Generalized Duality Theory on the General Multistage Recourse Problem

Abstract:

      The gerneralized duality theory and optimality condition of general multistage nonlinear stochastic programming with recourse is discussed in this paper. The meaning of concepts relevant to duality theories of usual programming problems is extended through exploring the essence of duality theories about convex programming, the generalized primal, dual functions of the discussed problem in the equivalent sense is then constructed and the corresponding duality theory is drived. The obtained results not only reflect properties of the problem itself properly and reasonably, but also describe the relative theorems concisely with strong conclusions, which can be directly and concretely applied to the study of other theoretical problems of multistage problem with recourse and the designing of their numerical solving algorithms.