Nonsmooth calculus in finite dimensions

Ward, D. E. and Borwein, Jonathan M. (1987) Nonsmooth calculus in finite dimensions. SIAM Journal on Control and Optimization, 25 . pp. 1312-1340. ISSN 0363-0129

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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.

Item Type: Article
Depositing User: Mrs Naghmana Tehseen
Date Deposited: 20 Feb 2015 16:20
Last Modified: 20 Feb 2015 16:20

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