Fast Interval Branch-And-Bound Methods For Unconstrained Global Optimization With Affine Arithmetic - de Figueiredo, Van Iwaarden, Stolfi (ResearchIndex)

Fast Interval Branch-And-Bound Methods For Unconstrained Global Optimization With Affine Arithmetic (1997) (Make Corrections) (1 citation)
Luiz Henrique de Figueiredo, Ronald Van Iwaarden, Jorge StolfiInstitute of Computing, Univ. of Campinas, Brazil

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Compares interval analysis with AA for branch-and-bound NL optimization.
Abstract: We show that faster solutions to unconstrained global optimization problems can be obtained by combining previous accelerations techniques for interval branch-and-bound methods with affine arithmetic, a recent alternative to interval arithmetic that often provides tighter estimates. We support this claim by solving a few well-known problems. Key words. global optimization, branch and bound, range analysis, reliable computation AMS subject classifications. 65K05, 65G10, 90C30 (Update)

Context of citations to this paper: More

.... affine arithmetic has been developed to overcome these shortcomings [1, 26] It has previously been applied to numerical optimization [5, 17, 13]. In this paper we apply affine arithmetic to embed deformable models within a statistical framework. This approach allows us to...

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BibTeX entry: (Update)

L. H. de Figueiredo, R. Van Iwaarden, and J. Stolfi. Fast interval branch-and-bound methods for unconstrained global optimization with affine arithmetic. Technical Report IC-9708, Institute of Computing, Univ. of Campinas, June 1997. http://citeseer.nj.nec.com/article/defigueiredo97fast.html More

@techreport{ figueiredo97fast,
  author = "L. de Figueiredo and R. Van Iwaarden and J. Stolfi",
  title = "Fast interval branch-and-bound methods for unconstrained global optimization with affine arithmetic",
  institution = "Institute of Computing, Univ. of Campinas, Brazil",
  number = "IC-97-08,
  month = jun,
  year = 1997,
  url = "citeseer.nj.nec.com/article/defigueiredo97fast.html" }

Citations (may not include all citations):
524 Practical Optimization (context) - Gill, Murray et al. - 1981
423 Linear and Nonlinear Programming (context) - Luenberger - 1989
309 Interval Analysis (context) - Moore - 1966
168 Interval Methods for Systems of Equations (context) - Neumaier - 1990
96 IEEE Standard for Binary Floating-Point Arithmetic (context) - IEEE - 1985
52 Global Optimization (context) - Horst, Tuy - 1990
50 Computer Methods for the Range of Functions (context) - Ratschek, Rokne - 1984
26 Algorithms for polynomials in Bernstein form (context) - Farouki, Rajan - 1988
24 A generalized interval arithmetic (context) - Hansen - 1975
21 A global minimization method: the multi-dimensional case (context) - Jansson, uppel - 1992
17 Rigorous methods for global optimization (context) - Moore, Hansen et al. - 1992
15 Computation of rational interval functions (context) - Skelboe - 1974
14 Box-splitting strategies for the interval Gauss-Seidel step .. - Ratz - 1994
13 Affine arithmetic and its applications to computer graphics - Comba, Stolfi - 1993
13 generalized bisection when there are singularities near root.. (context) - Kearfott, Newton - 1990
11 What can interval analysis do for global optimization (context) - Ratschek, Voller - 1991
11 Adaptive enumeration of implicit surfaces with affine arithm.. (context) - de Figueiredo, Stolfi - 1996
9 An interval arithmetic method for global optimization (context) - Ichida, Fujii - 1979
8 An interval branch and bound algorithm for bound constrained.. - Kearfott - 1992
6 An Improved Unconstrained Global Optimization Algorithm - van Iwaarden - 1996
5 Surface intersection using affine arithmetic - de Figueiredo - 1996
2 in Monographs and Textbooks in Pure and Applied Mathematics (context) - using, Analysis - 1988
2 Journal of Optimization Theory and Applications (context) - using, analysis et al. - 1979
2 Ellis Horwood Ltd (context) - Methods, Optimization - 1988
1 Numerische Mathematik (context) - using, analysis et al. - 1980

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