#### Abstract

In stratified sampling with k different variables and H strata it is often of interest to minimize the survey cost with respect to variance restrictions on each of the k variables. This problem has previously been solved using compromise solutions or using a linear approximation to this nonlinear problem. In this paper a nonlinear optimization routine is tested on this problem. The formulation of the problem in its original form proved problematic. For the test cases run, the transformation t_{h} = l/n_{h}, where n_{h} is the number of samples in stratum h, performed best when k and H are less than 7. As the number of strata and variables increase, the transformation t_{h } = n_{h} ^{2} performs better. In addition, simple modifications to the routine used can improve the convergence.

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A COMPARISON OF ALGORITHMS FOR SELECTING AN OPTIMUM SAMPLE FROM H STRATA USING k VARIABLES

In stratified sampling with k different variables and H strata it is often of interest to minimize the survey cost with respect to variance restrictions on each of the k variables. This problem has previously been solved using compromise solutions or using a linear approximation to this nonlinear problem. In this paper a nonlinear optimization routine is tested on this problem. The formulation of the problem in its original form proved problematic. For the test cases run, the transformation t_{h} = l/n_{h}, where n_{h} is the number of samples in stratum h, performed best when k and H are less than 7. As the number of strata and variables increase, the transformation t_{h } = n_{h} ^{2} performs better. In addition, simple modifications to the routine used can improve the convergence.