Symmetric Dual Programs Research Articles

Generalized Second-Order G-Wolfe Type Fractional Symmetric Program and their Duality Relations under Generalized Assumptions

In this article, we formulate the concept of generalize bonvexity/pseudobonvexity functions. We formulate duality results for second-order fractional symmetric dual programs of G-Wolfe-type model. In the next section, we explain the duality theorems under generalize bonvexity/pseudobonvexity assumptions. We identify a function lying exclusively in the class of generalize pseudobonvex and not in class of generalize bonvex functions. Our results are more generalized several known results in the literature.

Generalized $G$-Wolfe type fractional symmetric duality theorems over arbitrary cones under $(G,rho,theta)$-invexity assumptions

In this paper, we introduce the concept of $(G,rho,theta)$-invexity/pseudoinvexity. We formulate duality outcomes for $G$-Wolfe-type fractional symmetric dual programs over arbitrary cones. In the final section, we discuss the duality theorems under $(G,rho,theta)$-invexity/ $(G,rho,theta)$-psedoinvexity assumptions.

Symmetric duality in complex spaces over cones

Duality theory plays an important role in optimization theory. It has been extensively used for many theoretical and computational problems in mathematical programming. In this paper duality results are established for first and second order Wolfe and Mond-Weir type symmetric dual programs over general polyhedral cones in complex spaces. Corresponding duality relations for nondifferentiable case are also stated. This work will also remove inconsistencies in the earlier work from the literature.

Mixed Type Nondifferentiable Higher-Order Symmetric Duality over Cones

A new mixed type nondifferentiable higher-order symmetric dual programs over cones is formulated. As of now, in the literature, either Wolfe-type or Mond–Weir-type nondifferentiable symmetric duals have been studied. However, we present a unified dual model and discuss weak, strong, and converse duality theorems for such programs under higher-order F - convexity/higher-order F - pseudoconvexity. Self-duality is also discussed. Our dual programs and results generalize some dual formulations and results appeared in the literature. Two non-trivial examples are given to show the uniqueness of higher-order F - convex/higher-order F - pseudoconvex functions and existence of higher-order symmetric dual programs.

Multiobjective Fractional Symmetric Duality in Mathematical Programming with (C,Gf)-Invexity Assumptions

In this paper, a new class of ( C , G f ) -invex functions introduce and give nontrivial numerical examples which justify exist such type of functions. Also, we construct generalized convexity definitions (such as, ( F , G f ) -invexity, C-convex etc.). We consider Mond–Weir type fractional symmetric dual programs and derive duality results under ( C , G f ) -invexity assumptions. Our results generalize several known results in the literature.

Symmetric duality for multi-objective second-order fractional programs

A pair of symmetric dual second-order multi-objective fractional programming programs is formulated. Various duality results are established for this pair which further helps to study minimax mixed integer programming problems. Symmetric duality theorem is established under pseudobonvexity and multiplicative separability assumptions on the functions involved.

Symmetric duality for multi-objective second-order fractional programs

A pair of symmetric dual second-order multi-objective fractional programming programs is formulated. Various duality results are established for this pair which further helps to study minimax mixed integer programming problems. Symmetric duality theorem is established under pseudobonvexity and multiplicative separability assumptions on the functions involved.

Higher-order symmetric duality in multiobjective programming problems

In this paper, a pair of Mond-Weir type higher-order symmetric dual programs over arbitrary cones is formulated. The appropriate duality theorems, such as weak duality theorem, strong duality theorem and converse duality theorem, are established under higher-order (strongly) cone pseudoinvexity assumptions.

A note on strong duality theorem for a multiobjective higher order nondifferentiable symmetric dual programs

In this paper, we establish a strong duality theorem for a Mond-Weir type multiobjective higher order nondifferentiable symmetric dual programs. Our work relaxes the hypotheses used to prove the strong duality result (by omitting one of the condition (hypothesis (IV)), Theorem 2.1) in the recent paper (Yang et al. J. Ind. Manag. Optim. 9, 525–530, (2013)).

Symmetric duality for a higher-order nondifferentiable multiobjective programming problem

In this paper, a pair of Wolfe type higher-order nondifferentiable symmetric dual programs over arbitrary cones has been studied and then well-suited duality relations have been established considering K-F convexity assumptions. An example which satisfies the weak duality relation has also been depicted.MSC:90C29, 90C30, 49N15.

Second-order symmetric duality in non-differentiable multiobjective programming over cones

In this paper, a pair of Wolfe type second-order symmetric dual non-differentiable multiobjective programs is formulated over arbitrary cones. Weak, strong and converse duality theorems are established under K-η-bonvexity assumptions. Self-duality has also been discussed assuming the functions involved to be skew-symmetric.

Wolfe-type second-order fractional symmetric duality

Abstract In the present paper, we examine duality results for Wolfe-type second-order fractional symmetric dual programs. These duality results are then used to investigate minimax mixed integer symmetric dual fractional programs. We also discuss self-duality results at the end.

Higher-order symmetric duality with higher-order generalized invexity

Two different pairs of higher-order symmetric dual programs such as Wolfe type and Mond–Weir type are studied. The weak, strong and converse duality theorems are established for the higher-order symmetric dual programs under higher-order \(\rho -(\eta ,\theta )-\)invexity and \(\rho -(\eta ,\theta )-\)pseudo-invexity assumptions. Many examples and counterexamples are illustrated to justify our work. We also observe that several known results are obtained as special cases.

Second-Order Nondifferentiable Multiobjective Mixed Symmetric Dual Programs Over Cones

In this paper, a pair of second-order mixed symmetric nondifferentiable multiobjective dual programs over arbitrary cones where each of the objective functions contains a pair of support functions is considered. Further, weak, strong and converse duality theorems are established under the assumptions of second-order K- (F,ρ)-convexity. Moreover, we have illustrated a numerical example which is second-order K- (F,ρ)-convex but not second-order F-convex. Several special cases are also obtained.

Wolfe Type Second Order Nondifferentiable Symmetric Duality in Multiobjective Programming over Cone with Generalized (K, F)-Convexity

A new class of second order (K, F) pseudoconvex function is introduced with example. A pair of Wolfe type second order nondifferentiable symmetric dual programs over arbitrary cones with square root term is formulated. The duality results are established under second order (K, F) pseudoconvexity assumption. Also a Wolfe type second order minimax mixed integer programming problem is formulated and the symmetric duality results are established under second order (K, F) pseudoconvexity assumption.

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.

Second order symmetric duality in nondifferentiable multiobjective fractional programming with cone convex functions

In the present paper, we consider Mond-Weir type nondifferentiable second order fractional symmetric dual programs over arbitrary cones and derive duality results under second order K−F-convexity/K−F-pseudoconvexity assumptions. Our results generalize several known results in the literature.

A note on higher-order symmetric duality

In this paper, a pair of Wolfe type higher-order symmetric dual multiobjective programs is formulated. Strong and converse duality theorems are established under invexity assumptions. Duality relations for Mond–Weir type dual models have also been obtained under pseudoinvexity assumptions.

Mixed type symmetric duality for multiobjective variational problems with cone constraints

In this study, a pair of multiobjective variational mixed symmetric dual programs involving cone constraints is presented and usual duality results are established using the notion of generalized -convexity. Self-duality is discussed under additional condition of skew symmetry, and a time-independence (static) version of the problems is also incorporated.

Higher order symmetric duality in nondifferentiable multiobjective programming problems involving cones

In this paper, strong duality and converse duality theorems are established for a pair of Mond-Weir type multiobjective higher order symmetric dual programs over arbitrary cones. Our results ll some gaps in works of Agarwal et al. (2010) and Gupta et al. (2010).