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We develop novel dual-ascent and primal-dual methods to solve infinite-horizon nonstationary deterministic dynamic programs. These methods are finitely implementable and converge in value to optimality. Moreover, the dual-ascent method produces a sequence of improving dual solutions that pointwise converge to an optimal dual solution, while the primal-dual algorithm provides a sequence of primal basic feasible solutions with value error bounds from optimality that converge to zero. Our dual-based methods work on a more general class of infinite network flow problems that include the shortest-path formulation of dynamic programs as a special case. To our knowledge, these are the first dual-based methods proposed in the literature to solve infinite-horizon nonstationary deterministic dynamic programs.