Mond-Weir Type Duals Research Articles

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.

Optimality and duality for multiple-objective optimization under generalized type I univexity

In this paper, we extend the classes of generalized type I vector-valued functions introduced by Aghezzaf and Hachimi in [J. Global Optim. 18 (2000) 91–101] to generalized univex type I vector-valued functions and consider a multiple-objective optimization problem involving generalized type I univex functions. A number of Kuhn–Tucker type sufficient optimality conditions are obtained for a feasible solution to be an efficient solution. The Mond–Weir and general Mond–Weir type duality results are also presented.

Optimality and Duality in Nondifferentiable and Multiobjective Programming under Generalized d-Invexity

In this paper, we are concerned with the nondifferentiable multiobjective programming problem with inequality constraints. We introduce four new classes of generalized d-type-I functions. By utilizing the new concepts, Antczak type Karush-Kuhn-Tucker sufficient optimality conditions, Mond-Weir type and general Mond-Weir type duality results are obtained for non-differentiable and multiobjective programming.

MULTIOBJECTIVE VARIATIONAL PROGRAMMING UNDER GENERALIZED VECTOR VARIATIONAL TYPE I INVEXITY

Mond-Weir type duals for multiobjective variational problems are formulated. Under generalized vector variational type I invexity assumptions on the functions involved, sufficient optimality conditions, weak and strong duality theorems are proved efficient and properly efficient solutions of the primal and dual problems.

Optimality and duality in nonsmooth multiobjective optimization involving generalized type I functions

A nonsmooth multiobjective optimization problem involving generalized Type I vectorvalued functions is considered. Karush-Kuhn-Tucker type necessary and sufficient optimality conditions are obtained for a feasible point to be an efficient or properly efficient solution. Duality theorems are proved for Wolfe type and Mond-Weir type duals under the generalized Type I assumptions.

On nonlinear programming with support functions

Optimality conditions are derived for a nonlinear program in which a support function appears in the objective as well as in each constraint function. Wolfe and Mond-Weir type duals to this program are presented and various dualityresults are established under suitable convexity and generalized convexity assumptions. Special cases that often occur in the literature are those in which a support function is the square root of a positive semidefinite quadratic form or an Lp norm. It is pointed out that these special cases can easily be generated from our results.

Optimality and duality for generalized fractional variational control problems with (F, ρ)-convexity

A multiobjective fractional variational control problem is considered. Wolfe type and Mond-Weir type duality results are also established under generalized (F, ρ)-convexity assumptions.

Duality for multiobjective fractional variational control problems with (F, ρ)-convexity

A multiobjective fractional variational control problem is considered. Wolfe type and Mond-Weir type duality results are established under generalized (F, ρ)-convexity assumptions.

On multiobjective fractional programs

In this paper some optimality criteria are proved and some Mond-Weir type duality theorem for multiobjective fractional programming problems defined in a Banach space is obtained.

Mond-Weir type duality involving (B, η)-invex functions for a minmax programming problem

Several Mond-Weir type duals are proposed for a certain minmax programming problem and the notion of proper (b, η)-invexity is used to establish duality theorems relating the primal and the duals. The duals for a minmax (generalized) fractional programming problem are presented as special cases of the main problem considered in the paper.

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.

Optimality Conditions and Duality Involving Arcwise Connected and Generalized Arcwise Connected Functions

Some properties of arcwise connected functions in terms of their directional derivatives are investigated. These properties are then utilized to establish necessary and sufficient optimality conditions for scalar-valued nonlinear programming problems. Mond–Weir type duality results are also proved.

On Multiple-Objective Optimization with Generalized Univexity

A multiple-objective optimization problem involving generalized univex functions is considered. Kuhn–Tucker type sufficient optimality conditions are obtained for a feasible point to be an efficient or properly efficient solution. Mond–Weir type duality results are obtained. Further, a vector-valued Lagrangian is introduced and certain vector saddlepoint results are presented.

Duality in multiobjective nonlinear programming involving semilocally convex and related functions

Necessary optimality conditions are established for a multiobjective nonlinear programming problem involving semilocally convex and related functions in terms of their right differentials. Wolfe type and Mond-Weir type duals are formulated and duality results are proved under the assumptions of semilocal convexity, semilocal quasiconvexity and semilocal pseudoconvexity.

Duality for multiobjective fractional control problems with generalized invexity

Wolfe and Mond-Weir type duals for multiobjective control problems are formulated. Under pseudo-invexity/quasi-invexity assumptions on the functions involved, weak and strong duality theorems are proved to relate efficient solutions of the primal and dual problems.

Duality for multiobjective control problems with generalized invexity

Wolfe and Mond-Weir type duals for multiobjective control problems are formulated. Under pseudo-invexity/quasi-invexity assumptions on the functions involved, weak and strong duality theorems are proved to relate efficient solutions of the primal and dual problems.

On Efficiency and Duality for Multiobjective Variational Control Problems with (F − ρ)-Convexity

The concept of efficiency (pareto optimum) is used to formulate duality for multiobjective variational control problems. Wolfe and Mond–Weir type duals are formulated. Under the generalized (F−ρ)-convexity on the functions involved, weak and strong duality theorems are proved.

Duality for Multiobjective Variational Problems With Pseudo-Invexity

Wolfe and Mond-Weir type duals for multiobjective variational problems are formulated.Under pseudo-invexity assumption on the functions involved Weak and converse duality theorems are proved to relate efficient solutions/properly efficient solutions of the primal and dual problems. A close relationship between these variational problems and non-linear multiobjective prograrnmlng problems is also indicatcd

Duality for Multiobjective Variational Problems with Invexity

In this paper, Wolfe and Mond–Weir type duals for a class of nondifferentiable multiobjective variational problems are formulated. Under invexity assumptions on the objective and the constraint functions involved, weak and strong duality theorems are proved to related properly efficient solutions for primal and dual problems. Later, related problems with these variational problems are introduced.

Optimality and duality in nonlinear programming involving semilocally preinvex and related functions

Abstract For a nondifferentiable nonlinear programming problem, Fritz John and Kuhn-Tucker necessary optimality conditions and sufficient optimality conditions are given and duality results are stated for Wolfe’s type and Mond-Weir type duals by the concepts of semilocally quasi-preinvex and semilocally pseudo-preinvex functions.