A nonlinear preconditioner for optimum experimental design problems

• Verfasst von: Mommer, Mario Salvador [VerfasserIn]
• Verfasst von: Sommer, Andreas [VerfasserIn]
• Verfasst von: Schlöder, Johannes P. [VerfasserIn]
• Verfasst von: Bock, Hans Georg [VerfasserIn]
• Titel: A nonlinear preconditioner for optimum experimental design problems
• Verf.angabe: Mario S. Mommer, Andreas Sommer, Johannes P. Schlöder, H. Georg Bock
• E-Jahr: 2015
• Jahr: 17 March 2015
• Umfang: 16 S.
• Fussnoten: Gesehen am 30.01.2018
• Titel Quelle: Enthalten in: EURO journal on computational optimization
• Ort Quelle: Berlin : Springer, 2013
• Jahr Quelle: 2015
• Band/Heft Quelle: 3(2015), 2, Seite 131-146
• ISSN Quelle: 2192-4414
• DOI: doi:10.1007/s13675-015-0036-9
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1567870686

Abstract

We show how to efficiently compute A-optimal experimental designs, which are formulated in terms of the minimization of the trace of the covariance matrix of the underlying regression process, using quasi-Newton sequential quadratic programming methods. In particular, we introduce a modification of the problem that leads to significantly faster convergence. To derive this modification, we model each iteration in terms of an initial experimental design that is to be improved, and show that the absolute condition number of the model problem grows without bounds as the quality of the initial design improves. As a remedy, we devise a preconditioner that ensures that the absolute condition number will instead stay uniformly bounded. Using numerical experiments, we study the effect of this reformulation on relevant cases of the general problem class, and find that it leads to significant improvements in both stability and convergence behavior.