Division of Automatic Control
Department of Electrical Engineering
Many important applications of semidefinite programming in automatic control and signal processing involve constraints originating from the Kalman-Yakubovich-Popov lemma. Often the number of variables is very large making it difficult to use general purpose SDP solvers. However,if the structure of the SDP is utilized it is possible to solve a reduced order problem and afterwards reconstruct the solution to the original problem. This will reduce the computational cost significantly making it possible to solve large problems in reasonable time. Another advantage is that any general purpose primal-dual SDP solver can be used.
Some extensions to further improve efficency will also be discussed. This will require customized software though.