Convergent Design Sequences, for Sufficiently Regular Optimality Criteria

For an optimality criterion function Φ and a design ξₙ, approximate Φ(M(ξ)) near ξₙ by a quadratic Taylor expansion, let ξₙ + η minimize this approximation, and let ξₙ₊₁ = ξₙ + αη, with α minimizing Φ(M(ξₙ₊₁)). If Φ satisfies regularity conditions, including strict convexity, possession of three continuous derivatives, and finiteness only for nonsingular M, then M(ξₙ) converges to the optimal value for both the Federov steepest descent sequence and the above quadratic sequence, with the quadratic sequence having a faster asymptotic convergence rate. Methods are discussed for collapsing clusters of design points during the iterative process. In a simple example with D-optimality, the two methods are comparable. In a more complicated example the quadratic method is far superior.