An unconstrained-like control-based dynamic method for optimization problems with simple bounds

The optimization problems with simple bounds are an important class of problems. To facilitate the computation of such problems, an unconstrained-like dynamic method, motivated by the Lyapunov control principle, is proposed. This method employs the anti-windup limited integrator to address the bounds of parameters upon the dynamics for unconstrained problem, and then solves the transformed Initial-value Problems (IVPs) with common Ordinary Differential Equation (ODE) integration methods. It is proved that when the gain matrix is diagonal, the result is equivalent to that of the general dynamic method which involves an intermediate Quadratic Programming (QP) sub-problem. Thus, the global convergence to the optimal solution is guaranteed. Since the estimation of the right active constraints is avoided and no programming sub-problem is involved in the computation, it shows better performance than the general dynamic method and other common iterative methods through the numerical examples. Moreover, the implementation is simple, and thus the proposed method is easy-to-use.