Abstract:  This paper investigates the theory of primal linear-programming (LP) problem and its dual problems, which could be used to develop a kind of recurrent neural network for solving online LP problems as well as kinematic control of redundant manipulators. For example, a so-called usual primal-dual neural network (PDNN) initiated by Tang et al. However, due to the complexity and diversity of duality theory, that PDNN needs to be improved so as to obtain the optimal solution(s) instead of feasible solutions. Computer-simulation results substantiate the efficacy and correctness of the improved PDNN model for online solution of LP problems.