- Title
- Nonsmooth calculus in finite dimensions
- Creator
- Ward, D. E.; Borwein, J. M.
- Relation
- SIAM Journal on Control and Optimization Vol. 25, Issue 5, p. 1312-1340
- Publisher Link
- http://dx.doi.org/10.1137/0325072
- Publisher
- Society for Industrial and Applied Mathematics (SIAM)
- Resource Type
- journal article
- Date
- 1987
- Description
- The notion of subgradient, originally defined for convex functions, has in recent years been extended, via the “upper subderivative,” to cover functions that are not necessarily convex or even continuous. A number of calculus rules have been proven for these generalized subgradients. This paper develops the finite-dimensional generalized subdifferential calculus for (strictly) lower semicontinuous functions under considerably weaker hypotheses than those previously used. The most general finite-dimensional convex subdifferential calculus results are recovered as corollaries. Other corollaries given include new necessary conditions for optimality in a nonsmooth mathematical program. Various chain rule formulations are considered. Equality in the subdifferential calculus formulae is proven under hypotheses weaker than the usual “subdifferential regularity” assumptions.
- Subject
- Clarke tangent cone; upper subderivative; subgradient; contingent cone; subdifferential regularity
- Identifier
- http://hdl.handle.net/1959.13/940751
- Identifier
- uon:13086
- Identifier
- ISSN:0363-0129
- Language
- eng
- Full Text
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