A combination of the bundle approach and the trust region concept. (English) Zbl 0658.90074

Advances in mathematical optimization, Pap. Dedic. F. Nožička Occas. 70. Birthday, Math. Res. 45, 196-209 (1988).
[For the entire collection see Zbl 0649.00015.]
The paper studies the minimization of a convex, nonsmooth function. A new algorithm is introduced, which combines the bundle idea in nonsmooth optimization and the trust region concept in differentiable optimization. Convergence results and some numerical examples are reported. More elaborate investigations, including constrained and non-convex problems will be presented in another paper of the first author [“Eine Kombination von Bundle- und Trust-Region-Verfahren zur Lösung nichtdifferenzierbarer Optimierungsprobleme”, Bayreuther Mathematische Schriften, Heft 30 (1989)].
Reviewer: H.Schramm


90C25 Convex programming
65K05 Numerical mathematical programming methods


Zbl 0649.00015