Trust Region Algorithm For Constrained Optimization Research Articles

A Global Convergence Theory for Dennis, El-Alem, and Maciel's Class of Trust-Region Algorithms for Constrained Optimization without Assuming Regularity

This work presents a convergence theory for Dennis, El-Alem, and Maciel's class of trust-region-based algorithms for solving the smooth nonlinear programming problem with equality constraints. The results are proved under very mild conditions on the quasi-normal and tangential components of the trial steps. The Lagrange multiplier estimates and the Hessian estimates are assumed to be bounded. No regularity assumption is made. In particular, linear independence of the gradients of the constraints is not assumed. The theory proves global convergence for the class. In particular, it shows that a subsequence of the iteration sequence satisfies one of four types of Mayer--Bliss stationary conditions in the limit.

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.

An Algorithm for Least-Squares Estimation of Nonlinear Parameters

An Algorithm for Least-Squares Estimation of Nonlinear Parameters