Article ID: | iaor20134135 |
Volume: | 56 |
Issue: | 2 |
Start Page Number: | 713 |
End Page Number: | 725 |
Publication Date: | Jun 2013 |
Journal: | Journal of Global Optimization |
Authors: | Xiu Naihua, Peng Dingtao, Yu Jian |
Keywords: | calculus of variations, global optimization, mapping |
We first present a proper condition under which the image of a set‐valued mapping becomes a singleton and then obtain several generic uniqueness theorems which can be applied to study the uniqueness of the solutions for nonlinear problems. As applications, we prove that, in the sense of Baire category, most optimization problems (respectively, saddle point problems and variational inequality problems) have unique solution.