On the solution of nonlinear programming problems with equality constraints via continuation using special LU factorization

The use of continuation predictor-corrector methods for solving constrained optimization problems requires the use of a Newton-like method in the corrector part. This paper introduces a special LU factorization for this part that gives considerable time saving in the case of equality constraints. Numerical examples are included in order to demonstrate the superiority of this method over the regular LU factorization and Aesen’s method.