This paper presents a unified gradient flow approach to nonlinear constrained optimization problems. This method is based on a continuous gradient flow reformulation of constrained optimization problems and on a two level time discretization of the gradient flow equation with a splitting parameter theta. The convergence of the scheme is analyzed and it is shown that the scheme becomes first order when theta is an element of [0, 1] and second order when theta = 1 and the time discretization step length is sufficiently large. Numerical experiments for continuous, discrete and mixed discrete optimization problems were performed, and the numerical results show that the approach is effective for solving these problems.
Wang, S., Yang, X. Q., & Teo, K. L. (2003). A Unified Gradient Flow Approach to Constrained Nonlinear Optimization Problems. Computational Optimization and Applications, 25(1-3), 251-268. https://doi.org/10.1023/A:1022973608903