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 that give at least a fraction of Cauchy decrease in the quadratic model of the constraints and uses the augmented Lagrangian as a merit function. This theory is used to establish global convergence of the 1985 Celis-Dennis-Tapia algorithm with a different scheme for updating the penalty parameter. The behavior of the penalty parameter is also discussed