Abstract
The minimization of a quadratic function subject to bilinear constraints is proven to be equivalent to the unconstrained minimization of an augmented Lagrangian of the type introduced by Di Pillo and Grippo, under assumptions weaker than those used in the general case. Two applications are reported: the parameter identification problem for a discrete linear system and the optimal control of a bilinear discrete system.
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Di Pillo, G., andGrippo, L.,A New Class of Augmented Lagrangians in Nonlinear Programming, SIAM Journal on Control and Optimization, Vol. 17, pp. 618–628, 1979.
Carotenuto, L., andRaiconi, G.,Combined Parameter Identification and State Interpolation for the Diffusion Equation with Pointwise Measurement, Proceedings of the 11th IMACS World Congress, Oslo, Norway, Vol. 4, pp. 159–162, 1985.
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Communicated by F. Zirilli
This work was supported by the Ministry of Education (MPI), Rome, Italy.
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Carotenuto, L., Raiconi, G. On the minimization of quadratic functions with bilinear constraints via augmented Lagrangians. J Optim Theory Appl 55, 23–36 (1987). https://doi.org/10.1007/BF00939043
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DOI: https://doi.org/10.1007/BF00939043