The unifying purpose of the abstract dynamic programming models is to find sufficient conditions on the recursive definition of the objective function that guarantee the validity of the dynamic programming iteration. This paper presents backward, forward, and backward-forward models that weaken previous sufficient conditions and that include, but are not restricted to, optimization problems. The backward-forward model is devoted to the simultaneous solution of a collection of interrelated sequential problems based on the independent computation of a cost-to-arrive function and a cost-to-go function. Several extremization and nonextremization problems illustrate the applicability of the proposed models.
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