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)
Newton-type methods with generalized distances for constrained optimization. (English) Zbl 0905.49015
Authors’ abstract: “We consider a class of interior point algorithms for minimizing a twice continuously differentiable function over a closed convex set with nonempty interior. On one hand, our algorithms can be viewed as an approximate version of the generalized proximal point methods and, on the other hand, as an extension of unconstrained Newton-type methods to the constrained case. Each step consists of solving a strongly convex unconstrained program followed by a one-dimensional search along either a line or a curve segment in the interior of the feasible set. The information about the feasible set is contained in the generalized distance function whose gradient diverges on the boundary of this set. When the feasible set is the whole space, the standard regularized Newton method is a particular case in our framework. We show, under standard assumptions, that every accumulation point of the sequence of iterates satisfies a first-order necessary optimality condition for the problem and solves the problem if the objective function is convex. Some computational results are also reported”.
MSC:
49M37Methods of nonlinear programming type in calculus of variations
90C30Nonlinear programming
65K05Mathematical programming (numerical methods)
49K40Sensitivity, stability, well-posedness of optimal solutions