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.     

Second order symmetric duality for nonlinear multiobjective mixed integer programming

We formulate two pairs of second order symmetric duality for nonlinear multiobjective mixed integer programs for arbitrary cones. By using the concepts of efficiency and second order invexity, we establish weak, strong, converse and self-duality theorems for the dual models. Several known results are obtained as special cases.     

Multiobjective symmetric duality with cone constraints

We formulate a pair of multiobjective symmetric dual programs for pseudo-invex functions and arbitrary cones. Our model is unifying the Wolfe vector symmetric dual and the Mond-Weir vector symmetric dual models. We establish the weak, strong, converse and self duality theorems for our pair of dual models. Nanda and Das' results (Optimization 28 (1994) 267; Eur. J. Oper. Res. 88 (1996) 572) are obtained as special cases.     

Symmetric duality for minimax mixed integer programming problems with pseudo-invexity

In this paper, we consider the pair of symmetric dual multiobjective variational mixed integer programs proposed by Chen and Yang [X. Chen, J. Yang, Symmetric duality for minimax multiobjective variational mixed integer programming problems with partial-invexity, European Journal of Operational Research 181 (2007) 76-85.] and extend some of their results under the assumptions of partial-pseudo-invexity and separability on the functions involved. These results include several results available in literature as special cases.     

Symmetric duality for minimax multiobjective variational mixed integer programming problems with partial-invexity

A pair of symmetric dual multiobjective variational mixed integer programs for the polars of arbitrary cones are formulated, which some primal and dual variables are constrained to belong to the set of integers. Under the separability with respect to integer variables and partial-invexity assumptions on the functions involved, we prove the weak, strong, converse and self-duality theorems to related minimax efficient solution. These results include some of available results.     

Non-differentiable symmetric duality for multiobjective programming with cone constraints

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.     

Minimax and symmetric duality for nonlinear multiobjective mixed integer programming

We formulate two pairs of symmetric duality for nonlinear multiobjective mixed integer programs for arbitrary cones. By using the concept of efficiency, we establish the weak, strong, converse and self-duality theorems for our symmetric models. Several known results are obtained as special cases.     

Second order symmetric duality in non-differentiable multiobjective programming with F-convexity

This paper is concerned with a pair of Mond–Weir type second order symmetric dual non-differentiable multiobjective programming problems. We establish the weak and strong duality theorems for the new pair of dual models under second order F-convexity assumptions. Several results including many recent works are obtained as special cases.     

Higher-order symmetric duality in multiobjective programming problems under higher-order invexity

In this paper we present a pair of Wolfe and Mond-Weir type higher-order symmetric dual programs for multiobjective symmetric programming problems. Different types of higher-order duality results (weak, strong and converse duality) are established for the above higher-order symmetric dual programs under higher-order invexity and higher-order pseudo-invexity assumptions. Also we discuss many examples and counterexamples to justify our work.     

A note on higher-order nondifferentiable symmetric duality in multiobjective programming

In this work, we establish a strong duality theorem for Mond–Weir type multiobjective higher-order nondifferentiable symmetric dual programs. This fills some gaps in the work of Chen [X. Chen, Higher-order symmetric duality in nondifferentiable multiobjective programming problems, J. Math. Anal. Appl. 290 (2004) 423–435].     

Nondifferentiable second order symmetric duality in multiobjective programming

A pair of Mond–Weir type nondifferentiable multiobjective second order symmetric dual programs is formulated and symmetric duality theorems are established under the assumptions of second order F-pseudoconvexity/F-pseudoconcavity.     

Symmetric dual multiobjective programming

In this paper a pair of symmetric dual multiobjective programming problems is formulated and the duality theorems are established for pseudo-convex/pseudo-concave functions.     

Multiobjective second-order symmetric duality with F-convexity

We suggest a pair of second-order symmetric dual programs in multiobjective nonlinear programming. For these second-order symmetric dual programs, we prove the weak, strong and converse duality theorems under F-convexity conditions.     

Multiobjective symmetric duality involving cones

In this paper, a pair of multiobjective symmetric dual programs over arbitrary cones are formulated for cone-convex functions. Weak, strong, converse and self-duality theorems are proved for these programs.     

一类多目标分式规划的二阶对称对偶问题

研究一类多目标分式规划的二阶对称对偶问题.在二阶F-凸性假设下给出了对偶问题的弱对偶、强对偶和逆对偶定理.并在对称和反对称假设下研究了该问题的自身对偶性.     

On multiobjective generalized symmetric dual programs withρ − (η, θ)-invexity

A pair of multiobjective generalized symmetric dual nonlinear programming problems and weak, strong and converse duality theorems for these problems are established under generalized ρ ? (η, θ)-invexity assumptions. Several known results are obtained as special cases.     

锥约束多目标规划的二阶对称对偶性质

给出一对锥约束多目标非线性规划的二阶对称对偶问题,以及二阶F凸函数类的概念.在二阶F凸假设下证明了真有效解的对偶性质———弱对偶性、强对偶性及逆对偶性.     

Symmetric duality for invex multiobjective fractional variational problems

We introduce a symmetric dual for multiobjective fractional variational problems. Under certain invexity assumptions we establish weak, strong and converse duality theorems as well as self-duality relations. The paper includes an extension of previous symmetric duality results for the static case obtained by Weir to the dynamic case.     

不可微多目标规划的高阶对称对偶性

本文研究锥约束不可微多目标规划的Mond-Weir 型高阶对称对偶问题. 本文指出Agarwal 等人(2010) 和Gupta 等人(2010) 工作的不足, 给出规划问题的强对偶和逆对偶定理.     

Higher-order nondifferentiable symmetric duality with generalized F-convexity

A pair of nondifferentiable higher-order Wolfe type symmetric dual models is formulated and usual duality theorems are established under higher-order F-convexity assumption. Symmetric minimax mixed integer primal and dual problems are also discussed.