Optimality Conditions and Duality for Fractional Programming Problems Involving Arcwise Connected Functions and Their Generalizations

Abstract

In this paper, necessary and sufficient optimality conditions are obtained for fractional programming problems involving arcwise connected, P-connected, and Qconnected functions. Duality results have also been established. 

Convexity with respect to a differential equation

“…We are going to prove g • β is convex. As (E 1 ) and (E 2 ) are conjugated by Φ −1 : ) is convex with respect to (6). In fact, first we have that (6) is conjugated to x = 0 by Φ :…”

“…, x −1 n ln(x n ) is not monotone, but it is monotone with respect to (6). Actually, direct calculation shows…”

“…Since g is convex the statement follows from Proposition 4.0.8. where c i ∈ R ++ and b ij ∈ R is convex with respect to (6). Actually, first we have that (6) is…”

“…One such topic was introduced by Ortega and Rheinboldt [10], who defined arcwise connectivity by replacing the line joining two points by a continuous arc joining them. This idea has been investigated and further extended for different reasons by many authors, see, for example: Avriel and Zang [2], Kaul, Lyall and Kaur [9], Bhatia and Mehra [5], Suneja, Aggarwal and Davar [14], Davar and Mehra [6] and Fu and Wang [7].…”

Optimality for Multi-Objective Programming Involving Arcwise Connected d-Type-I Functions

“…Bhatia and Mehara [16] investigated some properties of arcwise connected functions in terms of their directional derivatives and established optimality conditions for scalar-valued nonlinear programming prblems involving these functions. Mehar and Bhatia [17] and Davar and Mehra [18] studied optimality conditions and duality results for minmax problems and fractional programming problems involving arcwise connected and generalized arcwise connected functions, respectively.…”