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 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 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.

scholarly journals Optimality and duality in set-valued optimization utilizing limit sets

2018 ◽  
Vol 16 (1) ◽  
pp. 1128-1139
Author(s):  
Xiangyu Kong ◽  
Yinfeng Zhang ◽  
GuoLin Yu
Keyword(s):  
Optimality Conditions ◽  
Duality Theory ◽  
Optimization Problem ◽  
Convex Set ◽  
Sufficient Optimality Conditions ◽  
Constraint Optimization ◽  
Limit Sets ◽  
Optimality And Duality ◽  
Wolfe Type Dual ◽  
Necessary And Sufficient

AbstractThis paper deals with optimality conditions and duality theory for vector optimization involving non-convex set-valued maps. Firstly, under the assumption of nearly cone-subconvexlike property for set-valued maps, the necessary and sufficient optimality conditions in terms of limit sets are derived for local weak minimizers of a set-valued constraint optimization problem. Then, applications to Mond-Weir type and Wolfe type dual problems are presented.

scholarly journals On generalized derivatives forC1,1vector optimization problems

2003 ◽  
Vol 2003 (7) ◽  
pp. 365-376 ◽  
Author(s):  
Davide La Torre
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Second Order ◽  
Clarke Subdifferential ◽  
Vector Optimization Problems ◽  
Directional Derivatives ◽  
Generalized Derivatives ◽  
Second Order Optimality Conditions

We introduce generalized definitions of Peano and Riemann directional derivatives in order to obtain second-order optimality conditions for vector optimization problems involvingC1,1data. We show that these conditions are stronger than those in literature obtained by means of second-order Clarke subdifferential.

scholarly journals Optimality and duality without a constraint qualification for minimax programming

2003 ◽  
Vol 67 (1) ◽  
pp. 121-130 ◽  
Author(s):  
Houchun Zhou ◽  
Wenyu Sun
Keyword(s):  
Optimality Conditions ◽  
Constraint Qualification ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Dual Model ◽  
Duality Theorems ◽  
Minimax Programming ◽  
Optimality And Duality ◽  
Necessary And Sufficient

Without the need of a constraint qualification, we establish the optimality necessary and sufficient conditions for generalised minimax programming. Using these optimality conditions, we construct a parametric dual model and a parameter-free mixed dual model. Several duality theorems are established.

scholarly journals Higher order optimality and duality in fractional vector optimization over cones

2017 ◽  
Vol 48 (3) ◽  
pp. 273-287 ◽  
Author(s):  
Muskan Kapoor ◽  
Surjeet Kaur Suneja ◽  
Meetu Bhatia Grover
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Convex Functions ◽  
Optimization Problem ◽  
Vector Optimization Problem ◽  
Higher Order ◽  
Sufficient Optimality Conditions ◽  
Dual Program ◽  
Duality Results ◽  
Optimality And Duality

In this paper we give higher order sufficient optimality conditions for a fractional vector optimization problem over cones, using higher order cone-convex functions. A higher order Schaible type dual program is formulated over cones.Weak, strong and converse duality results are established by using the higher order cone convex and other related functions.

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