Duality for a Nondifferentiable Multiobjective Second-Order Fractional Programming Problem Involving $$(F,\alpha ,\rho ,d)$$ —V-type-I Functions

2015 ◽  
pp. 729-741
Author(s):  
Ramu Dubey ◽  
S. K. Gupta
Keyword(s):  
Programming Problem ◽  
Fractional Programming ◽  
Second Order ◽  
Type I ◽  
Fractional Programming Problem

On duality for a second-order multiobjective fractional programming problem involving type-I functions

2019 ◽  
Vol 26 (3) ◽  
pp. 393-404 ◽  
Author(s):  
Ramu Dubey ◽  
S. K. Gupta
Keyword(s):  
Programming Problem ◽  
Fractional Programming ◽  
Compact Convex ◽  
Second Order ◽  
Type I ◽  
Multiobjective Fractional Programming ◽  
Fractional Programming Problem ◽  
Multiobjective Fractional Programming Problem ◽  
Compact Convex Set ◽  
Formula Type

Abstract The purpose of this paper is to study a nondifferentiable multiobjective fractional programming problem (MFP) in which each component of objective functions contains the support function of a compact convex set. For a differentiable function, we introduce the class of second-order {(C,\alpha,\rho,d)-V} -type-I convex functions. Further, Mond–Weir- and Wolfe-type duals are formulated for this problem and appropriate duality results are proved under the aforesaid assumptions.

scholarly journals A Full-Newton Step Interior Point Method for Fractional Programming Problem Involving Second Order Cone Constraint

2021 ◽  
pp. 427-433
Author(s):  
Mansour Saraj ◽  
Ali Sadeghi ◽  
Nezam Mahdavi Amiri
Keyword(s):  
Programming Problem ◽  
Interior Point ◽  
Barrier Function ◽  
Fractional Programming ◽  
Second Order ◽  
Fractional Programming Problem ◽  
Newton Step ◽  
Cone Constraint ◽  
Second Order Cone ◽  
Logarithmic Barrier

Some efficient interior-point methods (IPMs) are based on using a self-concordant barrier function related to the feasibility set of the underlying problem.Here, we use IPMs for solving fractional programming problems involving second order cone constraints. We propose a logarithmic barrier function to show the self concordant property and present an algorithm to compute $\varepsilon-$solution of a fractional programming problem. Finally, we provide a numerical example to illustrate the approach.

scholarly journals On Second-Order Duality for Minimax Fractional Programming Problems with Generalized Convexity

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Izhar Ahmad
Keyword(s):  
Programming Problem ◽  
Fractional Programming ◽  
Generalized Convexity ◽  
Second Order ◽  
Fractional Programming Problem ◽  
Second Order Duality ◽  
Minimax Fractional Programming ◽  
Dual Models

We focus our study on a discussion of duality relationships of a minimax fractional programming problem with its two types of second-order dual models under the second-order generalized convexity type assumptions. Results obtained in this paper naturally unify and extend some previously known results on minimax fractional programming in the literature.

scholarly journals Duality for multiobjective fractional programming problems involving d -type-I n-set functions

2009 ◽  
Vol 19 (1) ◽  
pp. 63-73
Author(s):  
I.M. Stancu-Minasian ◽  
Gheorghe Dogaru ◽  
Mădălina Stancu
Keyword(s):  
Programming Problem ◽  
Fractional Programming ◽  
Generalized Convexity ◽  
Type I ◽  
Multiobjective Fractional Programming ◽  
Fractional Programming Problem ◽  
Duality Results ◽  
Set Functions ◽  
Convexity Assumptions ◽  
Nonlinear Fractional Programming

We establish duality results under generalized convexity assumptions for a multiobjective nonlinear fractional programming problem involving d -type-I n -set functions. Our results generalize the results obtained by Preda and Stancu-Minasian [24], [25].

scholarly journals Minimax fractional programming problem involving nonsmooth generalized ?-univex functions

2012 ◽  
Vol 3 (1) ◽  
pp. 7-22 ◽  
Author(s):  
Anurag JAYSWAL ◽  
Rajnish KUMAR ◽  
Dilip KUMAR
Keyword(s):  
Programming Problem ◽  
Fractional Programming ◽  
Sufficient Optimality Conditions ◽  
Type I ◽  
Fractional Programming Problem ◽  
New Class ◽  
Locally Lipschitz ◽  
Minimax Fractional Programming ◽  
Generalized Type ◽  
Appl Math

In this paper, we introduce a new class of generalized ?-univex functions where the involved functions are locally Lipschitz. We extend the concept of ?-type I invex [S. K. Mishra, J. S. Rautela, On nondifferentiable minimax fractional programming under generalized ?-type I invexity, J. Appl. Math. Comput. 31 (2009) 317-334] to ?-univexity and an example is provided to show that there exist functions that are ?-univex but not ?-type I invex. Furthermore, Karush-Kuhn-Tucker-type sufficient optimality conditions and duality results for three different types of dual models are obtained for nondifferentiable minimax fractional programming problem involving generalized ?-univex functions. The results in this paper extend some known results in the literature.

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