A global convergence theory for a class of trust region algorithms for constrained optimization

In this research we present a trust region algorithm for solving the equality constrained optimization problem. This algorithm is a variant of the 1984 Celis-Dennis-Tapia algorithm. The augmented Lagrangian function is used as a merit function. A scheme for updating the penalty parameter is presented. The behavior of the penalty parameter is discussed. We present a global and local convergence analysis for this algorithm. We also show that under mild assumptions, in a neighborhood of the minimizer, the algorithm will reduce to the standard SQP algorithm; hence the local rate of convergence of SQP is maintained. Our global convergence 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.