A modified augmented Lagrangian method for a class of constrained problems (Q1872984)

The authors consider the penalty method \[ X^TA x/2-x^Tb+ \lambda\cdot \|Cx-d\|^2/2 \to\min \] for the solution of the quadratic programming problem \[ x^TA x/2-x^Tb \to\min \] subject to the constraint \(Cx-d= 0\). To overcome the difficulties when trying to solve the penalty problem, the given quadratic problem is formulated in an alternative form which is solved with a modified augmented Lagrangian method. A numerical example is given.