Restricted Linear Constrained Minimization of quadratic functionals

TL;DR

This paper investigates a linearly constrained minimization of positive semidefinite quadratic functionals in infinite-dimensional Hilbert spaces, focusing on vectors orthogonal to the kernel of associated operators, which extends previous approaches.

Contribution

It introduces a novel approach to quadratic minimization considering all vectors orthogonal to the kernel of the involved operators in infinite-dimensional spaces.

Findings

Extended minimization framework to all vectors perpendicular to the kernel

Applicable to singular positive operators in infinite-dimensional spaces

Provides new insights into constrained quadratic functional minimization

Abstract

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