scholarly journals Optimality conditions and duality for nonsmooth minimax programming problems under generalized invexity

Filomat ◽  
2016 ◽  
Vol 30 (5) ◽  
pp. 1253-1261
Author(s):  
Meraj Khan
Keyword(s):  
Optimality Conditions ◽  
Generalized Invexity ◽  
Minimax Programming ◽  
Invex Functions ◽  
Duality Results ◽  
Locally Lipschitz ◽  
Generalized Invex Functions ◽  
Usual Duality

In this paper, we consider a class of nonsmooth minimax programming problems in which functions are locally Lipschitz. Sucient optimality conditions are discussed under locally Lipschitz generalized (?,?)-invex functions. Moreover, usual duality results are proved under the said assumptions.

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 for nonsmooth minimax programming problems using convexifactor

Filomat ◽  
2017 ◽  
Vol 31 (14) ◽  
pp. 4555-4570 ◽  
Author(s):  
I. Ahmad ◽  
Krishna Kummari ◽  
Vivek Singh ◽  
Anurag Jayswal
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Vector Optimization ◽  
Duality Theory ◽  
Generalized Convexity ◽  
Clarke Subdifferential ◽  
Locally Lipschitz Functions ◽  
Minimax Programming ◽  
Locally Lipschitz ◽  
Optimality And Duality

The aim of this work is to study optimality conditions for nonsmooth minimax programming problems involving locally Lipschitz functions by means of the idea of convexifactors that has been used in [J. Dutta, S. Chandra, Convexifactors, generalized convexity and vector optimization, Optimization, 53 (2004) 77-94]. Further, using the concept of optimality conditions, Mond-Weir and Wolfe type duality theory has been developed for such a minimax programming problem. The results in this paper extend the corresponding results obtained using the generalized Clarke subdifferential in the literature.

scholarly journals On a Nonsmooth Vector Optimization Problem with Generalized Cone Invexity

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Hehua Jiao ◽  
Sanyang Liu
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Optimization Problem ◽  
Vector Optimization Problem ◽  
Sufficient Optimality Conditions ◽  
Generalized Gradients ◽  
Invex Functions ◽  
Duality Results ◽  
Nonsmooth Vector Optimization ◽  
Cone Constraints

By using Clarke’s generalized gradients we consider a nonsmooth vector optimization problem with cone constraints and introduce some generalized cone-invex functions calledK-α-generalized invex,K-α-nonsmooth invex, and other related functions. Several sufficient optimality conditions and Mond-Weir type weak and converse duality results are obtained for this problem under the assumptions of the generalized cone invexity. The results presented in this paper generalize and extend the previously known results in this area.

scholarly journals Sufficient Conditions and Duality Theorems for Nondifferentiable Minimax Fractional Programming

2011 ◽  
Vol 2011 ◽  
pp. 1-22
Author(s):  
Shun-Chin Ho
Keyword(s):  
Optimality Conditions ◽  
Fractional Programming ◽  
Sufficient Conditions ◽  
Sufficient Optimality Conditions ◽  
Duality Theorems ◽  
Invex Functions ◽  
Duality Results ◽  
Wolfe Duality ◽  
Minimax Fractional Programming

We consider nondifferentiable minimax fractional programming problems involving B-(p, r)-invex functions with respect to η and b. Sufficient optimality conditions and duality results for a class of nondifferentiable minimax fractional programming problems are obtained undr B-(p, r)-invexity assumption on objective and constraint functions. Parametric duality, Mond-Weir duality, and Wolfe duality problems may be formulated, and duality results are derived under B-(p, r)-invex functions.

scholarly journals Continuous programming containing arbitrary norms

1985 ◽  
Vol 39 (1) ◽  
pp. 28-38 ◽  
Author(s):  
S. Chandra ◽  
B. D. Craven ◽  
I. Husain
Keyword(s):  
Mathematical Programming ◽  
Constrained Optimization ◽  
Optimality Conditions ◽  
Duality Result ◽  
Duality Results ◽  
Continuous Programming ◽  
Arbitrary Norms ◽  
Abstract Spaces ◽  
Special Case

AbstractOptimality conditions and duality results are obtained for a class of cone constrained continuous programming problems having terms with arbitrary norms in the objective and constraint functions. The proofs are based on a Fritz John theorem for constrained optimization in abstract spaces. Duality results for a fractional analogue of such continuous programming problems are indicated and a nondifferentiable mathematical programming duality result, not explicitly reported in the literature, is deduced as a special case.

SEQUENTIAL LAGRANGE MULTIPLIER CONDITIONS FOR MINIMAX PROGRAMMING PROBLEMS

2008 ◽  
Vol 25 (02) ◽  
pp. 113-133 ◽  
Author(s):  
ANULEKHA DHARA ◽  
APARNA MEHRA
Keyword(s):  
Lagrange Multiplier ◽  
Constraint Qualification ◽  
Minimax Programming ◽  
Duality Results ◽  
Multiplier Rules ◽  
Cone Constraint

In this article, we study nonsmooth convex minimax programming problems with cone constraint and abstract constraint. Our aim is to develop sequential Lagrange multiplier rules for this class of problems in the absence of any constraint qualification. These rules are obtained in terms of ∊-subdifferentials of the functions. As an application of these rules, a sequential dual is proposed and sequential duality results are presented.

scholarly journals Optimality Conditions and Duality for Multiobjective Variational Problems with Generalized -B-Type-I Functions

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
C. Nahak ◽  
N. Behera
Keyword(s):  
Optimality Conditions ◽  
Variational Problems ◽  
Sufficient Optimality Conditions ◽  
Type I ◽  
Duality Results ◽  
Multiobjective Variational Problems ◽  
Generalized Type

We use -type-I and generalized -type-I functions to establish sufficient optimality conditions and duality results for multiobjective variational problems. Some of the related problems are also discussed.

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