A Global Convergence Theory for a Class of Trust Region Algorithms for Constrained Optimization
RICE UNIV HOUSTON TX DEPT OF COMPUTATIONAL AND APPLIED MATHEMATICS
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This research presents 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.
- Numerical Mathematics