# 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 method for solving generalized complementarity problems. (English) Zbl 0911.90324
Summary: Based on a semismooth equation reformulation using Fischer’s function, a trust region algorithm is proposed for solving the generalized complementarity problem (GCP). The algorithm uses a generalized Jacobian of the function involved in the semismooth equation and adopts the squared natural residual of the semismooth equation as a merit function. The proposed algorithm is applicable to the nonlinear complementarity problem because the latter problem is a special case of the GCP. Global convergence and, under a nonsingularity assumption, local $Q$-superlinear (or quadratic) convergence of the algorithm are established. Moreover, calculation of a generalized Jacobian is discussed and numerical results are presented.
##### MSC:
 90C33 Complementarity and equilibrium problems; variational inequalities (finite dimensions) 65K10 Optimization techniques (numerical methods)