| 一类具有连续变量的全局最优化问题的凸化方法 |
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| 引用本文： | 李博,杜杰,万立娟.一类具有连续变量的全局最优化问题的凸化方法[J].数学杂志,2016,36(4):851-858. |
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| 作者姓名： | 李博 杜杰 万立娟 |
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| 作者单位： | 青岛科技大学数理学院, 山东 青岛 266061,青岛科技大学数理学院, 山东 青岛 266061,青岛科技大学数理学院, 山东 青岛 266061 |
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| 基金项目： | 山东省优秀中青年科学家科研奖励基金资助(BS2013SF014). |
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| 摘 要： | 本文研究了一类非凸最优化问题的凸化方法与最优性条件的问题.利用构造含有参数的函数变换方法,将具有次正定性质的目标函数凸化,并获得了这一类非凸优化问题全局最优解的充要条件,推广了凸化方法在求解全局最优化问题方面的应用.
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| 关 键 词： | 全局优化 次正定函数 凸化 充要条件 |
| 收稿时间： | 2015/1/15 0:00:00 |
| 修稿时间： | 2015/5/6 0:00:00 |
CONVEXIFICATION APPROACHES FOR A CLASS OF CONTINUOUS GLOBAL OPTIMIZATION PROBLEM |
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| LI Bo,DU Jie and WAN Li-juan.CONVEXIFICATION APPROACHES FOR A CLASS OF CONTINUOUS GLOBAL OPTIMIZATION PROBLEM[J].Journal of Mathematics,2016,36(4):851-858. |
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| Authors: | LI Bo DU Jie and WAN Li-juan |
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| Institution: | School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China,School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China and School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China |
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| Abstract: | In this paper, we develop convexification approaches and optimization criteria for a general class of nonconvex optimization problem. By using the method of function trans-formations with parameter, a class of novel convexification schems is presented for solving global optimization problem with positive sub-definite objective function. The general class of nonconvex programming discussed in the paper can be solved to global optimality, which extends applications of convexification schems in solving global optimization problems. |
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| Keywords: | global optimization positive sub-definite function convexification necessary and sufficient condition |
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