scholarly journals Duality for Unified Higher-Order Minimax Fractional Programming with Support Function under Type-I Assumptions

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1034 ◽  
Author(s):  
Ramu Dubey ◽  
Vishnu Narayan Mishra ◽  
and Rifaqat Ali
Keyword(s):  
Programming Problem ◽  
Fractional Programming ◽  
Support Function ◽  
Final Section ◽  
Higher Order ◽  
Type I ◽  
Dual Model ◽  
Duality Theorems ◽  
Fractional Programming Problem ◽  
Minimax Fractional Programming

This article is devoted to discussing the nondifferentiable minimax fractional programming problem with type-I functions. We focus our study on a nondifferentiable minimax fractional programming problem and formulate a higher-order dual model. Next, we establish weak, strong, and strict converse duality theorems under generalized higher-order strictly pseudo ( V , α , ρ , d ) -type-I functions. In the final section, we turn our focus to study a nondifferentiable unified minimax fractional programming problem and the results obtained in this paper naturally unify. Further, we extend some previously known results on nondifferentiable minimax fractional programming in the literature.

Higher-order fractional programming problem and their duality theorems in vector optimization with cone-η − invex functions

2021 ◽  
Author(s):  
Tarun Kumar Gupta ◽  
Rajesh Kumar Tripathi ◽  
Chetan Swarup ◽  
Kuldeep Singh ◽  
Ramu Dubey ◽  
...  
Keyword(s):  
Programming Problem ◽  
Vector Optimization ◽  
Fractional Programming ◽  
Higher Order ◽  
Duality Theorems ◽  
Fractional Programming Problem ◽  
Invex Functions

scholarly journals Nondifferentiable generalized minimax fractional programming under (Ф,ρ)-invexity

2021 ◽  
pp. 18-18
Author(s):  
B.B. Upadhyay ◽  
T. Antczak ◽  
S.K. Mishra ◽  
K. Shukla
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Fractional Programming ◽  
Sufficient Optimality Conditions ◽  
Duality Theorems ◽  
Dual Problems ◽  
Fractional Programming Problem ◽  
Minimax Fractional Programming ◽  
Dual Models

In this paper, a class of nonconvex nondifferentiable generalized minimax fractional programming problems is considered. Sufficient optimality conditions for the considered nondifferentiable generalized minimax fractional programming problem are established under the concept of (?,?)-invexity. Further, two types of dual models are formulated and various duality theorems relating to the primal minimax fractional programming problem and dual problems are established. The results established in the paper generalize and extend several known results in the literature to a wider class of nondifferentiable minimax fractional programming problems. To the best of our knowledge, these results have not been established till now.

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.

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].

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.

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