On the numerical treatment of the inclusion 0\(\in \partial f(x)\). (English) Zbl 0663.65064

Strodiot, J.-J.; Nguyen, V. H.

Topics in nonsmooth mechanics, 267-294 (1988).

[For the entire collection see Zbl 0646.00014.]
The authors address the numerical analysis of the bundle method applied to the minimization of a locally Lipschitz function. The method consists of computing approximations to the generalized gradient of F. Clarke [Optimization and nonsmooth analysis (1983; Zbl 0582.49001)] in order to choose a search direction at each step. Convergence proofs are given.

Reviewer: H.Matthies

MSC:

65K05	Numerical mathematical programming methods
90C30	Nonlinear programming

Keywords:

line search; nonsmooth optimization; bundle method; locally Lipschitz function; Convergence

Citations:

Zbl 0646.00014; Zbl 0582.49001