Nonconvex problems of global optimization: Linear-quadratic control problems with quadratic constraints (Q676051)

In the paper, a class of global constrained optimization problems which may be nonconvex in general is studied. A simple approach to their solution is presented. Special attention is paid to the case when the objective and constraints functions are quadratic functionals on a Hilbert space. As an example of an application of the general approach, a method is presented by which an optimal controller can be synthesized for a finite-horizon linear-quadratic control problem with quadratic constraints. Both, inequality and equality constraints are considered. The objective and constraints functionals may be nonconvex and may contain both integral and terminal summands. It is shown that, under certain assumptions, the optimal control exists, is unique, and has feedback structure. Furthermore, the optimal controller can be computed by the methods of classic linear-quadratic control theory coupled with those of finite-dimensional convex programming.