Efficient solution of large-scale linear and quadratic programming problems

Abstract

Since the emergence of the interior point methods for linear optimization, computational codes based on these ideas have been shown as efficient alternatives for solving problems of linear and quadratic large-scale problems. Three research lines stand out in the search of efficiency: reducing the number of iterations to achieve convergence of the method; reduction of iteration computational time through the efficient solution of linear systems needed to compute the directions; the development of specific methods for optimization problems with particular structure and take advantage of this structure. These three lines of research are covered in this project. In the first two, the focus is linear optimization problems while quadratic programming problems on the third line originated from power systems form the core of the research. (AU)