Report Number: CS-TR-72-279
Institution: Stanford University, Department of Computer Science
Title: Topics in optimization.
Author: Osborne, Michael R.
Date: April 1972
Abstract: These notes are based on a course of lectures given at Stanford, and cover three major topics relevant to optimization theory. First an introduction is given to those results in mathematical programming which appear to be most important for the development and analysis of practical algorithms. Next unconstrained optimization problems are considered. The main emphasis is on that subclass of descent methods which (a) requires the evaluation of first derivatives of the objective function, and (b) has a family connection with the conjugate direction methods. Numerical results obtained using a program based on this material are discussed in an Appendix. In the third section, penalty and barrier function methods for mathematical programming problems are studied in some detail, and possible methods for accelerating their convergence indicated.