Abstract
We present second-order subdifferentials of Clarke's type of C 1,1 functions, defined in Banach spaces with separable duals. One of them is an extension of the generalized Hessian matrix of such functions in ℝn, considered by J. B. H.-Urruty, J. J. Strodiot and V. H. Nguyen. Various properties of these subdifferentials are proved. Second-order optimality conditions (necessary, sufficient) for constrained minimization problems with C 1,1 data are obtained.
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This work was partially supported by the National Foundation for Scientific Investigations in Bulgaria under contract No. MM-406/1994.
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Georgiev, P.G., Zlateva, N.P. Second-order subdifferentials of C 1,1 functions and optimality conditions. Set-Valued Anal 4, 101–117 (1996). https://doi.org/10.1007/BF00425960
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DOI: https://doi.org/10.1007/BF00425960