Convergence of optimal allocation sequence in regression models with cost consideration

We discuss the convergence of the optimal allocation problem in multi-level experiment regression models with cost of running the experiment at each level are studied. The objective function that balances between the cost and variation is proposed, where cost of the experiment can be the cost of the experiment or the risk arising from the experiment. We present the results for optimal allocation that minimizes the objective function, and study the algorithm of the optimal allocation. A detailed proof of the convergence of optimal allocation sequence basing on the algorithm is provided.