Saddle point criteria in semi-infinite minimax fractional programming under (Φ,ρ)-invexity

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2557-2574 ◽  
Author(s):  
Tadeusz Antczak
Keyword(s):  
Saddle Point ◽  
Fractional Programming ◽  
Generalized Convexity ◽  
Equality Constraints ◽  
New Class ◽  
Minimax Fractional Programming

Semi-infinite minimax fractional programming problems with both inequality and equality constraints are considered. The sets of parametric saddle point conditions are established for a new class of nonconvex differentiable semi-infinite minimax fractional programming problems under(?,?)-invexity assumptions. With the reference to the said concept of generalized convexity, we extend some results of saddle point criteria for a larger class of nonconvex semi-infinite minimax fractional programming problems in comparison to those ones previously established in the literature.

scholarly journals Optimality and Duality for Nondifferentiable Minimax Fractional Programming with Generalized Convexity

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Anurag Jayswal
Keyword(s):  
Fractional Programming ◽  
Generalized Convexity ◽  
Optimality Criteria ◽  
Sufficient Optimality Conditions ◽  
View Point ◽  
Generalized Convex Functions ◽  
Duality Results ◽  
Minimax Fractional Programming ◽  
Optimality And Duality ◽  
Dual Models

We establish several sufficient optimality conditions for a class of nondifferentiable minimax fractional programming problems from a view point of generalized convexity. Subsequently, these optimality criteria are utilized as a basis for constructing dual models, and certain duality results have been derived in the framework of generalized convex functions. Our results extend and unify some known results on minimax fractional programming problems.

scholarly journals On nondifferentiable minimax fractional programming involving higher order generalized convexity

Filomat ◽  
2013 ◽  
Vol 27 (8) ◽  
pp. 1497-1504 ◽  
Author(s):  
Anurag Jayswal ◽  
Kumar Prasad ◽  
Krishna Kummari
Keyword(s):  
Fractional Programming ◽  
Generalized Convexity ◽  
Higher Order ◽  
Minimax Fractional Programming

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 Sufficient optimality conditions for semi-infinite multiobjective fractional programming under (Ф,ρ)-V-invexity and generalized (Ф,ρ)-V-invexity

Filomat ◽  
2016 ◽  
Vol 30 (14) ◽  
pp. 3649-3665 ◽  
Author(s):  
Tadeusz Antczak
Keyword(s):  
Optimality Conditions ◽  
Fractional Programming ◽  
Generalized Convexity ◽  
Optimization Problems ◽  
Fundamental Property ◽  
Efficient Solutions ◽  
Sufficient Optimality Conditions ◽  
Multiobjective Fractional Programming ◽  
New Class ◽  
Multiobjective Programming Problems

A new class of nonconvex smooth semi-infinite multiobjective fractional programming problems with both inequality and equality constraints is considered. We formulate and establish several parametric sufficient optimality conditions for efficient solutions in such nonconvex vector optimization problems under (?,?)-V-invexity and/or generalized (?,?)-V-invexity hypotheses. With the reference to the said functions, we extend some results of efficiency for a larger class of nonconvex smooth semi-infinite multiobjective programming problems in comparison to those ones previously established in the literature under other generalized convexity notions. Namely, we prove the sufficient optimality conditions for such nonconvex semi-infinite multiobjective fractional programming problems in which not all functions constituting them have the fundamental property of convexity, invexity and most generalized convexity notions.

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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