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.