IJPAM: Volume 87, No. 4 (2013)

ON A NONDIFFERENTIABLE VECTOR OPTIMIZATION
INVOLVING SEMI $E$-TYPE-I MAPS IN BANACH SPACES

Hehua Jiao
College of Mathematics and Computer
Yangtze Normal University
Fuling, 408100, Chongqing, P.R.CHINA


Abstract. This paper deals with a vector optimization problem with restrictions of inequalities involving nondifferentiable maps in Banach spaces. Some new concepts of $\eta$-$E$-semidifferentiablity, semi $E$-invexity and semi $E$-type-I maps in Banach spaces are introduced. A necessary optimality condition and a few sufficient optimality conditions are obtained by generalizing alternative theorem of Gordan type and using semi $E$-type-I maps. Moreover, weak, strong and converse duality results are proved under various types of semi $E$-type-I maps assumptions.

Received: November 11, 2012

AMS Subject Classification: 90C46, 90C48

Key Words and Phrases: $\eta$-$E$-semidifferentiablity, semi $E$-invexity, semi $E$-type-I maps, vector optimization, optimality, duality

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DOI: 10.12732/ijpam.v87i4.1 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 87
Issue: 4