一般形式多阶段有补偿问题的广义对偶理论

本文在文［１］的基础上，讨论一般形式多阶段有补偿非线性随机规划问题的广义对偶理论与最优化性条件．通过发掘凸规划对偶理论的本质，首先推广了与通常规划问题对偶理论有关的概念的含义，由此构造出所论问题在等价意义下的广义原始泛函与广义对偶泛函，进而得到其广义对偶理论，所得结论不仅能恰当合理地反映问题本身的属性，而且有关定理的表述形式简明、结论较强，可直接应用于多阶段有补偿问题的其它理论研究与数值求解算法的设计中去．上述结果与所用研究方法均推广和发展了通常的对偶理论

Generalized Duality Theory on the General Multistage Recourse Problem

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.