Finding a c‐optimal design of a regression model is a basic optimization problem in statistics. We study the computational complexity of the problem in the case of a finite experimental domain. We formulate a decision version of the problem and prove its NP‐completeness. We provide examples of computationally complex instances of the design problem, motivated by cryptography. The problem, being NP‐complete, is then relaxed; we prove that a decision version of the relaxation, called approximate c‐optimality, is P‐complete. We derive an equivalence theorem for linear programming: we show that the relaxed c‐optimality is equivalent (in the sense of many‐one LOGSPACE‐reducibility) to general linear programming.
