Combining Convex-Concave Decompositions and Linearization Approaches for   solving BMIs, with application to Static Output Feedback
  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. 
Quoc Tran Dinh, Suat Gumussoy, Wim Michiels and Moritz Diehl
math.OC cs.SY