In this paper we present and discuss some recent results of the author [Ahmed 1,2,4,7] on the necessary conditions of optimality for linear regulators and filters with or without constraints on system parameters. The approach provides algorithms for optimizations directly on the space of operators giving optimal regulators and filters. These results have been successfuly applied in navigation problems [Ahmed and Lim 4, Dabbous, Ahmed, McMillan and Liang 5] and also in partially observed control problems [Teo, Ahmed and Fisher 3]. The author believes that this approach is simpler and useful for computer aided design both for finite and infinite dimensional problems.