Steepest descent algorithms in a space of measures

Statistics and Computing

Volumn 12, Issue 2, 2002, Pages 115-123

  Molchanov, Ilya ^a   Zuyev, Sergei ^b  

^a UNIVERSITY OF GLASGOW   (United Kingdom)

^b UNIVERSITY OF STRATHCLYDE   (United Kingdom)

Author keywords

Boolean model; Gradient methods; K means; Optimal experimental design; P means; Poisson process; R; Splus; Steepest descent

Indexed keywords

EID: 0141792082     PISSN: 09603174     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1014878317736     Document Type: Article

References (23)

1. Atkinson A.C. and Donev A.N. 1992. Optimum Experimental Designs. Clarendon Press, Oxford.
2. Fedorov V.V. and Hackl P. 1997. Model-Oriented Design of Experiments, vol. 125 of Lect. Notes Statist. Springer, New York.
3. Hartigan J.A. 1975. Clustering Algorithms. Wiley, New York.
4. Hartigan J.A. and Wong M.A. 1979. A k-means clustering algorithm. Appl. Statist. 28: 100-108.
5. Hille E. and Phillips R.S. 1957. Functional Analysis and Semigroups, vol. XXXI of AMS Colloquium Publications. American Mathematical Society, Providence.
6. Kellerer H.G. 1988. Measure theoretic versions of linear programming. Math. Z. 198: 367-400.
7. Lai H.C. and Wu S.Y. 1994. Linear programming in measure spaces. Optimization 29: 141-156.
8. Lindsay B.G. 1983. The geometry of mixture likelihoods: A general theory. Ann. Statist. 11: 86-94.
9. McClure D.E. and Vitale R.A. 1975. Polygonal approximation of plane convex bodies. J. Math. Anal. Appl. 51: 326-358.
10. Molchanov I.S. 1997. Statistics of the Boolean Model for Practitioners and Mathematicians. Wiley, Chichester.
11. Molchanov I.S., Chiu S.N., and Zuyev S.A. 2000. Design of inhomogeneous materials with given structural properties. Phys. Rev. E 62: 4544-4552.
12. Molchanov I.S. and Zuyev S.A. 2000a. Tangent sets in the space of measures: With applications to variational calculus. J. Math. Anal. Appl. 249: 539-552.
13. Molchanov I.S. and Zuyev S.A. 2000b. Variational analysis of functionals of a poisson process. Math. Oper. Res. 25: 485-508.
14. Molchanov I.S. and Zuyev S.A. 2000c. Variational calculus in space of measures and optimal design. In: Atkinson A., Bogacka B., and Zhigljavsky A. (Eds.), Optimum Design 2000: Prospects for the New Millennium. Kluwer, Dordrecht, pp. 79-90.
15. Okabe A., Boots B., Sugihara K., and Chiu S.N. 2000. Spatial Tessellations - Concepts and Applications of Voronoi Diagrams. 2nd edn. Wiley, Chichester.
16. Polak E. 1997. Optimization: Algorithms and Consistent Approximations. Springer, New York.
17. Pukelsheim F. 1983. Optimal Design of Experiments. Wiley, New York.
18. Robinson S.M. 1976. First order conditions for general nonlinear optimization. SIAM J. Appl. Math. 30: 597-607.
19. Schneider R. 1988. Random approximations of convex sets. J. Microscopy 151: 211-227.
20. Winkler G. 1988. Extreme points of moment sets. Math. Oper. Res. 13: 581-587.
21. Wu C.-F. and Wynn H.P. 1978. The convergence of general step-length algorithms for regular optimum design criteria. Am. Statist. 6: 1273-1285.
22. Wynn H.P. 1970. The sequential generation of D-optimum experimental designs. Am. Math. Statist. 41: 1655-1664.
23. Zowe J. and Kurcyusz S. 1979. Regularity and stability for the mathematical programming problem in Banach spaces. Appl. Math. Optim. 5: 49-62.