We present a class of new augmented Lagrangian functions with the essential property that each member is concave quadratic when viewed as a function of the multiplier. This leads to an improved duality theory and to a related class of exact penalty functions. In addition, a relationship between Newton steps for the classical Lagrangian and the new Lagrangians is established.
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This work was supported in part by ARO Grant No. DAAG29-77-G-0125.
Communicated by M. R. Hestenes
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Boggs, P.T., Tolle, J.W. Augmented Lagrangians which are quadratic in the multiplier. J Optim Theory Appl 31, 17–26 (1980). https://doi.org/10.1007/BF00934785
- Equality constrained nonlinear programming
- Lagrangian functions
- Exact penalty methods
- Newton and quasi-Newton methods