Optimality Conditions of Vector Set-Valued Optimization Problem Involving Relative Interior
College of Sciences, Shanghai University, Shanghai 200444, China
Department of Applied Mathematics, Chongqing University of Technology, Chongqing 400054, China
Journal of Inequalities and Applications 2011, 2011:183297 doi:10.1155/2011/183297Published: 8 February 2011
Firstly, a generalized weak convexlike set-valued map involving the relative interior is introduced in separated locally convex spaces. Secondly, a separation property is established. Finally, some optimality conditions, including the generalized Kuhn-Tucker condition and scalarization theorem, are obtained.