Improvements on removing nonoptimal support points in D-optimum design algorithms
By Radoslav Harman, Luc Pronzato. 2007
71 citations recorded by the source corpus.
We improve the inequality used in Pronzato [2003. Removing non-optimal support points in D-optimum design algorithms. Statist. Probab. Lett. 63, 223-228] to remove points from the design space during the search for a D-optimum design. Let [xi] be any design on a compact space with a nonsingular information matrix, and let m+[epsilon] be the maximum of the variance function d([xi],x) over all . We prove that any support point x* of a D-optimum design on must satisfy the inequality . We show that this new lower bound on d([xi],x*) is, in a sense, the best possible, and how it can be used to accelerate algorithms for D-optimum design.
Subfields: Computational Theory and Mathematics, Industrial and Manufacturing Engineering, Management Science and Operations Research
View Paper: https://www.semanticscholar.org/paper/5c9ed72f2faa41b090b9ef54a3af2aae6322242d
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In Computational Theory and Mathematics
In Industrial and Manufacturing Engineering
In Management Science and Operations Research
Citations in the corpus
- Monotonic convergence of a general algorithm for computing optimal designs (2009, background): “Hence methods that quickly eliminate non-optimal support points are valuable (Harman and Pronzato, 2007).”
- Design of Experiments in Nonlinear Models: Asymptotic Normality, Optimality Criteria and Small-Sample Properties (2013, background): “However, it is shown in (Harman and Pronzato, 2007) that any design point x satisfying”
- Minimax and maximin space-filling designs: some properties and methods for construction (2017, unknown): “Following an approach similar to Harman and Pronzato (2007), we can show that (cid:107) c ( w ) − c ∗ (cid:107) ≤ ε / 2 and that any z i such that (cid:107) z i − c ( w ) (cid:107) 2 φ ( w ) + ε − ε ( 2 φ ( w ) + ε ) necessarily lie in the interior of B ∗ , and therefore do not need to be…”