On the Low Rank Solutions for Linear Matrix Inequalities
نویسندگان
چکیده
In this paper we present a polynomial-time procedure to find a low rank solution for a system of Linear Matrix Inequalities (LMI). The existence of such a low rank solution was shown in AuYeung and Poon [1] and Barvinok [3]. In Au-Yeung and Poon’s approach, an earlier unpublished manuscript of Bohnenblust [6] played an essential role. Both proofs in [1] and [3] are nonconstructive in nature. The aim of this paper is to offer a constructive and polynomial-time procedure to find such a low rank solution approximatively. Extensions of our new results and their relations to some of the known results in the literature are discussed.
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عنوان ژورنال:
- Math. Oper. Res.
دوره 33 شماره
صفحات -
تاریخ انتشار 2008