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The second⁃order differential equation method with perturbation terms for solving variational inequality problem
Received date: 2023-04-10
Online published: 2023-12-22
The second-order differential equations with perturbation terms to solve variational inequality problem were focused on and discussed the convergence of its solution and the speed of the convergence. Firstly,the Karush-Kuhn-Tucker (KKT) conditions of the original variational inequality problem were equivalently transformed into a system of smoothing equations by using a smoothing complementary function,and it was furtherly equivalent to an unconstrained optimization problem. Secondly,a system of second-order differential equations with perturbation terms was established to solve the final unconstrained optimization problem and discuss the stability of the differential equation system and the speed of convergence under the certain conditions. The convergence and the speed of the convergence for the solution to the original variational inequality problem was discussed. Finally,numerical experiments were given to show the effectiveness of the differential equation method for solving the variational inequality problem.
Danna WANG Li JIA , Juhe SUN , Huiting ZHUANG , Yanhong YUAN . The second⁃order differential equation method with perturbation terms for solving variational inequality problem[J]. Journal of Shenyang Aerospace University, 2023 , 40(5) : 90 -96 . DOI: 10.3969/j.issn.2095-1248.2023.05.012
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