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存零约束优化问题的序列二次方法

罗美铃 李高西 黄应全 刘丽颖

罗美铃,李高西,黄应全,刘丽颖. 存零约束优化问题的序列二次方法 [J]. 应用数学和力学,2022,43(7):792-801 doi: 10.21656/1000-0887.420294
引用本文: 罗美铃,李高西,黄应全,刘丽颖. 存零约束优化问题的序列二次方法 [J]. 应用数学和力学,2022,43(7):792-801 doi: 10.21656/1000-0887.420294
LUO Meiling, LI Gaoxi, HUANG Yingquan, LIU Liying. SQP Methods for Mathematical Programs With Switching Constraints[J]. Applied Mathematics and Mechanics, 2022, 43(7): 792-801. doi: 10.21656/1000-0887.420294
Citation: LUO Meiling, LI Gaoxi, HUANG Yingquan, LIU Liying. SQP Methods for Mathematical Programs With Switching Constraints[J]. Applied Mathematics and Mechanics, 2022, 43(7): 792-801. doi: 10.21656/1000-0887.420294

存零约束优化问题的序列二次方法

doi: 10.21656/1000-0887.420294
基金项目: 国家自然科学基金(11901068);重庆市自然科学基金(cstc2019jcyj-msxmX0760;cstc2021jcyj-msxmX0499)
详细信息
    作者简介:

    罗美铃(1998—),女,硕士生(E-mail:hana_lml@163.com)

    李高西(1988—),男,博士(通讯作者. E-mail:ligaoxicn@163.com)

  • 中图分类号: O211

SQP Methods for Mathematical Programs With Switching Constraints

  • 摘要:

    存零约束优化(MPSC)问题是近年来提出的一类新的优化问题,因存零约束的存在,使得常用的约束规范不满足,以至于现有算法的收敛性结果大多不能直接应用于该问题。应用序列二次规划(SQP)方法求解该问题,并证明在存零约束的线性独立约束规范下,子问题解序列的聚点为原问题的Karush-Kuhn-Tucker点。同时为了完善各稳定点之间的关系,证明了强平稳点与KKT点的等价性。最后数值结果表明,序列二次规划方法处理这类问题是可行的。

  • 表  1  MPSCs数值结果

    Table  1.   MPSCs numerical results

    example${\boldsymbol{x}}^*$${\boldsymbol{x}}'$SNT
    1(1,1,1)(1.0,1.0,1.0)1190.0070
    2(0,0)(0.0,0.0)140.0043
    3(0,0)(−0.0,−0.0)1170.0065
    4(0,0)(−0.0,0.0)1360.0082
    下载: 导出CSV

    表  2  投资组合数值结果

    Table  2.   Portfolio numerical results

    $n$SNT
    501240.1685
    1001280.6690
    2001363.3620
    5000.964961.2914
    8000.90591387.5846
    10000.86632336.6510
    12000.82694425.9890
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-09-26
  • 修回日期:  2021-11-23
  • 刊出日期:  2022-07-15

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