Date of Award:
Master of Science (MS)
Mathematics and Statistics
Department name when degree awarded
Model estimation programming provides a method for obtaining extreme solutions subject to constraints. Functions which are continuous with continuous first and second derivatives in the neighborhood of the solution are approximated using quadratic polynomials (termed estimating functions) derived from computed or experimental data points. Using the estimating functions, an approximation problem is solved by a numerical adaptation of the method of Lagrange. The method is not limited by the concavity of the objective function.
Beginning with an initial array of data observations, an initial approximate solution is obtained. Using this approximate solution as a new datum point, the coefficients for the estimating function are recalculated with a constrained least squares fit which forces intersection of the functions and their estimating functions at the last three observations. The constraining of the least squares estimate provides a sequence of approximate solutions which converge to the desired extremal.
A digital computer program employing the technique is used extensively by Thiokol Chemical Corporation's Wasatch Division, especially for vehicle design optimization where flight performance and hardware constraints must be satisfied simultaneously.
Brimhall, Richard Kay, "Design Optimization Using Model Estimation Programming" (1967). All Graduate Theses and Dissertations. 6801.