Duality In Fractional Programming Research Articles

On robust duality for fractional programming with uncertainty data

In this paper, we present a duality theory for fractional programming problems in the face of data uncertainty via robust optimization. By employing conjugate analysis, we establish robust strong duality for an uncertain fractional programming problem and its uncertain Wolfe dual programming problem by showing strong duality between the deterministic counterparts: robust counterpart of the primal model and the optimistic counterpart of its dual problem. We show that our results encompass as special cases some programming problems considered in the recent literature. Moreover, we also show that robust strong duality always holds for linear fractional programming problems under scenario data uncertainty or constraint-wise interval uncertainty, and that the optimistic counterpart of the dual is tractable computationally.

Multiple objective fractional programming involving semilocally type I-preinvex and related functions

Sufficient optimality conditions are obtained for a nonlinear multiple objective fractional programming problem involving η-semidifferentiable type I-preinvex and related functions. Furthermore, a general dual is formulated and duality results are proved under the assumptions of generalized semilocally type I-preinvex and related functions. Our result generalize the results of Preda [V. Preda, Optimality and duality in fractional multiple objective programming involving semilocally preinvex and related functions, J. Math. Anal. Appl. 288 (2003) 365–382] and Stancu-Minasian [I.M. Stancu-Minasian, Optimality and duality in fractional programming involving semilocally preinvex and related functions, J. Inform. Optim. Sci. 23 (2002) 185–201].

Second order duality for fractional programming with support functions

A second order dual is formulated for a fractional programming problem with support functions. Subject to where f, g and h are differentiable, possibly nonlinear and appropriate duality theorems are validated.

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

A nonsmooth minmax programming problem, under the assumption of proper (b, η) – invexity conditions on the functions involved in the objective and in the constraints, is considered. For such a problem, a sufficient optimality theorem is proved, a Wolfe type dual is presented and duality theorems relating the primal and the dual are proved. Applications of these results to certain nonsmooth fractional and nonsmooth generalized fractional programming duality are also presented.

Optimality conditions and duality in fractional programming involving semilocally preinvex and related functions

In this paper, a nonlinear fractional programming problem is considered, where the functions involved are η-semidifferentiable. Necessary and sufficient optimality conditions are obtained. A dual is formulated and duality results are proved using concepts of semilocally preinvex, semilocally quasi-preinvex and semilocally pseudo-preinvex functions. Our results generalize the results obtained by Lyall, Suneja and Aggarwal [8].

Fractional Programming: Theory, Methods and Applications

Introduction. 1. Fractional Programming Applications. 2. Convex, Quasiconvex, Pseudoconvex, Logarithmic Convex, alpham-Convex, and Invex Functions. 3. Methods for Solving Linear Fractional Programming Problems. 4. Nonlinear Fractional Programming. 5. Duality in Fractional Programming. 6. Fractional Programming with Multiple Objective Functions. 7. Fractional Programming in the Complex Space. 8. Special Linear Fractional Programming Problems. 9. Integer and Mixed Integer Linear Fractional Programming. 10. Fractional Transportation Problem. Bibliography. Subject Index. Author Index.

A note on vector valued Lagrangian and multiobjective fractional programming duality via Dini derivatives

In this paper Bector type dual in terms of classical Dini derivatives has been presented for a non-linear multiobjective fractional programming problem and the duality theorems relating to primal and dual are established.

Optimality and Duality in Fractional Programming Involving Semilocally Convex and Related Functions

Necessary and sufficient optimality conditions are obtained for a nonlinear fractional programming problem involving semidifferentiable functions introduced by Ewing, Kaul and Kaur. A dual is formulated and duality results are proved using concepts of semilocally quasiconvex and semilocally pseudoconvex functions. An equivalent program using generalized Charnes Cooper transformation is given

Duality for minmax programming involving nonsmooth v-invex functions

Sufficient optimality conditions and Mond-Weir duality results for a class of nonsmooth minmax programming problems are obtained under V-invexity type assumptions on objective and constraint functions. Applications of these results to certain nonsmooth fractional and nonsmooth generalized fractional programming duality are also presented

Converse duality in fractional programming

Craven [1] established the weak duality and the strong duality for a nonlinear fractional programming problem (FP), and investigated the sensitivity for (FP). The purpose of this brief paper is to obtain the converse duality for (FP), by using the Fritz John theorem.

On duality concepts in fractional programming

The paper (Part I) describes an approach to duality in fractional programming on the basis of another kind of conjugate functions. The connections to some duality concepts (the Lagrange-duality and duality concepts of Craven and Schaible) are investigated and some new proofs of strong duality theorems are given.

Multiobjective fractional programming duality. a Lagrangian approach

Duality and converse duality are studied for a class of multiobjective fractional programming problems, where properly efficient solutions are required. These are related to vector saddle points of a suitable vector valued Lagrangian.

Vector-valued lagrangian and multiobjective fractional programming duality

A class of multiobjective fractional programming problems is considered and duality results are established in terms of properly efficient solutions of the primal and dual programs. Further a vector-valued ratio type Lagrangian is introduced and certain vector saddlepoint results are presented.

Generalized fractional programming duality: A parametric approach

Using a parametric approach, duality is presented for a minimax fractional programming problem that involves several ratios in the objective function.

Duality for Fractional Programming with Generalized Convexity Conditions

Consider the problem of minimizing f(x)/g(x) subject to h(x)≤0 where f and g are differentiable functions from Rn into R and h is a differentiable function from Rn into Rm . Under the assumptions that f is convex and nonnegative, g is concave and positive (or fconvex and g linear and positive) and h is convex, a number of duality results can be found in the literature. Here we give a number of different duals that allow the weakening of these convexity requirements. A specific example is given where h is quasi-convex and not convex for which standard fractional programming duality does not apply but for which the duals proposed here do hold. Weak, strong and converse dual theorems are given for these new dual programs.

Fractional programming duality via geometric programming duality

AbstractA duality theory for a class of fractional programs is developed. A fractionalprogram which is non-convex is convexified using a one-to-one transformation. The resulting convex equivalent is then dualized with generalized geometric programming duality.

On Duality for Fractional Programming

On Duality for Fractional Programming

Duality in Fractional Programming: A Unified Approach

This paper presents a unified method for obtaining duality results for concave-convex fractional programs. We obtain these results by transforming the original nonconvex programming problem into an equivalent convex program. Known results by several authors are related to each other. Moreover, we prove additional duality theorems, in particular, converse duality theorems for nondifferentiable as well as quadratic fractional programs.

Duality in fractional programming

AbstractThis paper develops theoretical and computational aspects of the dual problem in linear fractional programming. This is done on the basis of two alternative methods for solving the primal fractional programming problem, both of which were presented in earlier literature. Parametric changes in the resource‐vector are considered, and attention is given to infinitesimal as well as to discrete changes.

Duality in fractional programming

In this paper, a dual problem to linear fractional functionals programming i. e. $$\begin{gathered} Maximise Z = \frac{{c'x}}{{d'x}} \hfill subject to Ax = b \hfill x \geqslant 0 \hfill \end{gathered} $$ is formulated. Certain duality theorems regarding the relationship between primal and dual problems are established.