Lokale konvergenzeigenschaften einer klasse von iterationsverfahren der nichtlinearen optimierung

Abstract

We show that every method of nonlinear optimization satisfying the conditions that every iterated point x ^k-1belongs to the same component of the level set of the objective function as x ^k-1and that every accumulation point is a stationary point converges to a strong local minimal point if it starts in a neighbourhood of it. These conditions are satisfied by a modified version of the P1-algorithm of Zoutendijk.

Keywords:

• Components of a level set
• local convergence in nonlinear optimization
• methods of feasible directions

AMS 1980 Subject Classification:

• Primary:90 C 30
• Secondary:65 K 05