| Although many efficient solvers exist for solving nonlinear optimization problems, there is none that performs well on all problems or outperforms all methods. Therefore, developing new methods for solving optimization problems continues to be important. Exterior-point methods (EPMs) for solving nonlinear optimization problems have promising convergence properties established by theoretical analysis, but no numerically efficient implementation of exterior-point methods exists.;This dissertation extends development of primal-dual exterior point methods and investigates the application of exterior point methods in several directions. First, a numerically efficient algorithm for solving large scale optimization problems based on exterior point methods is investigated. Second, an implementation of the algorithm is developed in C++ and the algorithm is tested on several hundred nonlinear optimization problems from the CUTEr test set. Third, the use of exterior-point methods for solving the support vector machine (SVM) problem is investigated. Finally, properties of the EPM are utilized to implement active-passive strategies to reduce the size of the primal-dual system when solving optimization problems. |
