arXiv subjects
Publications and source records attributed to Santiago Gonzalez Zerbo.
A quadratically constrained quadratic programming problem is considered in a Hilbert space setting, where neither the objective nor the constraint are convex functions. Necessary and sufficient conditions are provided to guarantee that the problem admits solutions for every initial data (in an adequate set).
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).
An abstract indefinite least squares problem with a quadratic constraint is considered. This is a quadratic programming problem with one quadratic equality constraint, where neither the objective nor the constraint are convex functions. Necessary and sufficient conditions are found for the existence of solutions.
Along this work we study an indefinite abstract smoothing problem. After establishing necessary and sufficient conditions for the existence of solutions to this problem, the set of admissible parameters is discussed in detail. Then, its relationship with a linearly constrained interpolation problem is analyzed.