zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A trust region algorithm for nonlinearly constrained optimization. (English) Zbl 0631.65068

The authors describe a method using trust regions to solve the general nonlinearly equality constrained optimization problem xR n f(x) subject to c(x)=0. The method works by iteratively minimizing a quadratic model of the Lagrangian subject to a possibly relaxed linearization of the problem constraints and a trust region constraint. It is shown that this method is globally convergent even if singular or indefinite Hessian approximations are made.

A second order correction step that brings the iterates closer to the feasible set is described. If sufficiently precise Hessian information is used, the correction step allows one to prove that the method is also locally quadratically convergent, and that the limit satisfies the second order necessary conditions for constrained optimization. An example is given to show that, without this correction, a situation similar to the Maratos effect may occur where the iteration is unable to move away from a saddle point.

MSC:
65K05Mathematical programming (numerical methods)
90C30Nonlinear programming