zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Effect of the subdivision strategy on convergence and efficiency of some global optimization algorithms. (English) Zbl 0744.90083
Author’s summary: “We investigate subdivision strategies that can improve the convergence and efficiency of some branch-and-bound algorithms of global optimization. In particular, a general class of so- called weakly exhaustive simplicial subdivision processes is introduced that subsumes all previously known radial exhaustive processes. This result provides the basis for constructing flexible subdivision strategies that can be adapted to take advantage of various problem conditions”.
Reviewer: V.Veliov (Sofia)

90C30Nonlinear programming
90-08Computational methods (optimization)
Full Text: DOI
[1] Falk, J. E. and Soland, R. M. (1969), An Algorithm for Separable Nonconvex Programming Problems, Management Science 15, 550-569. · Zbl 0172.43802 · doi:10.1287/mnsc.15.9.550
[2] Hamami, M. and Jacobsen, S. E. (1988), Exhaustive Nondegenerate Conical Processes for Concave Minimization on Convex Polytope, Mathematics of Operations Research 13, 479-481. · Zbl 0651.90058 · doi:10.1287/moor.13.3.479
[3] Horst, R. (1976), An Algorithm for Nonconvex Programming Problems, Mathematical Programming 10, 312-321. · Zbl 0337.90062 · doi:10.1007/BF01580678
[4] Horst, R. and Thoai, N. V. (1989), Modification, Implementation and Comparison of Three Algorithms for Globally Solving Linearly Constrained Concave Minimization Problems, Computing 42, 271-289. · Zbl 0675.65063 · doi:10.1007/BF02239754
[5] Horst, R. and Tuy, H. (1990), Global Optimization (Deterministic Approaches), Springer-Verlag. · Zbl 0704.90057
[6] Kalantari, B. and Rosen, J. B. (1987), An Algorithm for Global Mimization of Linearly Constrained Concave Quadratic Functions, Mathematics of Operations Research 12, 544-562. · Zbl 0638.90081 · doi:10.1287/moor.12.3.544
[7] Thoai, N. V. and Tuy, H. (1980), Convergent Algorithm for Minimizing a Concave Function, Mathematics of Operations Research 5, 556-566. · Zbl 0472.90054 · doi:10.1287/moor.5.4.556
[8] Tuy, H. (1991), Normal Conical Algorithm for Concave Minimization, Mathematical Programming. Forthcoming. · Zbl 0743.90103
[9] Tuy, H. and Horst, R. (1988), Convergence and Restart in Branch and Bound Algorithms for Global Optimization. Application to Concave Minimization and D.C. Optimization Problems, Mathematical Programming 41, 161-183. · Zbl 0651.90063 · doi:10.1007/BF01580762
[10] Tuy, H. and Horst, R. (submitted), The Geometric Complementarity Problem and Transcending Stationarity in Global Optimization. · Zbl 0813.90115
[11] Tuy, H., Khachaturov, V., and Utkin, S. (1987), A Class of Exhaustive Cone Splitting Procedures in Conical Algorithms for Concave Minimization, Optimization 18, 791-807. · Zbl 0637.90074 · doi:10.1080/02331938708843294
[12] Utkin, S., Khachaturov, V., and Tuy, H. (1988), On Conical Algorithms for Solving Concave Programming Problems and Some of Their Extensions, USSR Computational Mathematics and Mathematical Physics 28, 992-999. · Zbl 0684.90070 · doi:10.1016/0041-5553(88)90106-1