New approach for nonseparable dynamic programming problems

A general class of nonseparable dynamic problems is studied in a dynamic programming framework by introducingkth-order separability. The solution approach uses multiobjective dynamic programming as a separation strategy forkth-order separable dynamic problems. The theoretical grounding on which the optimal solution of the original nonseparable dynamic problem can be attained by a noninferior solution of the corresponding multiobjective dynamic programming problem is established. The relationship between the overall optimal Lagrangian multipliers and the stage-optimal Lagrangian multipliers and the relationship between the overall weighting vector and the stage weighting vector are explored, providing the basis for identifying the optimal solution of the original nonseparable problem from among the set of noninferior solutions generated by the envelope approach.This work was supported in part by NSF Grant No. CES-86-17984. The authors appreciate the comments from Dr. V. Chankong and the editorial work by Mrs. V. Benade and Dr. S. Hitchcock.