A New Class of Augmented Lagrangians in Nonlinear Programming
Gianni Di Pillo, Luigi Grippo · SIAM Journal on Control and Optimization · 1979
In this paper a new class of augmented Lagrangians is introduced, for solving equality constrained problems via unconstrained minimization techniques. It is proved that a solution of the constrained problem and the corresponding values of the Lagrange multipliers can be found by performing a single unconstrained minimization of the augmented Lagrangian. In particular, in the linear quadratic case, the solution is obtained by minimizing a quadratic function. Numerical examples are reported.