Rate preserving discretization strategies for semi-infinite programming and optimal control

Discretization of semi-infinite programming and optimal control problems is addressed. Three sets of discretization refinement rules are presented: (i) for unconstrained semi-infinite minimax problems; (ii) for constrained semi-infinite problems, and (iii) for unconstrained optimal control problems. These rules are built into a master algorithm which calls certain linearly converging algorithms for finite-dimensional, finitely described optimization problems. The discretization refinement rules ensure that the sequences constructed by the overall scheme converge to a solution of the original problem with the same rate constant as applied for the finite-dimensional, finitely described approximations. Hence the resulting scheme is more efficient than fixed discretization