| 次b凸函数和次b凸规划 |
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| 引用本文： | 晁绵涛,简金宝,梁东颖. 次b凸函数和次b凸规划[J]. 运筹学学报, 2012, 16(2): 1-8 |
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| 作者姓名： | 晁绵涛 简金宝 梁东颖 |
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| 作者单位： | 1. 北京工业大学应用数理学院，北京，1000124；;2. 广西教育学院数学与计算机科学系，南宁，530023；;3. 广西大学数学与信息科学学院，南宁，530004；;4. 广西交通职业技术学院，南宁，530023 |
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| 基金项目： | 国家自然科学基金，广西自然科学基金 |
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| 摘 要： | 研究一种称为次b 凸函数的广义凸函数, 并介绍了次b 凸集的概念. 分别在一般情形及可微情形下讨论了次b 凸函数的相关性质, 得到了次b 凸函数成为拟凸函数及伪凸函数的充分条件. 最后, 在次b 凸函数的条件下给出了无约束及带不等式约束规划的最优性条件.
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| 关 键 词： | 凸函数 次b 凸集合 次b 凸函数 伪次b凸函数 最优性条件 |
| 收稿时间： | 2011-05-30 |
| 修稿时间： | 2011-08-21 |
Sub-b-convex functions and sub-b-convex programming |
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| CHAO Miantao , JIAN Jinbao , LIANG Dongying. Sub-b-convex functions and sub-b-convex programming[J]. OR Transactions, 2012, 16(2): 1-8 |
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| Authors: | CHAO Miantao JIAN Jinbao LIANG Dongying |
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| Affiliation: | 1. College of Applied Sciences, Beijing University of Technology, Beijing 100124, China; 2. Department of Mathematics and Computer Science, Guangxi College of Education, Nanning 530023, China; 3. College of Mathematics and Information Science, Guangxi University, Nanning 530004, China; 4. Guangxi Vocational and Technical College of Communications, Nanning 530023, China |
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| Abstract: | The paper studied a new generalized convex function which called sub-b-convex function,and introduced a new concept of sub-b-convex set.The basic properties of sub-b-convex functions were discussed in general case and differentiable case,respectively. And,obtained the sufficient conditions that the sub-b-convex function become quasi-convex function or pseudo-convex function.Furthermore,the sufficient conditions of optimality for unconstrained and inequality constrained programming were obtained under the sub-b-convexity. |
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| Keywords: | convex function sub-b-convex set sub-b-convex function pseudo-sub-b-convex function optimality conditions |
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