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Abstract: . The paper describes descent type algorithms suitable for solving optimisation problems for functionals that depend on measures. We mention several examples of such problems that appear in optimal design, cluster analysis and optimisation of spatial distribution of coverage processes. Keywords: gradient methods, steepest descent, k-means, P-means, optimal experimental design, Poisson process, Boolean model, Splus, R Abbreviations: KAP { Kluwer Academic Publishers; compuscript {... (Update)
Context of citations to this paper: More
...8 w 1 ; w k 1 are called affinely independent if w 2 w 1 ; w k 1 w 1 are linearly independent. Theorem 3 (see Molchanov and Zuyev, 2000). Theminimum of D ( over all 2 with k k is achieved on a signed measure = such that has at most k...
.... descent algorithm The minimisation of functionals of measures can be done eciently using steepest descent algorithms, as described in [23, 26]. At every step, the idea is to move from to for some suitably chosen (signed) measure such that the value of the objective...
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BibTeX entry: (Update)
Molchanov, I. and Zuyev, S. (2000). Steepest descent algorithms in space of measures. To appear. http://citeseer.ist.psu.edu/molchanov00steepest.html More
@misc{ molchanov00steepest,
author = "I. Molchanov and S. Zuyev",
title = "Steepest descent algorithms in space of measures",
text = "Molchanov, I. and Zuyev, S. (2000). Steepest descent algorithms in space
of measures. To appear.",
year = "2000",
url = "citeseer.ist.psu.edu/molchanov00steepest.html" }
Citations (may not include all citations):295 Clustering Algorithms (context) - Hartigan - 1975
74 Functional Analysis and Semigroups (context) - Hille, Phillips - 1957
50 Optimal Design of Experiments (context) - Pukelsheim - 1983
39 Optimum Experimental Designs (context) - Atkinson, Donev - 1992
30 Optimization: Algorithms and Consistent Approximations (context) - Polak - 1997
23 A k-means clustering algorithm (context) - Hartigan, Wong - 1979
16 The geometry of mixture likelihoods: a general theory (context) - Lindsay - 1983
14 Polygonal approximation of plane convex bodies (context) - McClure, Vitale - 1975
13 First order conditions for general nonlinear optimization (context) - Robinson - 1976
10 Variational Analysis of Functionals of a Poisson Process - Molchanov, Zuyev
9 Statistics of the Boolean Model for Practitioners and Mathem.. (context) - Molchanov - 1997
5 Variational calculus in space of measures and optimal design - Molchanov, Zuyev - 2000
4 Model-Oriented Design of Experiments (context) - Fedorov, Hackl - 1997
4 The sequential generation of D-optimum experimental designs (context) - Wynn - 1970
2 Measure theoretic versions of linear programming (context) - Kellerer - 1988
2 Linear programming in measure spaces (context) - Lai, Wu - 1994
1 Design of inhomogeneous materials with given structural prop.. (context) - Molchanov, Chiu et al. - 2000
1 Tangent sets in the space of measures: with applications to .. - Molchanov, Zuyev
1 Random approximations of convex sets (context) - for, Schneider - 1988
1 Spatial Tessellations | Concepts and Applications of Voronoi.. (context) - Okabe, Boots et al. - 2000
Documents on the same site (http://www.stams.strath.ac.uk/~sergei/publications.html): More
Steepest Descent Algorithms in Space of Measures - Molchanov, Zuyev (2000) (Correct)
Design of Inhomogeneous Materials With Given Global Properties - Molchanov, Chiu, Zuyev (2000) (Correct)
Variational Calculus in Space of Measures and Optimal Design - Molchanov, Zuyev (2000) (Correct)
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