Davinder Bhatia

Sensitivity analysis in fuzzy multiobjective linear fractional programming problem

In this paper, we study measurement of sensitivity for changes of violations in the aspiration level for the fuzzy multiobjective linear fractional programming problem.

Duality for a class of nondifferentiable mathematical programming problems in complex space

Craven and Mond [ 1 ] have given Fritz John type necessary conditions for a class of nonlinear programming problems in complex space over polyhedral cones. Here we derive the necessary and sufficient conditions for the static minimax problems in complex space which are extensions of the corresponding real space conditions of [4]. These conditions are then used to extend some duality results of [2] for a general class of nondifferentiable programming problems to complex space over arbitrary polyhedral cones. The complex minimax problem that we consider seeks to choose

On Multi-Objective Fractional Duality for Hanson-Mond Classes of Functions

Abstract Bector type dual for multiobjective fractional programming problem is introduced and certain duality results have been derived in the framework of Hanson-Mond classes of functions.

Optimality and duality for multiobjective nonsmooth programming

Abstract Necessary and sufficient conditions are derived for nonlinear nonsmooth multiobjective programming problems. A dual is introduced and certain duality results are established.

Duality for non smooth non linear fractional multiobjective programs via (F,ρ) - convexity

(F,ρ) convexity and related definitions are used to establish duality results for nonsmooth non-linear multiobjective fractional programming.

Optimality via generalized approximate convexity and quasiefficiency

In this article, we look beyond convexity and introduce the four new classes of functions, namely, approximate pseudoconvex functions of type I and type II and approximate quasiconvex functions of type I and type II. Suitable examples illustrating the non emptiness of the newly defined classes and distinguishing them from the existing classical notions of pseudoconvexity and quasiconvexity are provided. These newly defined concepts are then employed to establish sufficient optimality conditions for the quasi efficient solutions of a vector optimization problem.

Multiparametric sensitivity analysis of the constraint matrix in linear-plus-linear fractional programming problem

Abstract In this paper, we study multiparametric sensitivity analysis for programming problems with linear-plus-linear fractional objective function using the concept of maximum volume in the tolerance region. We construct critical regions for simultaneous and independent perturbations of one row or one column of the constraint matrix in the given problem. Necessary and sufficient conditions are given to classify perturbation parameters as ‘focal’ and ‘nonfocal’. Nonfocal parameters can have unlimited variations, because of their low sensitivity in practice, these parameters can be deleted from the analysis. For focal parameters, a maximum volume tolerance region is characterized. Theoretical results are illustrated with the help of a numerical example.

Higher Order Efficiency, Saddle Point Optimality, and Duality for Vector Optimization Problems

In this paper, we intend to characterize the strict local efficient solution of order m for a vector minimization problem in terms of the vector saddle point. A new notion of strict local saddle point of higher order of the vector-valued Lagrangian function is introduced. The relationship between strict local saddle point and strict local efficient solution is derived. Lagrange duality is formulated, and duality results are presented.

Generallized Linear Complementarity Problem and Multiobjective Programming Problem

In this paper we establish an equivalence between the solutions of a generalized linear complementarity problem and efficient points of a related nonlinear (quadratic) multiobjective programming problem. An algorithm based on multiple objective programming approach is presented to solve generalized linear complementarity problem

Characterizing strict efficiency for convex multiobjective programming problems

The article pertains to characterize strict local efficient solution (s.l.e.s.) of higher order for the multiobjective programming problem (MOP) with inequality constraints. To create the necessary framework, we partition the index set of objectives of MOP to give rise to subproblems. The s.l.e.s. of order m for MOP is related to the local efficient solution of a subproblem. This relationship inspires us to adopt the D.C. optimization approach, the convex subdifferential sum rule, and the notion of ε-subdifferential to derive the necessary and sufficient optimality conditions for s.l.e.s. of order