Large-Scale Constrained Optimization

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9424639 Gill The objective of this research is to develop, study, and implement algorithms for solving large-scale, nonlinear optimization problems. A large-scale optimization problem is characterized by a large number of variables and constraints. Two solution approaches form the focus of the research. These approaches are respectively, the interior point (barrier) method and the sequential quadratic programming (SQP) method. The interest in in the interior point stems from their success on linear programming problems, and some interesting properties that may be of value when certain difficult constraints are encountered. The interior point method can be used to eliminate constraints on the eigenvalues of a matrix. On the other hand, interest on the use of SQP is prompted by the success of the approach on small and medium-sized problems, and the experiences of the investigators on the performance of the technique on two classes of large, practical problems that differ substantially in character. If successful with these approaches, the developed algorithms will be coded into a software to facilitate their applications by practitioners. There are several engineering, manufacturing, scientific, and business problems that can be described by large-scale nonlinear optimization models. To date, finding a general solution algorithm to large scale optimization problems similar to the simplex method to linear programming problems has been a challenge to the optimization community. If successful, the algorithms being investigated in this research could open the window to a better understanding of this class of optimization problems. Many problems in various areas of human endeavor stand to benefit from the results of this work.