Open Access
2014 On Nonsmooth Semi-Infinite Minimax Programming Problem with (Φ,ρ)-Invexity
X. L. Liu, G. M. Lai, C. Q. Xu, D. H. Yuan
Abstr. Appl. Anal. 2014: 1-7 (2014). DOI: 10.1155/2014/317304


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.


Download Citation

X. L. Liu. G. M. Lai. C. Q. Xu. D. H. Yuan. "On Nonsmooth Semi-Infinite Minimax Programming Problem with (Φ,ρ)-Invexity." Abstr. Appl. Anal. 2014 1 - 7, 2014.


Published: 2014
First available in Project Euclid: 2 October 2014

MathSciNet: MR3178864
Digital Object Identifier: 10.1155/2014/317304

Rights: Copyright © 2014 Hindawi

Vol.2014 • 2014
Back to Top