Affiliations: [a] Department of Mathematics and Physics, Mälardalen University, Västerås, Sweden | [b] Division of Scientific Computing, Department of Information Technology, Uppsala University, Uppsala, Sweden | [c] Linnæus Centre for Bioinformatics, Uppsala University, Uppsala, Sweden
Abstract: Robust and efficient optimization methods for variance component estimation using Restricted Maximum Likelihood (REML) models for genetic mapping of quantitative traits are considered. We show that the standard Newton-AI scheme may fail when the optimum is located at one of the constraint boundaries, and we introduce different approaches to remedy this by taking the constraints into account. We approximate the Hessian of the objective function using the average information matrix and also by using an inverse BFGS formula. The robustness and efficiency is evaluated for problems derived from two experimental data from the same animal populations.
Keywords: Quantitative trait loci (QTL), restricted maximum likelihood (REML), average information matrix, identity-by-descent matrix, variance components, Newton-type optimization methods, Active-Set method, inverse BFGS formula, Hessian approximation
