Nonlinear programming feasibility: restoration and applications

Author(s)

Juliano de Bem Francisco

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica
• Defense date: 2005-10-02

Examining board members

José Mario Martínez Pérez; Rogério Custodio; Clovis Caesar Gonzaga; Mario Cesar Zambaldi; Sandra Augusta Santos

• Advisor: José Mario Martínez Pérez

Abstract

Abstract Robust and numerically feasible algorithms for solving optimization problems have been demanded for solving practice problems that appear in Engineering, Chemistry, Physics and others. This work present a new globally convergent method based on trust regions for solving box-constrained underdetermined nonlinear systems (more unknowns than equations), that can be used on the feasibility fase of algorithms based on periodic restoration. Under some assumptions, it will be proved locally quadratic convergence. In other part of this work, a new globally convergent algorithm is introduced, based on trust regions, for solving the optimization problem min f(x); s:t: x 2 D; where f : Rn ! R is continuously dierentiable and D C Rn is an arbitrary closed subset. Instead of considering explicitly the trust region on the subproblems, the method introduces a regularization parameter that mimics the trust region. With this characterization, the subproblems consist on minimizing a quadratic model of f subject to D. numerically feasible globally convergent algorithm for electronic structure calculations is obtained. (AU)