A Global Convergence Theory for the Celis–Dennis–Tapia Trust-Region Algorithm for Constrained Optimization

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 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.