# Sufficiency and duality for a nonsmooth vector optimization problem with generalized $\alpha$-$d_{I}$-type-I univexity over cones‎

Document Type: Research Paper

Author

School of Mathematics and Statistics, Yangtze Normal University, Chongqing 408100‎, P. R. ‎China.

Abstract

In this paper, using Clarke’s generalized directional derivative and dI-invexity we introduce new concepts of nonsmooth K-α-dI-invex and generalized type I univex functions over cones for a nonsmooth vector optimization problem with cone constraints. We obtain some sufficient optimality conditions and Mond-Weir type duality results under the foresaid generalized invexity and type I cone-univexity assumptions.

Keywords

Main Subjects

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### History

• Receive Date: 05 October 2013
• Revise Date: 28 October 2014
• Accept Date: 20 December 2014