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.
A new class of augmented Lagrangians in nonlinear programming / DI PILLO, Gianni; Grippo, Luigi. - In: SIAM JOURNAL ON CONTROL AND OPTIMIZATION. - ISSN 0363-0129. - STAMPA. - 17:5(1979), pp. 618-628. [10.1137/0317044]
A new class of augmented Lagrangians in nonlinear programming
DI PILLO, Gianni;GRIPPO, Luigi
1979
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.