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)
An ellipsoidal branch and bound algorithm for global optimization. (English) Zbl 1198.90318
A branch and bound algorithm is developed for the global optimization problem of minimizing a weakly convex function f over a compact set Ω from n . Starting with a known ellipsoid E containing Ω, the algorithm uses successive ellipsoidal bisections of E as proposed by L. T. H. An [Math. Progr. 87, 401–426 (2000; Zbl 0952.90031)]. To obtain a lower bound for f(x) over an ellipsoid, f is written as the sum of a convex and a concave function and the concave term is underestimated by an affine function. Convergence of the general algorithm is verified. Furthermore, for the special case that both f and Ω are convex, an algorithm is presented which generalizes the ball approximation algorithm by A. Lin and S.P. Han [SIAM J. Optim. 15, 129–138 (2005; Zbl 1077.90045)] in the sense that the norm objective in the original algorithm is replaced by an arbitrary convex function. The numerical performance of this new ball approximation algorithm is compared with that of SEDUMI 1.1 (see http://sedumi.ie.lehigh.edu/) and that of two gradient projection algorithms where the algorithms are applied to a number of quadratically constrained quadratic optimization problems. Moreover, the branch and bound algorithm is compared with a scheme given in the above mentioned paper by L. T. H. An [loc. cit.].
MSC:
90C25Convex programming
90C26Nonconvex programming, global optimization
90C30Nonlinear programming
90C57Polyhedral combinatorics, branch-and-bound, branch-and-cut
Software:
SeDuMi; SPG