Matrix Completion Problems
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 . The relationships between the two is discussed in e.g. [465, 464, 380].)
KeywordsSemidefinite Program Complementary Slackness Completion Problem Euclidean Distance Matrix Positive Semidefinite Matrice
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