Newton-type methods for linear and nonlinear optimization

Abstract

In this research project we will present some alternatives for computational optimization methods. Our focus is to investigate Newton type methods and its relations with some optimization methods. Much of the research will be associated with the Inexact Restoration and type Augmented Lagrangian methods. In Inexact Restoration methods we plan to develop an algorithm that uses Newtonian techniques in its subproblems to take advantage of the good performance of Sequential Quadratic Programming methods, when it is possible. In addition, we hope to expand the convergence results for algorithms without derivatives. For Augmented Lagrangian methods we propose a very unusual idea of penalizing simple constraints. With this concept we hope to get significant results even in linear programming. Finally, we also intend to propose an efficient method for nonlinear programming that combines the advances made on the Inexact Restoration with the penalization of simple constraints to address inequalities. (AU)