  We propose a primal--dual technique that applies to infinite dimensional
equality constrained problems, in particular those arising from optimal
control. As an application of our general framework, we solve a
control-constrained double integrator optimal control problem and the
challenging control-constrained free flying robot optimal control problem by
means of our primal--dual scheme. The algorithm we use is an
epsilon-subgradient method that can also be interpreted as a penalty function
method. We provide extensive comparisons of our approach with a traditional
numerical approach.
