Verdu, Sergio; Poor, H. Vincent Abstract dynamic programming models under commutativity conditions. (English) Zbl 0631.90082 SIAM J. Control Optimization 25, 990-1006 (1987). 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. Cited in 6 Documents MSC: 90C39 Dynamic programming Keywords:operator models; finite and infinite horizon sequential optimization; discrete-time Markov processes; fixed-interval detection and smoothing; abstract dynamic programming; backward-forward models PDFBibTeX XMLCite \textit{S. Verdu} and \textit{H. V. Poor}, SIAM J. Control Optim. 25, 990--1006 (1987; Zbl 0631.90082) Full Text: DOI