Robust Semidefinite Programming Problems with General Nonlinear Parameter Dependence: Application of the DC-Representations

Two conservative approaches are proposed to a semidefinite programming problem nonlinearly dependent on uncertain parameters. These approaches are applicable to general nonlinear parameter dependence not necessarily polynomial or rational. They are based on a mild assumption that the parameter dependence is expressed as the difference of two convex functions. The first approach uses constant bounds on the parameter dependence. Optimization of the bounds is reduced to convex nonsmooth minimization in general. The second approach uses parameter-dependent bounds for a less conservative result. Optimization of the bounds is immediate when the gravity center is computable for the parameter set. Numerical examples are presented for illustration of the approaches.