Article ID: | iaor20134045 |
Volume: | 56 |
Issue: | 2 |
Start Page Number: | 417 |
End Page Number: | 430 |
Publication Date: | Jun 2013 |
Journal: | Journal of Global Optimization |
Authors: | Kanzi Nader |
Keywords: | differential equations, Programming (semi-infinite), Lagrangian methods |
This paper aims to study a broad class of generalized semi‐infinite programming problems with (upper and lower level) objectives given as the difference of two convex functions, and (lower level) constraints described by a finite number of convex inequalities and a set constraints. First, we are interested in some various lower level constraint qualifications for the problem. Then, the results are used to establish efficient upper estimate of certain subdifferential of value functions. Finally, we apply the obtained subdifferential estimates to derive necessary optimality conditions for the problem.