Minimization of Degenerate Integral Quadratic Functionals

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.