A Trust Region Algorithm for Equality Constrained Minimization: Convergence Properties and Implementation

Abstract

In unconstrained minimization, trust region algorithms use directions that are a combination of the quasi-Newton direction and the steepest descent direction, depending on the fit between the quadratic approximation of the function and the function itself. Algorithms for nonlinear constrained minimization problems usually determine a quasi-Newton direction and use a line search technique to determine the step. Since trust region strategies have proved to be successful in unconstrained minimization, we develop a new trust region strategy for equality constrained minimization. This algorithm is analyzed and global as well as local superlinear convergence theorems are proved for various versions. We demonstrate how to implement this algorithm in a numerically stable way. A computer program based on this algorithm has performed very satisfactorily on test problems; numerical results are provided.