Abstract
Certain nonsmooth functions are viewed as piecewise smooth functions, which are composed of a finite number of smooth functions. Second order necessary and sufficient conditions are established for this class of nonsmooth functions. However when a piecewise smooth function cannot be expressed as the maximum of its component functions there are severe limitations in the usual first order necessary conditions, and simple examples are given to illustrate these limitations. Interpretations of the multipliers arising in the first order conditions and of the curvature information in the second order conditions are also given.
This paper was prepared while the author was visiting the University of Kentucky, Lexington, and was partially supported by National Science Foundation Grant #ECS-7923272.
Present address: School of Mathematics, University of New South Wales, Kensington, N.S.W., Australia 2031.
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© 1982 The Mathematical Programming Society, Inc.
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Womersley, R.S. (1982). Optimality conditions for piecewise smooth functions. In: Sorensen, D.C., Wets, R.J.B. (eds) Nondifferential and Variational Techniques in Optimization. Mathematical Programming Studies, vol 17. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120957
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DOI: https://doi.org/10.1007/BFb0120957
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