Duality For Multiobjective Programming Problems Research Articles

Duality for Multiobjective Programming Problems with Equilibrium Constraints on Hadamard Manifolds under Generalized Geodesic Convexity

This article is devoted to the study of a class of multiobjective mathematical programming problems with equilibrium constraints on Hadamard manifolds (in short, (MPPEC)). We consider (MPPEC) as our primal problem and formulate two different kinds of dual models, namely, Wolfe and Mond-Weir type dual models related to (MPPEC). Further, we deduce the weak, strong as well as strict converse duality relations that relate (MPPEC) and the corresponding dual problems employing geodesic pseudoconvexity and geodesic quasiconvexity restrictions. Several suitable numerical examples are incorporated to demonstrate the significance of the deduced results. The results derived in this article generalize and extend several previously existing results in the literature.

On sufficiency and duality for multiobjective programming problems using convexificators

In this paper, we consider a multiobjective programming problem with inequality and set constraints. We derive sufficient conditions for the optimality of a feasible point under generalized invexity assumptions in terms of convexificators. We give an example to illustrate that the concept of invexity in terms of convexificators is weaker than invexity in terms of other subdifferentials. We formulateWolfe and Mond-Weir type duals for the nonsmooth multiobjective programming problem with inequality and set constraints in terms of convexificators. We establish weak, strong, converse, restricted converse and strict converse duality results under the assumptions of invexity and strict invexity using convexificators between the primal and the Wolfe dual. We derive the respective results between the primal and the Mond-Weir dual under the assumptions of generalized pseudoinvexity, strict pseudoinvexity and quasiinvexity in terms of convexificators. We also derive the relationship between a weak vector saddle-point and a weakly efficient solution of the multiobjective programming problem.

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.

Higher-Order Duality for Multiobjective Programming Problems Involving (F, α, ρ, d)-V-Type I Functions

A class of functions called higher-order (F, α, ρ, d)-V-type I functions and their generalizations is introduced. Using the assumptions on the functions involved, weak, strong and strict converse duality theorems are established for higher-order Wolfe and Mond-Weir type multiobjective dual programs in order to relate the efficient solutions of primal and dual problems.

Lagrangian Duality for Multiobjective Programming Problems in Lexicographic Order

This paper deals with a constraint multiobjective programming problem and its dual problem in the lexicographic order. We establish some duality theorems and present several existence results of a Lagrange multiplier and a lexicographic saddle point theorem. Meanwhile, we study the relations between the lexicographic saddle point and the lexicographic solution to a multiobjective programming problem.

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

Abstract 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 mixed type converse duality in multiobjective programming problems

In this note, we establish a mixed type converse duality for a class of multiobjective programming programs. This clarifies several omissions in an earlier work by Yang et al. [Mixed type converse duality in multiobjective programming problems, J. Math. Anal. Appl. 304 (2005) 394-398].

Mixed type converse duality in multiobjective programming problems

In this paper, we use the Fritz John necessary optimality conditions to establish some results on the mixed type converse duality for a class of multiobjective programming problems.

Second Order Duality in Multiobjective Programming Involving Generalized Type I Functions

Recently Hachimi and Aghezzaf introduced the notion of (F, α, ρ, d)-type I functions, a new class of functions that unifies several concepts of generalized type I functions. In this paper, we extend the notion of (F, α, ρ, d)-type I functions to second order and establish several mixed duality results under second order generalized (F, α, ρ, p, d)-type I functions. Our results generalize the duality results recently given by Aghezzaf [Aghezzaf, B. (2003). Second order mixed type duality in multiobjective programming problems. J. Math. Anal. Appl. 285:97–106] and Hachimi and Aghezzaf [Hachimi, M., Aghezzaf, B. (2004). Sufficiency and duality in differentiable multiobjective programming involving generalized type I functions. J. Math. Anal. Appl. 296:382–392].

Second order mixed type duality in multiobjective programming problems

Second order mixed type dual is introduced for multiobjective programming problems. Results about weak duality, strong duality, and strict converse duality are established under generalized second order ( F, ρ)-convexity assumptions. These results generalize the duality results recently given by Aghezzaf and Hachimi involving generalized first order ( F, ρ)-convexity conditions.

On optimality and duality for multiobjective programming problems involving generalized d-type-I and related n-set functions

In this paper we establish some optimality and duality results under generalized convexity assumptions for a multiobjective programming problem involving generalized d-type-I and related n-set functions.

Generalized Invexity and Duality in Multiobjective Programming Problems

In this paper, we are concerned with the multiobjective programming problem with inequality constraints. We introduce new classes of generalized type I vector-valued functions. Duality theorems are proved for Mond–Weir and general Mond–Weir type duality under the above generalized type I assumptions.

Mixed Type Duality in Multiobjective Programming Problems

Two mixed type duals are introduced for multiobjective programming and for multiobjective fractional programming, respectively. Results about weak duality, strong duality, and strictly reverse duality are presented under more suitable conditions.

Proper efficiency conditions and duality for multiobjective programming problems involving semilocally invex functions

The purpose of this paper is to prove Mond-Weir-type duality theorems for multi-objective programming problems involving semi-locally invex functions and arbitrary cones

A Linearization Approach to Multiobjective Programming Duality

Duality for multiobjective programming problems having pseudo-convex objective functions and linear constraints is studied through a linearization approach. Its application to a multiobjective fractional programming problem with different denominators is discussed.