Centering, Trust Region, Reflective Techniques for Nonlinear Minimization Subject to Bounds

Abstract

Bound-constrained nonlinear minimization problems occur frequently in practice. Most existing methods belong to an active set type which can be slow for large scale problems. Recently, we proposed a new approach [7,6,8] which generates iterates within the strictly feasible region. The method in [8] is a trust region type and, unlike the existing trust region method for bound-constrained problems, the conditions for its strong convergence properties are consistent with algorithm implementation. A reflective technique can be included in the method. In this paper, we motivate techniques which are important for our new approach. Numerical experience on some medium size problems is included.