Augmented Lagrangian applied to convex quadratic problems

摘要

An algorithm based on the Augmented Lagrangian method is proposed to solve convex quadratic programming problem. The quadratic penalty is considered here. Hence, the Augmented Lagrangian function is quadratic when applied to quadratic programming problem. For this penalty, we show that if the Lagrangian function associated with the original problem is strict convex (or convex), then the hessian matrix of Augmented Lagrangian function is positive definite (or positive semi-definite). Numerical experiments are presented illustrating the performance of the algorithm for the CUTE test set.