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Abstract: The paper applies abstract optimisation principles in the space of measures within the context of optimal design problems. It is shown that within this framework it is possible to treat various design criteria and constraints in a unified manner providing a "universal" variant of the Kiefer-Wolfowitz theorem and giving a full spectrum of optimality criteria for particular cases. The described steepest descent algorithm uses the true direction of the steepest descent and descends faster than the ... (Update)
Context of citations to this paper: More
.... discussion of our algorithm in comparison with other descent algorithms suggested in the optimal design literature can be found in [13]. Here we just give an example. 11 Example 6.1. Consider the polynomial regression problem of order 4 with X = 0; 1] For computational...
...If this number is instead set at a nite value, numerical optimisation is called for. We adapt the steepest descent algorithm of [26] to the present context (Section 4) and evaluate its performance on synthetic and real life examples 3 (Section 5) The paper is...
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Acceleration Of D-Optimum Design Algorithms By Removing.. - Pronzato (2002) (Correct)
Steepest Descent Algorithms in Space of Measures - Molchanov, Zuyev (2000) (Correct)
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0.7: Variational Analysis of Functionals of a Poisson Process - Molchanov, Zuyev (1997) (Correct)
0.7: Constrained Optimization of Experimental Design - Cook, Fedorov (1995) (Correct)
0.5: A Nonparametric Mixture Approach to Case-Control Studies .. - Roeder, Carroll, Lindsay (1996) (Correct)
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0.6: Tangent Sets in the Space of Measures: with Applications to.. - Molchanov, Zuyev (Correct)
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5: Variational analysis of functionals of a Poisson process - Molchanov, Zuyev - 2000
3: Statistics of the Boolean Model for Practitioners and Mathematicians J (context) - Molchanov - 1997
3: Optimisation in space of measures and optimal design (context) - Molchanov, Zuyev - 2000
BibTeX entry: (Update)
I. Molchanov and S. Zuyev. Variational calculus in space of measures and optimal design. In A. C. Atkinson, B. Bogacka, and A. Zhigljavsky, editors, Optimum Experimental Design: Prospects for the New Millennium. Kluwer, Dordrecht, 2000. To appear. http://citeseer.ist.psu.edu/article/molchanov00variational.html More
@article{ molchanov00variational,
author = "I. S. Molchanov and S. A. Zuyev",
title = "Variational Analysis of Functionals of a {Poisson} Process",
journal = "Math. Oper. Res.",
volume = "25",
pages = "485--508",
year = "2000",
url = "citeseer.ist.psu.edu/article/molchanov00variational.html" }
Citations (may not include all citations):132 Theory of Optimal Experiments (context) - Fedorov - 1972
74 Functional Analysis and Semigroups (context) - Hille, Phillips - 1957
39 Optimum Experimental Designs (context) - Atkinson, Donev - 1992
18 Regularity and stability for the mathematical programming pr.. (context) - Zowe, Kurcyusz - 1979
13 New York (context) - Polak - 1997
10 Variational analysis of functionals of a Poisson process - Molchanov, Zuyev - 1997
5 The convergence of general step-length algorithms for regula.. (context) - Wu, Wynn - 1978
5 Constrained optimization of experimental design - Cook, Fedorov - 1995
4 Model-Oriented Design of Experiments (context) - Fedorov, Hackl - 1997
4 The sequential generation of D-optimum experimental designs (context) - Wynn - 1970
3 Some algorithmic aspects of the theory of optimal design (context) - Wu
2 Sequences converging to D-optimal designs of experiments (context) - Atwood - 1973
2 Steepest descent algorithms in space of measures - Molchanov, Zuyev - 2000
2 Results in the theory and construction of D-optimum experime.. (context) - Wynn - 1972
2 Some iterative procedures for generating nonsingular optimal.. (context) - Wu
1 Optimal Static and Sequential Design: a Critical Review (context) - Ford - 1976
1 Convergent design sequences (context) - Atwood - 1976
The graph only includes citing articles where the year of publication is known.
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)
Tangent Sets in the Space of Measures: with Applications to.. - Molchanov, Zuyev (Correct)
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