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An ellipsoid trust region bundle method for nonsmooth convex minimization. (English) Zbl 0694.65026
Author’s summary: This paper presents a bundle method of descent for minimizing a convex (possibly nonsmooth) function f of several variables. At each iteration the algorithm finds a trial point by minimizing a polyhedral model of f subject to an ellipsoid trust region constraint. The quadratic matrix of the constraint, which is updated as in the ellipsoid method, is intended to serve as a generalized “Hessian” to account for “second-order” effects, thus enabling faster convergence. The interpretation of generalized Hessians is largely heuristic, since so far this notion has been made precise by J. L. Goffin [Math. Program. 30, 147-162 (1984; Zbl 0567.90068)] only in the solution of linear inequalities. Global convergence of the method is established and numerical results are given.
Reviewer: S.Zlobec

MSC:
65K05 Numerical mathematical programming methods
90C25 Convex programming
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