A bundle method for efficiently solving large structured linear matrix inequalities
Scott A. Miller, Roy S. Smith · 2000
An algorithm is proposed for solving large LMI feasibility problems, which exploits the structure of the LMI and avoids forming and manipulating large matrices. It is derived from the spectral bundle method of Helmberg and Rendl (1997), but modified to properly handle inexact eigenvalues and eigenvectors obtained from Lanczos iterations. The complexity is estimated from numerical experiments and it compares favorably with structured interior-point methods; moreover, this approach applies to more general structures.