Nondifferentiable Multiobjective Programming Research Articles

Multiobjective programming under d-invexity

In this paper, a generalization of convexity is considered in the case of nonlinear multiobjective programming problem where the functions involved are nondifferentiable. By considering the concept of Pareto optimal solution and substituting d-invexity for convexity, the Fritz John type and Karush–Kuhn–Tucker type necessary optimality conditions and duality in the sense of Mond–Weir and Wolfe for nondifferentiable multiobjective programming are given.

Duality for a Class of Nondifferentiable Multiobjective Programming Problems

In this paper, both the Wolfe type and Mond–Weir type dual problems for a class of nondifferentiable multiobjective programs in which every component of the objective function contains a term involving the support function of a compact convex set are formulated. Weak duality theorems are established under suitable conditions. A special case which appears repeatedly in the literature is that the support function is the square root of a positive semidefinite quadratic form. This and other special cases can be readily generated from our results.

ϵ-properly efficient solutions to nondifferentiable multiobjective programming problems

We introduce the concept of an ϵ-properly efficient solution and establish the equivalence between ϵ-optimality for a convex multiobjective program and ϵ-optimality for a related parametric (scalar) objective program. Using this equivalence, we establish the necessary and sufficient conditions for an ϵ-properly efficient solution of a nondifferentiable multiobjective objective functions subject to nondifferentiable convex inequality constraints, linear equality constraints, and abstract constraints.

Symmetric duality for a class of multiobjective programming

We formulate a pair of symmetric dual nondifferentiable multiobjective programming and establish appropriate duality theorems. We also show that differentiable and nondifferentiable analogues of several pairs of symmetric dual problems can be obtained as special cases of our general symmetric programs.

ϵ-Pareto Optimality for Nondifferentiable Multiobjective Programming via Penalty Function

Necessary and sufficient conditions without a constraint qualification for ϵ-Pareto optimality of multiobjective programming are derived. The necessary Kuhn–Tucker condition suggests the establishment of a Wolf-type duality theorem for nondifferentiable, convex, multiobjective minimization problems. The generalized ϵ-saddle point for Pareto optimality of the vector Lagrangian is studied.

?-Duality theorem of nondifferentiable nonconvex multiobjective programming

?-Duality theorem of nondifferentiable nonconvex multiobjective programming

D-Invexity and optimality conditions

In this paper, a generalization of convexity, called d-invexity, is introduced. Substituting d-invex for convex, we get some optimality conditions for nondifferentiable multiobjective programming. The application is demonstrated by an example.

?-duality theorem of nondifferentiable nonconvex multiobjective programming

Necessary Kuhn-Tucker conditions up to precision ɛ without constraint qualification for ɛ-Pareto optimality of multiobjective programming are derived. This article suggests the establishment of a Wolfe-type ɛ-duality theorem for nondifferentiable, nonconvex, multiobjective minimization problems. The ɛ-vector Lagrangian and the generalized ɛ-saddle point for Pareto optimality are studied.

Non-Differentiable Multiobjective Fractional Programming with Hanson-Mond Glasses of Functions

Abstract In this paper we consider non-linear nondifferentiable multiobjective fractional programming problem in which numerator of each component of the objective function contains a term involving square root of a certain positive semi-definite quadratic form. Necessary and sufficient conditions for a feasible point to be properly efficient are established. A dual is also formulated. Weak and Strong duality theorems are given in the framework of Hanson-Mond classes of functions.

Saddlepoint Theory for Nondifferentiable Multiobjective Fractional Programming

Abstract Saddlepoint theory is developed for the nondifferentiable multiobjective fractional programming problem. Necessary and sufficient conditions of Fritz John and Kuhn-Tucker type are established. As expected, only necessary conditions require convexity restrictions. All functions are assumed to be nondifferentiable.

Second-order duality for nondifferentiable multiobjective programming involving (Φ,ρ)-univexity

The concepts of (Φ, ρ)-invexity have been given by Carsiti,Ferrara and Stefanescu[32]. We consider a second-order dual model associated to a multiobjective programming problem involving support functions and a weak duality result is established under appropriate second-order (Φ, ρ)-univexity conditions. AMS 2002 Subject Classification: 90C29; 90C30; 90C46. Key words: Second-order (Φ, ρ)-(pseudo/quasi)-convexity; multiobjective programming; second-order duality; duality theorem. DOI: http://dx.doi.org/ 10.3126/kuset.v7i1.5426 KUSET 2011; 7(1): 92-104