| 拟凸多目标优化问题近似解的最优性条件 |
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| 引用本文： | 陈瑞婷,徐智会,高英.拟凸多目标优化问题近似解的最优性条件[J].运筹学学报,2019,23(1):35-44. |
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| 作者姓名： | 陈瑞婷 徐智会 高英 |
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| 作者单位： | 重庆师范大学数学科学学院, 重庆 400047 |
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| 基金项目： | 国家自然科学基金（Nos.11771064，11431004），重庆市科委项目（Nos.cstc2015jcyjA00005，cstc2018jcyj-yszxX0009），重庆市教委项目（No.KJ1500309） |
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| 摘 要： | 研究了拟凸多目标优化问题近似弱有效解、近似有效解的最优性条件.首先,在已有拟凸函数次微分的基础上引进4种近似次微分的概念,并给出它们之间的关系.然后,将4种近似次微分的概念应用到拟凸多目标优化问题中,给出了拟凸多目标优化问题近似弱有效解和近似有效解的充分条件和必要条件,并给出实例加以说明.
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| 关 键 词： | 拟凸函数 多目标优化 近似次微分 近似解 最优性条件 |
| 收稿时间： | 2017-07-10 |
The optimality conditions of approximate solutions for quasiconvex multiobjective optimization problem |
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| CHEN Ruiting,XU Zhihui,GAO Ying.The optimality conditions of approximate solutions for quasiconvex multiobjective optimization problem[J].OR Transactions,2019,23(1):35-44. |
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| Authors: | CHEN Ruiting XU Zhihui GAO Ying |
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| Institution: | School of Mathematical Sciences, Chongqing Normal University, Chongqing 400047, China |
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| Abstract: | In this paper, we study the optimality conditions of approximate weak efficient solutions and approximate efficient solutions for quasiconvex multiobjective optimization problems. We introduce four concepts of approximate subdifferentials based on the existing subdifferentials of quasiconvex function, and give the relationship among them. And then, we apply these concepts to the quasiconvex multiobjective optimization problems, derive the sufficient conditions and necessary conditions for the approximate weak efficient solutions and the approximate efficient solution, and give some examples to illustrate the main results. |
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| Keywords: | quasiconvex function multiobjective optimization problems approximate subdifferentials approximate solutions optimality conditions |
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