K-Optimal Design via Semidefinite Programming and Entropy Optimization

• 成果类型: Article
• 署名作者: Marechal, Pierre; Ye, Jane J.; Zhou, Julie
• 署名单位: Universite de Toulouse; Universite Toulouse III - Paul Sabatier; University of Victoria
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2014.0682
• 发表日期: 2015
• 页码: 495-511
• 关键词: convex functionals; condition number; regression; INTEGRALS

摘要

In this paper, we consider the problem of optimal design of experiments. A two-step inference strategy is proposed. The first step consists in minimizing the condition number of the so-called information matrix. This step can be turned into a semidefinite programming problem. The second step is more classical, and it entails the minimization of a convex integral functional under linear constraints. This step is formulated in some infinite-dimensional space and is solved by means of a dual approach. Numerical simulations will show the relevance of our approach.