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has been cited by the following article:

• TITLE: The Second-Order Differential Equation System with the Feedback Controls for Solving Convex Programming

  AUTHORS: Xingxu Chen, Li Wang, Juhe Sun, Yanhong Yuan

  KEYWORDS: Convex Programming, Lagrange Function, Projection Operator, Second-Order Differential Equation

  JOURNAL NAME: Open Journal of Applied Sciences, Vol.12 No.6, June 24, 2022

  ABSTRACT: In this paper, we establish the second-order differential equation system with the feedback controls for solving the problem of convex programming. Using Lagrange function and projection operator, the equivalent operator equations for the convex programming problems under the certain conditions are obtained. Then a second-order differential equation system with the feedback controls is constructed on the basis of operator equation. We prove that any accumulation point of the trajectory of the second-order differential equation system with the feedback controls is a solution to the convex programming problem. In the end, two examples using this differential equation system are solved. The numerical results are reported to verify the effectiveness of the second-order differential equation system with the feedback controls for solving the convex programming problem.