Variational conditions with smooth constraints: structure and analysis

 This is an expository paper about the analysis of variational conditions over sets defined in finite-dimensional spaces by fairly smooth functions satisfying a constraint qualification. The primary focus is on results that can provide quantitative and computable sensitivity information for particular instances of the problems under study, and our objective is to give a personal view of the state of current knowledge in this area and of gaps in that knowledge that require future work. The writing style is informal, in keeping with the objective of focusing the reader's attention on the basic concepts and the relationships between them, rather than on details of the particular results themselves. Received: December 1, 2002 / Accepted: April 25, 2003 Published online: May 28, 2003 Key words. variational condition – variational inequality – complementarity – sensitivity – stability – nondegeneracy Mathematics Subject Classification (2000): Primary: 90C31. Secondary: 47J20, 49J40, 49J53, 90C33