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| 一类非凸区域的拟法锥构造方法及其在非凸规划求解中的应用 | |
| 引用本文： | 李洪伟,刘庆怀,陶敏.一类非凸区域的拟法锥构造方法及其在非凸规划求解中的应用[J].应用数学学报,2006,29(6):1024-1032. |
| 作者姓名： | 李洪伟 刘庆怀 陶敏 |
| 作者单位： | 1. 山东科技大学经济管理学院,青岛,266510;南京航空航天大学经济与管理学院,南京,210016 2. 长春工业大学应用数学研究所,长春,130012 3. 山东科技大学经济管理学院,青岛,266510;吉林大学生物与农业工程学院,长春,130025 |
| 摘 要： | 本文给出基于球形的一类满足拟法锥条件区域的拟法锥构造方法,基于该可行域的拟法锥,建立求解在该类非凸区域上的规划问题的K-K-T点的部分凝聚同伦组合方程,并证明了该同伦内点法的整体收敛性,给出实现同伦内点法的具体数值跟踪算法步骤,并通过数值例子证明算法是可行的和有效的． |
| 关 键 词： | 非凸规划 拟法锥条件 凝聚函数 同伦内点法 |
| 收稿时间： | 2004-12-30 |
| 修稿时间： | 2004-12-302006-05-18 |
A Method to Construct a Quasi-normal Cone for a Class of Nonconvex Sets and its Applications in Solving Noncovex Programming |
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| LI HONGWEI,LIU QINGHUAI,TAO MIN.A Method to Construct a Quasi-normal Cone for a Class of Nonconvex Sets and its Applications in Solving Noncovex Programming[J].Acta Mathematicae Applicatae Sinica,2006,29(6):1024-1032. | |
| Authors: | LI HONGWEI LIU QINGHUAI TAO MIN |
| Institution: | 1Institute of Economics and Management, Shandong University of Science and Technology, Qingdao 266510;2The College of Economics and Management of Nanjing University of Aeronautics Astronautics, Nanjing 210016;3 The Institute of Applied Mathematics Changchun University of Technology, Changchun 130021;4 The School of Biological and Agricultural Engineering of Jinlin University, Changchun 130025 |
| Abstract: | In this paper, we give a method to construct a quasi-normal cone for a class of nonconvex sets based on a global, which satisfies quasi-normal cone condition, and construct a Partially Aggregate Combined Homotopy Interior Point method (PACHIP method) to solve the K-K-T point of Non-convex programming according to this quasi-normal set. We prove that PACHIP method has global convergence. The concrete procedures for numerically tracing of the arithmetic are given and it is proved that it is feasible and available by a numerical example. |
| Keywords: | non-convex programming quasi-normal cone condition coherent function combined homotopy interior point method |
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