• 论文 •

### 一类不可微二次规划逆问题

1. 1. 辽宁工程技术大学理学院, 阜新 123000;
2. 大连理工大学数学科学学院, 大连 116024
• 收稿日期:2019-11-18 发布日期:2021-05-13
• 基金资助:
国家自然科学基金（No.11971089，11731013）和辽宁省教育厅项目（No.LJ2020QNL008）资助.

Li Lidan, Zhang Liwei, Zhang Hongwei. A TYPE OF NON-DIFFERENTIABLE INVERSE QUADRATIC PROGRAMMING PROBLEMS[J]. Mathematica Numerica Sinica, 2021, 43(2): 227-240.

### A TYPE OF NON-DIFFERENTIABLE INVERSE QUADRATIC PROGRAMMING PROBLEMS

Li Lidan1, Zhang Liwei2, Zhang Hongwei2

1. 1. College of Science, Liaoning Technical University, Fuxin 123000, China;
2. School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
• Received:2019-11-18 Published:2021-05-13

In this paper, a type of inverse quadratic programming problem is considered, which is a minimization problem of the sum of the matrix spectrum norm and the vector infinite norm. Firstly, the problem is transformed into a convex optimization problem with the objective function separable, and G-ADMM method is proposed to solve it. Then, we use the singular value threshold method, Moreau-Yosida regularization algorithm and the quadprog function in MATLAB optimization toolbox to solve the corresponding subproblem accurately. It is found that one subproblem is still a convex optimization problem with separable variables objective function. Because its variables are all matrices, so we adopt the alternative direction method suitable for multiple matrix variables to solve it. By introducing a new variable, we obtain that the solution of each subproblem has a display expression. Finally, the convergence analysis and numerical experiments of the G-ADMM method are given. The numerical experiments show that this method can solve the inverse quadratic programming problem efficiently and quickly.

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