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Augmented Lagrangians which are quadratic in the multiplier

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Abstract

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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Additional information

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

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Key Words

  • Equality constrained nonlinear programming
  • Lagrangian functions
  • Exact penalty methods
  • Newton and quasi-Newton methods