Nonconvex Optimization and Its Applications

By: Anthony Atkinson (Editor), Barbara Bogacka (Editor), Anatoly A. Zhigljavsky (Editor)

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Hardcover | 31 March 2001

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324 Pages

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23.88 x 15.88 x 1.78

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This volume contains many of the papers presented at the conference "Optimum Design 2000: Prospects for the New Millennium" held in Cardiff, UK on April 12th - 14th, 2000. The majority of the papers consider aspects of optimum experimental design from the theoretical to applications. Many of the optimisation problems arising in the optimum design theory in general and the articles in this volume in particular, fall into the category of nonconvex, including global, optimization. The papers are organised in two sections. Since we are at the beginning of a new millennium the first paper starts by looking back at the beginnings of optimum exper- imental design in 1917 and sketches the development up to Kiefer's paper read to the Royal Statistical Society in 1959. This is the first in a group of papers which we have labelled "Theory", which cover the more general aspects, such as the properties and methods of construction of designs. In the "Applications" section there are papers on sequential design problems arising in the pharmaceutical industry and on the designs with discrete factors which occur in agriculture. There are also papers on training neural networks, on the efficient design of sampling methods, on design problems in mixtures, arising from a study of glass manufacturing, and on the resistance of Brazilian weeds to herbicides. The number attending the meeting was deliberately limited to 50 in order to encour- age a workshop atmosphere and the exchange of ideas.

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Non-Fiction Science Science in General Medicine Medicine in General Mathematics Probability & Statistics Reference, Information & Interdisciplinary Subjects Research & Information Research Methods Optimisation Linear Programming

Applied Mathematics Engineering & Technology Technology in General Maths for Engineers

Preface
Some History Leading to Design Criteria for Bayesian Prediction	p. 3
Optimal Designs for the Evaluation of an Extremum Point	p. 15
On Regression Experiment Design in the Presence of Systematic Error	p. 25
Grobner Basis Methods in Mixture Experiments and Generalisations	p. 33
Efficient Designs for Paired Comparisons with a Polynomial Factor	p. 45
On Generating and Classifying All q[superscript n-m] Regular Designs for Square-Free q	p. 57
Second-Order Optimal Sequential Tests	p. 67
Variational Calculus in the Space of Measures and Optimal Design	p. 79
On the Efficiency of Generally Balanced Designs Analysed by Restricted Maximum Likelihood	p. 91
Concentration Sets, Elfving Sets and Norms in Optimum Design	p. 101
Sequential Construction of an Experimental Design from an I.I.D. Sequence of Experiments without Replacement	p. 113
Optimal Characteristic Designs for Polynomial Models	p. 123
A Note on Optimal Bounded Designs	p. 131
Construction of Constrained Optimal Designs	p. 141
Pharmaceutical Applications of a Multi-Stage Group Testing Method	p. 155
Block Designs for Comparison of Two Test Treatments with a Control	p. 167
Optimal Sampling Design with Random Size Clusters for a Mixed Model with Measurement Errors	p. 181
Optimizing a Unimodal Response Function for Binary Variables	p. 195
An Optimizing Up-And-Down Design	p. 211
Further Results on Optimal and Efficient Designs for Constrained Mixture Experiments	p. 225
Coffee-House Designs	p. 241
(D[subscript t],C)-Optimal Run Orders	p. 249
Optimal Design in Flexible Models, including Feed-Forward Networks and Nonparametric Regression	p. 261
On Optimal Designs for High Dimensional Binary Regression Models	p. 275
Planning Herbicide Dose-Response Bioassays Using the Bootstrap	p. 287
Photo Gallery	p. 295
Optimum Design 2000: List of Participants	p. 303
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Nonconvex Optimization and Its Applications

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