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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(X):1-10 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(X):1-10 doi: 10.21656/1000-0887.420294
Meiling LUO, Gaoxi LI, Yingquan HUANG, Liying LIU. SQP Methods for Mathematical Program With Switching Constraint[J]. Applied Mathematics and Mechanics. doi: 10.21656/1000-0887.420294
Citation: Meiling LUO, Gaoxi LI, Yingquan HUANG, Liying LIU. SQP Methods for Mathematical Program With Switching Constraint[J]. Applied Mathematics and Mechanics. 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-msxmX0456,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 Program With Switching Constraint

  • 摘要: 存零约束优化(MPSG)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的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
  • 网络出版日期:  2022-06-09

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