| 一类优化问题的线性松弛方法 |
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| 引用本文： | 焦红伟,张万琴,陈永强.一类优化问题的线性松弛方法[J].苏州科技学院学报(自然科学版),2008,25(3). |
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| 作者姓名： | 焦红伟 张万琴 陈永强 |
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| 作者单位： | 1. 河南科技学院,数学系,河南,新乡,453003
2. 河南师范大学,数学系,河南,新乡,453007 |
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| 基金项目： | 河南省自然科学基金，河南省教育厅自然科学基金 |
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| 摘 要： | 对一类优化问题（P）给出了一线性松弛方法。利用对数的性质建立了问题（P）的等价问题（P1），利用切平面和凹包逼近，建立了问题（P1）的松弛线性规划（LRP）。通过对可行域线性松弛的逐次细分以及求解一系列的线性规划（LRP），提出的算法收敛到问题（P1）的全局最优解。数值实验结果表明了提出方法的可行性。
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| 关 键 词： | 全局优化 线性松弛方法 分枝定界 |
A Linear Relaxation Method for a Class of Optimization Problems |
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| JIAO Hong-wei,ZHANG Wan-qin,CHEN Yong-qiang.A Linear Relaxation Method for a Class of Optimization Problems[J].Journal of University of Science and Technology of Suzhou,2008,25(3). |
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| Authors: | JIAO Hong-wei ZHANG Wan-qin CHEN Yong-qiang |
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| Abstract: | In this paper a linear relaxation method is proposed for a class of optimization problems(P).By utilizing logarithrnic property,we have established an equivalent problem(P1)of the(P).By utilizing tangential hyper-surfaces and concave envelope approximations,we have received a linear relaxation programming of the(P1).The proposed algorithm is convergent to the global minimum of(P1)through the successive refinement of a feasible regional linear relaxation and solutions of a series of linear programming problems．Numerical results show the feasibility of the proposed algorithm. |
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| Keywords: | global optimization linear relaxation method branch and bound |
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