| 多目标凸规划凝聚同伦内点算法 |
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| 引用本文： | 杨轶华,赵立芹,吕显瑞,刘庆怀. 多目标凸规划凝聚同伦内点算法[J]. 吉林大学学报(理学版), 2006, 44(6): 883-887 |
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| 作者姓名： | 杨轶华 赵立芹 吕显瑞 刘庆怀 |
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| 作者单位： | 吉林大学,数学学院,长春,130012;吉林大学,学报编辑部,长春,130021;长春工业大学,应用数学研究所,长春,130012 |
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| 摘 要： | 研究凝聚同伦内点法求解多个约束的多目标凸光滑优化问题. 用凝聚函数将多目标凸函数凝聚为单目标凸函数, 再利用凝聚函数将多个凸约束凝聚为单个凸约束, 使原来的多约束多目标凸优化转变为单目标单个约束的凸规划问题, 再利用同伦内点法求得单目标凸优化的最优解， 即为原多目标凸优化的弱有效解.
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| 关 键 词： | 光滑优化 多目标优化 凝聚函数 凸规划 |
| 文章编号： | 1671-5489(2006)06-0883-05 |
| 收稿时间： | 2005-12-24 |
| 修稿时间： | 2005-12-24 |
The Aggregate Homotopy Interior-point Method for Multi-objective Convex Programming |
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| YANG Yi-hua,ZHAO Li-qin,L Xian-rui,LIU Qing-huai. The Aggregate Homotopy Interior-point Method for Multi-objective Convex Programming[J]. Journal of Jilin University: Sci Ed, 2006, 44(6): 883-887 |
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| Authors: | YANG Yi-hua ZHAO Li-qin L Xian-rui LIU Qing-huai |
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| Affiliation: | 1. College of Mathematics, Jilin University, Changchun 130012, China;2. Editorial Department of Journal of Jilin University, Changchun 130021, China; 3. Institute of Applied Mathematics, Changchun Industry University, Changchun 130012, China |
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| Abstract: | We solved the multi-objective convex smooth programming problem.At first we turned multi-(objective) convex smooth programming into convex smooth programming by means of aggregate funtion,then we turned convex smooth multi-constrains into convex smooth single constrain by virtue of aggregate function,at last we solved convex smooth programming via the aggregate homotopy method and got the weak effective(solutions) of multi-objective smooth programming.This method reduces the scale of the homotopy method,so it is easier to practice. |
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| Keywords: | smooth optimization multi-objective optimization aggregate function convex programming |
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