scholarly journals Minimax fractional programming with nondiferentiable (G,β)-invexity

Filomat ◽  
2014 ◽  
Vol 28 (10) ◽  
pp. 2027-2035 ◽  
Author(s):  
Xiaoling Liu ◽  
Dehui Yuan
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Fractional Programming ◽  
Dual Problem ◽  
Necessary Optimality Conditions ◽  
Minimax Programming ◽  
Fractional Programming Problem ◽  
Duality Results ◽  
Locally Lipschitz ◽  
Minimax Fractional Programming

In this paper, we consider the minimax fractional programming Problem (FP) in which the functions are locally Lipschitz (G,?)-invex. With the help of a useful auxiliary minimax programming problem, we obtain not only G-sufficient but also G-necessary optimality conditions theorems for the Problem (FP). With G-necessary optimality conditions and (G,?)-invexity in the hand, we further construct dual Problem (D) for the primal one (FP) and prove duality results between Problems (FP) and (D). These results extend several known results to a wider class of programs.

scholarly journals Generalized Minimax Programming with Nondifferentiable (G,β)-Invexity

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
D. H. Yuan ◽  
X. L. Liu
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Dual Problem ◽  
Necessary Optimality Conditions ◽  
Minimax Programming ◽  
Duality Results ◽  
Locally Lipschitz

We consider the generalized minimax programming problem (P) in which functions are locally Lipschitz (G,β)-invex. Not onlyG-sufficient but alsoG-necessary optimality conditions are established for problem (P). WithG-necessary optimality conditions and (G,β)-invexity on hand, we construct dual problem (DI) for the primal one (P) and prove duality results between problems (P) and (DI). These results extend several known results to a wider class of programs.

scholarly journals Optimality and duality in continuous-time nonlinear fractional programming

1992 ◽  
Vol 34 (2) ◽  
pp. 229-244 ◽  
Author(s):  
S. Suneja ◽  
C. Singh ◽  
R. N. Kaul
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Continuous Time ◽  
Fractional Programming ◽  
Dual Problem ◽  
Fractional Programming Problem ◽  
Duality Results ◽  
Perturbation Functions ◽  
Optimality And Duality ◽  
Nonlinear Fractional Programming

AbstractOptimality conditions via subdifferentiability and generalised Charnes-Cooper transformation are obtained for a continuous-time nonlinear fractional programming problem. Perturbation functions play a key role in the development. A dual problem is presented and certain duality results are obtained.

scholarly journals Optimality and duality for a class of nondifferentiable minimax fractional programming problems

2009 ◽  
Vol 19 (1) ◽  
pp. 49-61
Author(s):  
Antoan Bătătorescu ◽  
Miruna Beldiman ◽  
Iulian Antonescu ◽  
Roxana Ciumara
Keyword(s):  
Optimality Conditions ◽  
Fractional Programming ◽  
Dual Problem ◽  
Sufficient Optimality Conditions ◽  
Square Root ◽  
Duality Results ◽  
Minimax Fractional Programming ◽  
Optimality And Duality ◽  
Necessary And Sufficient

Necessary and sufficient optimality conditions are established for a class of nondifferentiable minimax fractional programming problems with square root terms. Subsequently, we apply the optimality conditions to formulate a parametric dual problem and we prove some duality results.

scholarly journals Multiobjective programming under nondifferentiable G-V-invexity

Filomat ◽  
2016 ◽  
Vol 30 (11) ◽  
pp. 2909-2923 ◽  
Author(s):  
Tadeusz Antczak
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Dual Problem ◽  
Multiobjective Programming ◽  
Necessary Optimality Conditions ◽  
Vector Optimization Problem ◽  
Alternative Theorem ◽  
Nonsmooth Multiobjective Programming ◽  
Locally Lipschitz ◽  
Multiobjective Programming Problem

In the paper, new Fritz John type necessary optimality conditions and new Karush-Kuhn-Tucker type necessary opimality conditions are established for the considered nondifferentiable multiobjective programming problem involving locally Lipschitz functions. Proofs of them avoid the alternative theorem usually applied in such a case. The sufficiency of the introduced Karush-Kuhn-Tucker type necessary optimality conditions are proved under assumptions that the functions constituting the considered nondifferentiable multiobjective programming problem are G-V-invex with respect to the same function ?. Further, the so-called nondifferentiable vector G-Mond-Weir dual problem is defined for the considered nonsmooth multiobjective programming problem. Under nondifferentiable G-V-invexity hypotheses, several duality results are established between the primal vector optimization problem and its G-dual problem in the sense of Mond-Weir.

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 Nonsmooth Semi-Infinite Minimax Programming Problem with(Φ,ρ)-Invexity

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
X. L. Liu ◽  
G. M. Lai ◽  
C. Q. Xu ◽  
D. H. Yuan
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Necessary Optimality Conditions ◽  
Duality Theorems ◽  
Converse Duality ◽  
Minimax Programming ◽  
Carathéodory’S Theorem

We are interested in a nonsmooth minimax programming Problem (SIP). Firstly, we establish the necessary optimality conditions theorems for Problem (SIP) when using the well-known Caratheodory's theorem. Under the Lipschitz(Φ,ρ)-invexity assumptions, we derive the sufficiency of the necessary optimality conditions for the same problem. We also formulate dual and establish weak, strong, and strict converse duality theorems for Problem (SIP) and its dual. These results extend several known results to a wider class of problems.

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