  A novel optimization method is proposed to minimize a convex function subject
to bilinear matrix inequality (BMI) constraints. The key idea is to decompose
the bilinear mapping as a difference between two positive semidefinite convex
mappings. At each iteration of the algorithm the concave part is linearized,
leading to a convex subproblem.Applications to various output feedback
controller synthesis problems are presented. In these applications the
subproblem in each iteration step can be turned into a convex optimization
problem with linear matrix inequality (LMI) constraints. The performance of the
algorithm has been benchmarked on the data from COMPleib library.
