Article ID: | iaor200971924 |
Country: | Germany |
Volume: | 70 |
Issue: | 2 |
Start Page Number: | 195 |
End Page Number: | 218 |
Publication Date: | Oct 2009 |
Journal: | Mathematical Methods of Operations Research |
Authors: | Zhang Liwei, Wang Yun |
Keywords: | programming: quadratic |
We give an equation reformulation of the Karush–Kuhn–Tucker (KKT) condition for the second order cone optimization problem. The equation is strongly semismooth and its Clarke subdifferential at the KKT point is proved to be nonsingular under the constraint nondegeneracy condition and a strong second order sufficient optimality condition. This property is used in an implicit function theorem of semismooth functions to analyze the convergence properties of a local sequential quadratic programming type (for short, SQP-type) method by Kato and Fukushima (2007). Moreover, we prove that, a local solution