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

Leonid Faybusovich and John Moore

An infinite-dimensional convex quadratic programming problem with linear-quadrat ic constraints in a Hilbert space is considered. We generalize the interior-poin t technique of Nesterov -Nemirovsky to this situaton. The obtained complexity es timates are similar to finite-dimensional ones. We apply our results to the line ar-quadratic control problem with quadratic constraints. It is shown that for th is problem the Newton step is basically reduced to solving the matrix Riccati d ifferential equation plus a system of linear algebraic equations of the size m b y m where m is the number of inequality constraints. The results of this paper have been reported during recent Stockholm Optimization days.

Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden, January, 1995.