Solving convex programs by means of ordinary differential equations

Within a Hilbert space nonsmooth convex programs with sharp constraints are considered. Examples include all problem instances that are bounded and strictly feasible. To solve such programs, an absolutely continuous trajectory generated by a differential inclusion of subgradient type is pursued. Whenever this inclusion offers some freedom of choice, a steepest descent direction is selected. It is shown that the proposed algorithm converges to an optimal solution in finite time.