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Date of Publication:2022-10-04

Journal:Mathematica Numerica Sinica

Volume:43

Issue:2

Page Number:227-240

ISSN No.:0254-7791

Key Words:"Spectrum norm; infinite norm; quadratic programming; G-ADMM method"

CN No.:11-2125/O1

Abstract: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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