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.     

A note on multiobjective second-order symmetric duality

In this paper, we establish a strong duality theorem for a pair of multiobjective second-order symmetric dual programs. This removes an omission in an earlier result by Yang et al. [X.M. Yang, X.Q. Yang, K.L. Teo, S.H. Hou, Multiobjective second-order symmetric duality with F-convexity, Euro. J. Oper. Res. 165 (2005) 585–591].     

Nondifferentiable multiobjective symmetric dual programs over cones

Wolfe and Mond-Weir type nondifferentiable multiobjective symmetric dual programs are formulated over arbitrary cones and appropriate duality theorems are established under K-preinvexity/K-convexity/pseudoinvexity assumptions.     

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$\eta$-bonvexity/η$\eta$-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.     

Higher-order symmetric duality in multiobjective programming problems

Acta Mathematicae Applicatae Sinica, English Series - In this paper, a pair of Mond-Weir type higher-order symmetric dual programs over arbitrary cones is formulated. The appropriate duality...     

Second order symmetric duality in multiobjective programming

A pair of Mond–Weir type multiobjective second order symmetric dual programs are formulated without non-negativity constraints. Weak duality, strong duality and converse duality theorems are established under η-bonvexity and η-pseudobonvexity assumptions. A second order self-duality theorem is given by assuming the functions involved to be skew-symmetric.     

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.     

Higher-order symmetric duality in nondifferentiable multiobjective programming problems

In this paper, a pair of nondifferentiable multiobjective programming problems is first formulated, where each of the objective functions contains a support function of a compact convex set in Rⁿ. For a differentiable function h :Rⁿ×Rⁿ→R, we introduce the definitions of the higher-order F-convexity (F-pseudo-convexity, F-quasi-convexity) of function f :Rⁿ→R with respect to h. When F and h are taken certain appropriate transformations, all known other generalized invexity, such as η-invexity, type I invexity and higher-order type I invexity, can be put into the category of the higher-order F-invex functions. Under these the higher-order F-convexity assumptions, we prove the higher-order weak, higher-order strong and higher-order converse duality theorems related to a properly efficient solution.     

Mixed symmetric duality in non-differentiable multiobjective mathematical programming

Two mixed symmetric dual models for a class of non-differentiable multiobjective nonlinear programming problems with multiple arguments are introduced in this paper. These two mixed symmetric dual models unify the four existing multiobjective symmetric dual models in the literature. Weak and strong duality theorems are established for these models under some mild assumptions of generalized convexity. Several special cases are also obtained.     

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.     

Second order symmetric duality in multiobjective programming involving cones

An attempt is made to remove certain omissions and inconsistencies in the recent work of Mishra and Lai (European J. Oper. Res., 178:20–26, 2007).     

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.     

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.     

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.     

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].     

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 multiobjective programming involving generalized cone-invex functions

In this paper, cone-second order pseudo-invex and strongly cone-second order pseudo-invex functions are defined. A pair of Mond–Weir type second order symmetric dual multiobjective programs is formulated over arbitrary cones. Weak, strong and converse duality theorems are established under aforesaid generalized invexity assumptions. A second self-duality theorem is also given by assuming the functions involved to be skew-symmetric.     

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.     

Nondifferentiable multiobjective programming under generalized d-univexity

In this paper, we are concerned with a nondifferentiable multiobjective programming problem with inequality constraints. We introduce four new classes of generalized convex functions by combining the concepts of weak strictly pseudoinvex, strong pseudoinvex, weak quasi invex, weak pseudoinvex and strong quasi invex functions in Aghezzaf and Hachimi [Numer. Funct. Anal. Optim. 22 (2001) 775], d-invex functions in Antczak [Europ. J. Oper. Res. 137 (2002) 28] and univex functions in Bector et al. [Univex functions and univex nonlinear programming, Proc. Admin. Sci. Assoc. Canada, 1992, p. 115]. By utilizing the new concepts, we derive a Karush–Kuhn–Tucker sufficient optimality condition and establish Mond–Weir type and general Mond–Weir type duality results for the nondifferentiable multiobjective programming problem.     

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.