Global convergence theory for the Celis-Dennis-Tapia trust-region algorithm for constrained optimization

Abstract

A global convergence theory for a class of trust-region algorithms for solving the equality constrained optimization problem is presented. This theory is sufficiently general that it holds for any algorithm that generates steps giving at least a fraction of Cauchy decrease in the quadratic model of the constraints, and that it uses the augmented Lagrangian as a merit function. This theory is used to establish global convergence of the 1984 Celis-Dennis-Tapia algorithm with a different scheme for updating the penalty parameter. The behavior of the penalty parameter is also discussed.