A Corollary and Proof about Sequential Quadratic Programming and lp Penalty Function

Miao Qing; Tang Song; Ling Bingo Wing-Kuen

doi:10.3969/j.issn.1007-7162.2016.05.001

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A Corollary and Proof about Sequential Quadratic Programming and lp Penalty Function

更新时间：2026-05-27

- A Corollary and Proof about Sequential Quadratic Programming and lp Penalty Function
- Vol. 33, Issue 5, Pages: 1-4(2016)
- 作者机构：
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- DOI：10.3969/j.issn.1007-7162.2016.05.001
  CLC：
- Online First：10 September 2016，
  
  Published：2016
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苗晴, 唐颂, 凌永权. 一种关于序列二次规划和l_p罚函数的推论与证明[J]. 广东工业大学学报, 2016, 33(5): 1-4. DOI: 10.3969/j.issn.1007-7162.2016.05.001.

Miao Qing, Tang Song, Ling Bingo Wing-Kuen. A Corollary and Proof about Sequential Quadratic Programming and lp Penalty Function[J]. 2016, 33(5): 1-4.
苗晴, 唐颂, 凌永权. 一种关于序列二次规划和l_p罚函数的推论与证明[J]. 广东工业大学学报, 2016, 33(5): 1-4. DOI: 10.3969/j.issn.1007-7162.2016.05.001. DOI：

Miao Qing, Tang Song, Ling Bingo Wing-Kuen. A Corollary and Proof about Sequential Quadratic Programming and lp Penalty Function[J]. 2016, 33(5): 1-4. DOI： 10.3969/j.issn.1007-7162.2016.05.001.

摘要

针对一般的含有不等式和等式约束的非线性优化问题，给出了一个关于序列二次规划和lp罚函数的推论与证明.推导了当取相应的二次规划子问题的解作为搜索方向时，则lp罚函数沿该搜索方向的方向导数满足一定的不等式条件；同时通过确定罚参数的取值范围，证明了该搜索方向是lp罚函数在原问题处的下降方向.

Abstract

For a general nonlinear optimization problem with both inequality and equality constraints

a corollary on the optimization problem with a lp penalty function is studied and proved based on the sequential quadratic programming approach. In particular

the corollary defines the inequality condition for the search direction of the optimization problem. Moreover

it proves that the derived search direction is a descent direction of the penalty function in the original problem by determining the range of penalty parameter.

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