Restricted linear constrained minimization of quadratic functionals

摘要

In this work, a linearly constrained minimization of a positive semidefinite quadratic functional is examined. We propose two different approaches to this problem. Our results are concerning infinite dimensional real Hilbert spaces, with a singular positive semidefinite operator related to the functional, and considering as constraint a singular operator. The difference between the proposed approaches for the minimization and previous work on this problem is that it is considered for all vectors belonging to the least squares solutions set, or to the vectors perpendicular to the kernel of the related operator or matrix.