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The optimization problems with simple bounds are an important class ofproblems. To facilitate the computation of such problems, an unconstrained-likedynamic method, motivated by the Lyapunov control principle, is proposed. Thismethod employs the anti-windup limited integrator to address the bounds ofparameters upon the dynamics for unconstrained problem, and then solves thetransformed Initial-value Problems (IVPs) with mature Ordinary DifferentialEquation (ODE) integration methods. It is proved that when the gain matrix isdiagonal, the result is equivalent to that of the general dynamic method whichinvolves an intermediate Quadratic Programming (QP) sub-problem. Thus, theglobal convergence to the optimal solution is guaranteed without therequirement of the strict complementarity condition. Since the estimation ofthe right active constraints is avoided and no programming sub-problem isinvolved in the computation process, it shows higher efficiency than thegeneral dynamic method and other common iterative methods through the numericalexamples. In particular, the implementation is simple, and the proposed methodis easy-to-use.

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