Generalized second-order derivative in nonsmooth optimization

R. Cominetti, R. Correa

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104 Scopus citations


In this work a new notion of generalized second-order directional derivative and generalized Hessian for nonsmooth real-valued functions is studied. The general properties of these mathematical objects are investigated together with some calculus rules that may facilitate their practical computation. Two applications of these derivatives in optimization theory are considered: first, to obtaining necessary and sufficient second-order optimality conditions for problems with or without constraints; and second, to extending the Newton method for the minimization of a c1.1 function.

Original languageEnglish
Pages (from-to)789-809
Number of pages21
JournalSIAM Journal on Control and Optimization
Issue number4
StatePublished - 1990


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