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Matrix Completion Problems

  • Abdo Alfakih
  • Henry Wolkowicz
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 27)

Abstract

In the matrix completion problem we are given a partial symmetric real matrix A with certain elements specified or fixed and the rest are unspecified or free; and, we are asked whether A can be completed to satisfy a given property (P) by assigning certain values to its free elements. In this chapter, we are interested in the following two completion problems: the positive semidefinite matrix completion problem corresponding to (P) being the positive semi-defmiteness (PSD) property; and the Euclidean distance matrix completion problem corresponding to (P) being the Euclidean distance (ED) property. (We concentrate on the latter problem. A survey of the former is given in [373]. The relationships between the two is discussed in e.g. [465, 464, 380].)

Keywords

Semidefinite Program Complementary Slackness Completion Problem Euclidean Distance Matrix Positive Semidefinite Matrice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Abdo Alfakih
  • Henry Wolkowicz

There are no affiliations available

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