted]-convexity

A pair of nondifferentiable symmetric dual problems for a class of multiobjective fractional variational programs over arbitrary cones is formulated. Weak, strong and converse duality relations are then proved under generalized (F,α,ρ,d)-convexity assumptions.

On vector matrix game and symmetric dual vector optimization problem

Abstract A vector matrix game with more than two skew symmetric matrices, which is an extension of the matrix game, is defined and the symmetric dual problem for a nonlinear vector optimization problem is considered. Using the Kakutani fixed point theorem, we prove an existence theorem for a vector matrix game. We establish equivalent relations between the symmetric dual problem and its related vector matrix game. Moreover, we give an example illustrating the equivalent relations.

Mixed type second-order symmetric duality under F-convexity

We introduce a pair of second order mixed symmetric dual problems. Weak, strong and converse duality theorems for this pair are established under $F-$convexity assumptions.

Symmetric duality for second-order fractional programs

In this paper, a pair of symmetric dual second-order fractional programming problems is formulated and appropriate duality theorems are established. These results are then used to discuss the minimax mixed integer symmetric dual fractional programs.

On symmetric and self duality in vector optimization problem

In this paper, we point out some errors in a recent paper of M.A.E.H.Kassen (Applied Mathematics and Computation 183(2006) 1121-1126). And a pair of the first-order symmetric dual model for vector optimization problem is proposed in this paper. Then, we prove the weak, strong and converse duality theorems for the formulated first-order symmetric dual programs under invexity conditions.

Second-order multiobjective symmetric duality with cone constraints

In this paper, we formulate Wolfe and Mond–Weir type second-order multiobjective symmetric dual problems over arbitrary cones. Weak, strong and converse duality theorems are established under η -bonvexity/ η -pseudobonvexity assumptions. This work also removes several omissions in definitions, models and proofs for Wolfe type problems studied in Mishra [9]. Moreover, self-duality theorems for these pairs are obtained assuming the function involved to be skew symmetric.

NONDIFFERENTIABLE MULTIOBJECTIVE SECOND ORDER SYMMETRIC DUALITY WITH CONE CONSTRAINTS

We introduce two pairs of nondifferentiable multiobjective second order symmetric dual problems with cone constraints over arbitrary closed convex cones, which is different from the one proposed by Mishra and Lai [12]. Under suitable second order pseudo-invexity assumptions we establish weak, strong and converse duality theorems as well as self-duality relations. Our symmetric duality results include an extension of the symmetric duality results for the first order case obtained by Kim and Kim [7] to the second order case. Several known results are abtained as special cases.

SECOND ORDER SYMMETRIC DUALITY FOR NONDIFFERENTIABLE MULTIOBJECTIVE PROGRAMMING INVOLVING CONES

We construct Mond-Weir and Wolfe types of nondifferentiable multiobjective second order symmetric dual problems with cone constraints over arbitrary closed convex cones. Weak, strong, and converse duality theorems for weakly efficient solutions are established under the assumptions of second order invex and pseudo-invex functions. Several known results are obtained as special cases of our symmetric duality.

Non-differentiable symmetric duality for multiobjective programming with cone constraints

Abstract Two pairs of non-differentiable multiobjective symmetric dual problems with cone constraints over arbitrary cones, which are Wolfe type and Mond–Weir type, are considered. On the basis of weak efficiency with respect to a convex cone, we obtain symmetric duality results for the two pairs of problems under cone-invexity and cone-pseudoinvexity assumptions on the involved functions. Our results extend the results in Khurana [S. Khurana, Symmetric duality in multiobjective programming involving generalized cone-invex functions, European Journal of Operational Research 165 (2005) 592–597] to the non-differentiable multiobjective symmetric dual problem.

Symmetric duality for multiobjective fractional variational problems involving cones

In this paper, a pair of multiobjective fractional variational symmetric dual problems over cones is formulated. Weak, strong and converse duality theorems are established under generalized F-convexity assumptions. Moreover, self duality theorem is also discussed.

SECOND ORDER SYMMETRIC DUALITY FOR NONDIFFERENTIABLE MULTIOBJECTIVE PROGRAMMING INVOLVING CONES

We construct Mond-Weir and Wolfe types of nondifferentiable multiobjective second order symmetric dual problems with cone constraints over arbitrary closed convex cones. Weak, strong, and converse duality theorems for weakly efficient solutions are established under the assumptions of second order invex and pseudo-invex functions. Several known results are obtained as special cases of our symmetric duality.

A NOTE ON MOND-WEIR TYPE SECOND-ORDER SYMMETRIC DUALITY

In this paper, we establish a strong duality theorem for a pair of Mond–Weir type second-order nondifferentiable symmetric dual problems. This removes certain inconsistencies in some of the earlier results.

Minimax mixed integer symmetric duality for multiobjective variational problems

A Mond–Weir type multiobjective variational mixed integer symmetric dual program over arbitrary cones is formulated. Applying the separability and generalized F-convexity on the functions involved, weak, strong and converse duality theorems are established. Self duality theorem is proved. A close relationship between these variational problems and static symmetric dual minimax mixed integer multiobjective programming problems is also presented.

Mixed symmetric duality for nondifferentiable programming problems

A pair of nondifferentiable mixed symmetric dual programming problems is introduced and duality theorems are proved. This unifies two existing formulations of symmetric dual problems appeared in the literature.