Favorable Classes of Lipschitz Continuous Functions in Subgradient Optimization

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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/1793 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/1793 http://eprints.org/relation/isCoversheetVersionOf https://pure.iiasa.ac.at/id/document/1793 archive 351 disk0/00/00/17/60 2016-01-15 01:50:23 2021-08-27 17:10:31 2016-01-15 01:50:23 monograph show 2 Rockafellar R.T. AL0338 Favorable Classes of Lipschitz Continuous Functions in Subgradient Optimization pub iis_met prog_sds Clarke has given a robust definition of subgradients of arbitrary Lipschitz continuous functions f on R^n, but for purposes of minimization algorithms it seems essential that the subgradient multifunction partial f have additional properties, such as certain special kinds of semicontinuity, which are not automatic consequences of f being Lipschitz continuous. This paper explores properties of partial f that correspond to f being subdifferentially regular, another concept of Clarke's, and to f being a pointwise supremum of functions that are k times continuously differentiable. 1981-01 published WP-81-001 WP-81-001 2336 public working_paper IIASA, Laxenburg, Austria 22 FALSE info:eu-repo/semantics/book