A stable differential equation approach for inequality constrained optimization problems

This paper presents a first-order derivatives based and a second-order derivatives based differential equation systems for inequality constrained optimization problems by using the modified barrier function. Under the suitable conditions, we prove the asymptotic stability of the two differential systems and local convergence properties of their Euler discrete schemes, including the locally quadratic convergence rate of the discrete algorithm for second-order derivatives based differential equation system. Numerical tests are presented that confirm the robustness and efficiency of the approach.