On the rank minimization problem over a positive semidefinite linear matrix inequality
Mehran Mesbahi, George P. Papavassilopoulos · IEEE Transactions on Automatic Control · 1997
We consider the problem of minimizing the rank of a positive semidefinite matrix, subject to the constraint that an affine transformation of it is also positive semidefinite. Our method for solving this problem employs ideas from the ordered linear complementarity theory and the notion of the least element in a vector lattice. This problem is of importance in many contexts, for example in feedback synthesis problems, and such an example is also provided.