Linear pencils and quadratic programming problems with a quadratic constraint

Given bounded selfadjoint operators $A$ and $B$ acting on a Hilbert space $\mathcal{H}$, consider the linear pencil $P(λ)=A+λB$, $λ\in\mathbb{R}$. The set of parameters $λ$ such that $P(λ)$ is a positive (semi)definite operator is characterized. These results are applied to solving a quadratic programming problem with an equality quadratic constraint (or a QP1EQC problem).

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