Geodesic
Minimization of Degenerate Integral Quadratic Functionals
Informatics and Automation, Optimal Control and Differential Games, Tome 315 (2021), pp. 108-127.

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We present a method for finding the infimum of a degenerate integral quadratic functional by passing from a given functional to another quadratic functional that is nondegenerate with respect to some new control. The minimum point of the latter can be found by a standard procedure. This point corresponds to a minimizing sequence for the original functional. The advantage of this method over the well-known regularization method (addition of a small nondegenerate term) is that the latter requires solving a parametric series of problems with a vanishingly small additional term, while our method deals with a single problem. 
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A. V. Dmitruk; N. A. Manuilovich. Minimization of Degenerate Integral Quadratic Functionals. Informatics and Automation, Optimal Control and Differential Games, Tome 315 (2021), pp. 108-127. http://geodesic.mathdoc.fr/item/TRSPY_2021_315_a7/

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