We study an extension to Krein spaces of the abstract interpolating spline problem in Hilbert spaces, introduced by M. Atteia. This is a quadratically constrained quadratic programming problem, where the objective function is not convex, while the equality constraint is sign indefinite. We characterize the existence of solutions and, if there are any, we describe the set of solutions as the union of a family of affine manifolds parallel to a fixed subspace, which depend on the original data.

中文翻译：

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具有二次约束的不定抽象样条

我们研究了 M. Atteia 介绍的 Hilbert 空间中抽象插值样条问题的 Kerin 空间的扩展。这是一个二次约束二次规划问题，其中目标函数不是凸的，而等式约束是符号不定的。我们描述解的存在性，如果有的话，我们将解集描述为与固定子空间平行的仿射流形族的并集，这取决于原始数据。