A method of approximating a quasidifferential
The theory of quasidifferentials (QD) is a convenient mechanism for solving many problems in non smooth analysis and non smooth optimization. A calculus with equalities has been constructed for QD. Numerical minimization techniques have been devised which use QD. However, in the best case the components of the QD of non smooth functions are mappings which are semicontinuous from above, making them difficult to use in numerical minimization. This explains the importance of investigating continuous approximations of QD. The numerical method of approximating QD proposed in this paper uses the function values only. Thus, first, a relation is established between the QD of a function and its value and, second, a method for constructing a continuous approximation of the QD of a function, using the concept of a discrete gradient, is proposed.
scientific article; zbMATH DE number 921577