Barycentric algorithm for computing D-optimal size- and cost-constrained designs of experiments

Construction of constrained experimental designs on finite spaces for a modified Ek-optimality criterion

“…Although much work has been done in this respect as regards theory (e.g., Cook and Fedorov, 1995), the number of publications on the algorithmic aspects of constrained optimization of experimental design is still very limited. Harman and Benková (2017) proposed a nontrivial and efficient barycentric algorithm, which draws on the idea of the multiplicative algorithm and is specialized in two linear inequality constraints (the size and cost constraints) on the weights. Problems with larger numbers of linear equality/inequality constraints can be treated by employing either interior-point methods (Joshi and Boyd, 2009;Chepuri and Leus, 2015;Lu and Pong, 2013), most often using existing SDP solvers, or the simplicial decomposition (SD), an inner-linearization polyhedral approximation method (Bertsekas, 2015).…”

On optimal designs for nonregular models

“…Optimal experimental design is a classical problem with substantial recent developments. For example, Biedermann et al (2006), Dette et al (2008), Feller et al (2017), and Schorning et al (2017) studied optimal designs for dose-response models; Dette et al (2016) and Dette et al (2017) investigated optimal designs for correlated observations; Dror and Steinberg (2006) and Gotwalt et al (2009) studied robustness issues in optimal designs; López-Fidalgo et al (2007), Waterhouse et al (2008), Biedermann et al (2009), Dette and Titoff (2009), and Dette et al (2018) studied optimal discrimination designs; Biedermann et al (2011) studied optimal design for additive partially nonlinear models; Yu (2011), Yang et al (2013), Sagnol and Harman (2015), and Harman and Benková (2017) investigated algorithms for deriving optimal designs; and Yang and Stufken (2009), Yang (2010), Dette and Melas (2011), Yang and Stufken (2012), and Dette and Schorning (2013) built a new theoretical framework for studying optimal designs. The focus of these developments has been exclusively on regular models that enjoy certain normal features asymptotically, such as generalized linear models.…”

“…For example, Biedermann et al (2006), Dette et al (2008), Feller et al (2017), and Schorning et al (2017) studied optimal designs for dose-response models; Dette et al (2016) and Dette et al (2017) investigated optimal designs for correlated observations; Dror and Steinberg (2006) and Gotwalt et al (2009) Sagnol and Harman (2015), and Harman and Benková (2017) investigated algorithms for deriving optimal designs; and Yang and Stufken (2009), Yang (2010), Dette and Melas (2011), Yang and Stufken (2012), and Dette and Schorning…”