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Second-Order Nonsmooth Analysis in Nonlinear Programming

By René Poliquin and Terry Rockafellar

Abstract

Problems of nonlinear programming are placed in a broader framework of composite optimization. This allows second-order smoothness in the data structure to be utilized despite apparent nonsmoothness in the objective. Second-order epi-derivatives are shown to exist as expressions of such underlying smoothness, and their connection with several kinds of second-order approximation is examined. Expansions of the Moreau envelope functions and proximal mappings associated with the essential objective functions for certain optimization problems in composite format are studied in particular

Publisher: World Scientific Publishers
Year: 1995
OAI identifier: oai:CiteSeerX.psu:10.1.1.161.7174
Provided by: CiteSeerX
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