Abstract
A common optimization problem is the minimization of a symmetric positive definite quadratic form $\langle x,Tx\rangle$ under linear constraints. The solution to this problem may be given using the Moore-Penrose inverse matrix. In this work at first we extend this result to infinite dimensional complex Hilbert spaces, where a generalization is given for positive operators not necessarily invertible, considering as constraint a singular operator. A new approach is proposed when $T$ is positive semidefinite, where the minimization is considered for all vectors belonging to $\mathcal{N}(T)^\perp$.
Citation
Dimitrios Pappas. "Minimization of constrained quadratic forms in Hilbert spaces." Ann. Funct. Anal. 2 (1) 1 - 12, 2011. https://doi.org/10.15352/afa/1399900257
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