Optimality conditions for Pareto efficiency and proper ideal point in set-valued nonsmooth vector optimization using contingent cone

Document Type : Research Paper


Department of Mathematics, Xidian University, Xi'an 710071, China


In this paper, we first present a new important property for Bouligand tangent cone (contingent cone) of a star-shaped set. We then establish optimality conditions for Pareto minima and proper ideal efficiencies in nonsmooth vector optimization problems by means of Bouligand tangent cone of image set, where the objective is generalized cone convex set-valued map, in general real normed spaces.


Main Subjects

  • Receive Date: 04 September 2013
  • Revise Date: 14 February 2014
  • Accept Date: 22 April 2014
  • First Publish Date: 15 June 2015