非线性约束最优化在广义投影下强次可行方向法的统一模型  

A Unified Model of Strongly Subfeasible Directions Method Using Generalized Projection for Nonlinear Constrained Optimization

作　　者：梁元星[1] 曾友芳[2] 

机构地区：[1]广西民族学院预科部,南宁530006 [2]广西大学数学与信息科学学院,南宁530004

出　　处：《桂林工学院学报》2005年第3期377-382,共6页Journal of Guilin University of Technology

基　　金：国家自然科学基金资助项目(10261001)

摘　　要：对非线性不等式约束最优化问题进行了讨论,借助广义投影建立求解问题的一个含系列自由参数的统一算法模型.该算法模型能以任意点为初始迭代点,并且迭代点列所满足的约束函数的个数单调不减,不断累加;进一步地,一旦迭代点进入可行域,模型就能保持在可行域内迭代,成为可行下降类算法.称具有这种性质的算法为强次可行方向法.在适当的条件下证明了算法模型的全局收敛性.文中模型同时提供了一种求解非线性不等式组的叠累型方法.Optimization problem with nonlinear inequality constraints is discussed. With the help of the generalized projection, a unified algorithm model with a series of free parameters is presented. The proposed algorithm model can start with an arbitrary initial point and the number of constrained functions, which satisfies the inequality constraints of the problem with a monotone nondecreasing in the iterative sequence. Furthermore, the model will keep iterating within the feasible region whenever the iterative point is feasible, and become feasible decreasing directions method. The algorithm with such properties is called Strongly Subfeasible Directions Method. The global convergence of the algorithm model is proved under suitable conditions. This model provides a kind of monotone build - up method for solving nonlinear inequalitics.

关 键 词：非线性约束最优化 广义投影 强次可行方向法 统一算法模型 全局收敛性 

分 类 号：O211.2[理学—概率论与数理统计]