Second-order Dini set-valued directional derivative in C^1,1 vector optimization

Abstract

The constrained vector optimization problem is studied, where , and are C ^1,1 functions, and and are closed convex cones. In terms of the second-order Dini set-valued directional derivative, second-order necessary conditions a point x ⁰ to be a weakly efficient point and second-order sufficient conditions x ⁰ to be an isolated minimizer of order two are established.

Keywords:

• vector optimization
• C ^1,1 optimization
• second-order optimality conditions
• second-order directional derivatives
• Dini derivatives
• set-valued derivatives

AMS Subject Classification :

• 90C29
• 90C30
• 90C46
• 49J52