DC optimization approach to robust controls: The optimal scaling value problem

The optimal scaling problem (OSP) for constant scaling in output feedback c ontrol is an inherently difficult nonconvex problem for which in general ex isting local search algorithms can at best locate a local solution. However , it can be restated as a problem of globally minimizing a convex function under de constraints, i.e., constraints that can be expressed in terms of d ifferences of convex functions. A particular structure of this de optimizat ion problem is that it becomes convex when a relatively small number of "co mplicating" variables are held fixed. We propose alternative branch and bou nd algorithms for OSP, which exploit this structure by branching upon the c omplicating variables and use adaptive subdivision strategies to speed up t he convergence to the global solution.