In the past decade or so, semi-definite programming (SDP) has emerged as a powerful tool capable of handling a remarkably wide range of problems. This article describes an innovative application of SDP techniques to quadratic inverse eigenvalue problems (QIEPs). The notion of QIEPs is of fundamental importance because its ultimate goal of constructing or updating a vibration system from some observed or desirable dynamical behaviors while respecting some inherent feasibility constraints well suits many engineering applications. Thus far, however, QIEPs have remained challenging both theoretically and computationally due to the great variations of structural constraints that must be addressed. Of notable interest and significance are the uniformity and the simplicity in the SDP formulation that solves effectively many otherwise very difficult QIEPs.

中文翻译：

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结构化二次特征值反问题的半定规划技术。


在过去十年左右的时间里，半定规划（SDP）已经成为一种强大的工具，能够处理非常广泛的问题。本文介绍了 SDP 技术在二次逆特征值问题 (QIEP) 中的创新应用。 QIEP 的概念至关重要，因为其最终目标是根据一些观察到的或理想的动态行为构建或更新振动系统，同时尊重一些固有的可行性约束，非常适合许多工程应用。然而，到目前为止，由于必须解决结构约束的巨大变化，QIEP 在理论和计算上仍然具有挑战性。值得注意和重要的是 SDP 公式的一致性和简单性，它有效地解决了许多原本非常困难的 QIEP。