The mathematical basis of the general theory is Bellman's dynamic programming (DP) and associated maximum principles. Our original contribution develops a generalized theory for multistage discrete processes in which time intervals can reside in the model nonlinearly and can be constrained. The new theory removes the requirement of the free intervals θn, yet preserves the most powerful features of the continuous theory of Pontryagin in the discrete context. Applications deal with dynamic optimization of diverse energy and chemical systems in which a minimum of entropy generation is the criterion of performance; from this basic criterion reasonable partial criteria are derived. It is possible to handle optimality conditions for complex systems with state dependent coefficients, and thus to generalize analytical solutions obtained in linear cases to nonlinear situations. Correspondence is shown with basic theoretical mechanics and classical Hamilton-Jacobi theory when the number of stages approaches an infinity. This paper was presented at the ECOS'00 Conference in Enschede, July 5-7, 2000