Partial Second-Order Subdifferentials in Variational Analysis and Optimization

Abstract

This article presents a systematic study of partial second-order subdifferentials for extended-real-valued functions, which have already been applied to important issues of variational analysis and constrained optimization in finite-dimensional spaces. The main results concern developing extended calculus rules for these second-order constructions in both finite-dimensional and infinite-dimensional frameworks. We also provide new applications of partial second-order subdifferentials to Lipschitzian stability of stationary point mappings in parametric constrained optimization and discuss some other applications.

Keywords:

• Coderivatives
• Generalized differentiation
• Parametric constrained optimization
• Second-order subdifferentials
• Stability
• Stationary point mappings
• Variational analysis

Mathematics Subject Classification:

• 49J53
• 49J52
• 90C31

ACKNOWLEDGMENTS

The authors gratefully acknowledge helpful discussions with René Henrion, Jiří Outrata, Nguyen Thanh Qui, Terry Rockafellar, Alex Shapiro, and Nguyen Dong Yen on the topics and results of the article.

Part of the special issue, “Variational Analysis and Applications.”