  We introduce an alternative approach for the analysis and numerical
approximation of the optimal feedback control mapping. It consists in looking
at a typical optimal control problem in such a way that feasible controls are
mappings depending both in time and space. In this way, the feedback form of
the problem is built-in from the very beginning. Optimality conditions are
derived for one such optimal mapping, which by construction is the optimal
feedback mapping of the problem. In formulating optimality conditions, costates
in feedback form are solutions of linear, first-order transport systems, while
optimal descent directions are solutions of appropriate obstacle problems. We
treat situations with no constraint-sets for control and state, as well as the
more general case where a constraint-set is considered for the control
variable. Constraints for the state variable are deferred to a coming
contribution.
