Algorithms, Applications and Theory of Mathematical Programming

并行算法将用于一般的非线性规划以及线性和二次规划。重点将放在最近提出的并行处理器之间的约束分配思想，以及线性互补问题的不精确和精确矩阵分裂方法。数学规划在模式识别和神经网络方面的应用也将进行，优化算法的潜力尚未充分实现。将特别注意医疗诊断问题，其中一些已经成功地解决了线性规划。上述算法和应用所需的数学理论将得到发展和完善。一个重要而有前途的领域是各种数学程序的误差界。

Parallel algorithms will be developed for general nonlinear programs as well as for linear and quadratic programs. Emphasis will be placed on the recently proposed idea of constraint distribution among parallel processors as well as inexact and exact matrix splitting methods for the linear complementarity problem. Applications of mathematical programming to pattern recognition and neural networks will also be made, where the potential of optimization algorithms has not been fully realized. Particular attention will be given to medical diagnostic problems, some of which have been successfully solved by linear programming. Mathematical theory that is needed for the above algorithms and applications will be developed and sharpened. An important and promising area to be focused on is that of error bounds for various types of mathematical programs.