Infinite-dimensional quadratic optimization: Interior-point methods and control applications

An infinite-dimensional convex optimization problem with the linear-quadratic cost function and linear-quadratic constraints is considered. We generalize the interior-point techniques of Nesterov-Nemirovsky to this infinite-dimensional situation. The complexity estimates obtained are similar to finite-dimensional ones. We apply our results to the linear-quadratic control problem with quadratic constraints. It is shown that for this problem the Newton step is basically reduced to the standard LQ problem. This research was supported in part by the Cooperative Research Centre for Robust and Adaptive Systems while the first author visited the Australian National University and by NSF Grant DMS 94-23279.