Conditions on Twice Continuous Codifferentiability of Quasidifferentiable Functions

The authors study the twice codifferentiable functions introduced by Professor V.F. Demyanov and how to calculate their second codifferentials. We proved that a twice hypodifferentiable positively homogeneous (p.h.) function of the second order is the maximum of quadratic forms over some set of matr...

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Bibliographic Details
Published in:Journal of optimization theory and applications 2024-12, Vol.203 (3), p.2848-2869
Main Authors: Prudnikov, I. M., Duxbury, N. S.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Calculus of Variations and Optimal Control
Optimization
Codification
Continuity (mathematics)
Decomposition
Engineering
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Quadratic forms
Theorems
Theory of Computation
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Summary:The authors study the twice codifferentiable functions introduced by Professor V.F. Demyanov and how to calculate their second codifferentials. We proved that a twice hypodifferentiable positively homogeneous (p.h.) function of the second order is the maximum of quadratic forms over some set of matrices from a convex compact set, which coincides with the subdifferential of the second order introduced by the authors. This paper is the logical continuation of previous papers. The subdifferentials of the first and second orders are used to calculate the second codifferential at a point up to equivalence. The proved theorems give the rules for calculation of the second codifferentials. The theorem deals with twice continuous codifferentiability of a locally Lipschitz quasidifferentiable function whose second subdifferential and second superdifferential are upper semicontinuous (USC).
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-024-02549-5