Journal Article10.1137/0328045
A generalized second-order derivative in nonsmooth optimization
Roberto Cominetti,R. Correa +1 more
144
TL;DR: In this paper, a new notion of generalized second-order directional derivatives and generalized Hessian for nonsmooth real-valued functions is studied, together with some calculus rules that may facilitate their practical computation.
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Abstract: 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 $\mathcal{C}^{1,1} $ function.
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Citations
The -Lagrangian of a convex function
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Generalized second-order directional derivatives and optimization with C1,1 functions
TL;DR: In this paper, a generalized second-order directional derivative and a set-valued generalized Hessian for C 1, 1 functions in real Banach spaces are presented. But the generalized Hessians are not generalized to general functions.
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Second-order global optimality conditions for convex composite optimization
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