"A Numerical Study of Active-Set and Interior-Point Methods for Bound Constrained Optimization"
L. Hei, J. Nocedal, R. Waltz
“Modeling, Simulation and Optimization of Complex Processes”,
editors Bock H. G., Kostina E. A., Phu H. X., Rannacher R. (2008).
This papers studies the performance of several interior-point and active- set methods on bound constrained optimization problems. The numerical tests show that the sequential linear-quadratic programming (SLQP) method is robust, but is not as eective as gradient projection at identifying the optimal active set. Interior- point methods are robust and require a small number of iterations and function evaluations to converge. An analysis of computing times reveals that it is essential to develop improved preconditioners for the conjugate gradient iterations used in SLQP and interior-point methods. The paper discusses how to efficiently implement incomplete Cholesky preconditioners and how to eliminate ill-conditioning caused by the barrier approach. The paper concludes with an evaluation of methods that use quasi-Newton approximations to the Hessian of the Lagrangian.