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Semi-definite programming techniques for structured quadratic inverse eigenvalue problems

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, North Carolina State University, Raleigh, NC, 27695-8205, USA

    Matthew M. Lin & Moody T. Chu

  2. Department of Applied Mathematics, Dalian University of Technology, Dalian, Liaoning, 116024, China

    Bo Dong

Authors
  1. Matthew M. Lin
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  2. Bo Dong
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  3. Moody T. Chu
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Correspondence to Matthew M. Lin.

Additional information

Matthew M. Lin’s research was supported in part by the National Science Foundation under grants DMS-0505880 and DMS-0732299.

Bo Dong’s work is partially supported by Chinese Scholarship Council and DLUT (Dalian University of Technology) under grands 3004-893327 and 3004-842321.

Moody T. Chu’s research was supported in part by the National Science Foundation under grants DMS-0505880 and DMS-0732299 and NIH Roadmap for Medical Research grant 1 P20 HG003900-01.

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Lin, M.M., Dong, B. & Chu, M.T. Semi-definite programming techniques for structured quadratic inverse eigenvalue problems. Numer Algor 53, 419–437 (2010). https://doi.org/10.1007/s11075-009-9309-9

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