A Subdifferential Condition for Calmness of Multifunctions

✍ Scribed by René Henrion; Jirı́ Outrata

• Book ID: 102594798
• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 159 KB
• Volume: 258
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.2000.7363

✦ Synopsis

A condition ensuring calmness of a class of multifunctions between finite-dimensional spaces is derived in terms of subdifferential concepts developed by Mordukhovich. The considered class comprises general constraint set mappings as they occur in optimization or mappings associated with a certain type of variational system. The condition ensuring calmness is obtained as an appropriate reduction of Mordukhovich's well-known characterization of the stronger Aubin property. ŽRoughly spoken, one may pass to the boundaries of normal cones or subdifferen-. tials when aiming at calmness. It allows one to derive dual constraint qualifications in nonlinear optimization that are weaker than conventional ones Ž . e.g., Mangasarian᎐Fromovitz but still sufficient for the existence of Lagrange multipliers.