Application of the theory of optimization under constraints to D-optimal designs characterization and computation in nonlinear regressions

This paper illustrates a direct contribution of modern Numerical Analysis (theory of optimization under constraints) to the solution of a problem of long standing (Atkinson et al., Box) in the theory of optimal design in nonlinear regression: the determination of optimality conditions for designs made of replications of the minimal D-optimal design points. The resulting practical consequence of interest is the computing time reduction in determining D-optimal design of any size, and an improvement of the problem numerical conditioning.