Computing -optimal experimental designs using the simplex method of linear programming

Adaptive grid semidefinite programming for finding optimal designs

“…Examples of applications of mathematical programming algorithms for finding M-bODE are Linear Programming (Gaivoronski, 1986;Harman and Jurík, 2008), Second Order Conic Programming (Sagnol, 2011;Sagnol and Harman, 2015), Semidefinite Programming (SDP) (Vandenberghe and Boyd, 1999;Papp, 2012;, Semi Infinite Programming (SIP) (Duarte and Wong, 2014;, and Nonlinear Programming (NLP) (Chaloner and Larntz, 1989;Molchanov and Zuyev, 2002). In this paper, we focus on SDP, which is not new; details on general use and application of SDP to search for optimal designs for linear models are available in Vandenberghe and Boyd (1996).…”

On computational complexity of construction of c -optimal linear regression models over finite experimental domains

“…Theorem 1 is an important consequence of optimization-theoretic characterization of asymptotic c-optimality shown in [7], which will be discussed in Section 3.2. Theorem 2 was proved in [3]; some of its consequences can be found in [4].…”

“…The reduction (R1) was constructed in [7] and the reduction (R2) in [3]. The existence of these reductions is the essence of proofs of Theorems 1 and 3.…”

“…In [7], a special version of the Simplex Algorithm adapted for the c-optimality problem, called SAC, has been proposed. The algorithm leans on the reduction (R1).…”

Two complexity results on c-optimality in experimental design

“…The term approximately c-optimal design is used in statistical literature (see Harman and Jurík [6]) and reflects the fact that N can be so large that in practice, rarely so many observations can be obtained. If we are able to make N < N observations only, then the vector N ξ need not be integral, and ξ is approximate in the sense that the entries of N ξ have to be rounded.…”