A Dynamic Inversion Approach to Time-Varying Optimization

In this paper, we solve a class of time-varying optimization problems. A dynamic inversion approach is used to provide a continuous-time optimization algorithm. The dynamic inversion yield a Newton-based time varying continuoustime dynamics that guarantees asymptotic convergence of the algorithm to the optimal time-varying solution. The Newtonbased implementation of the algorithm avoids the explicitly computation of the inverse of the time-varying Hessian matrix which significantly reduces the computational complexity while preserving the accuracy of the optimization process. The study provides a detailed stability analysis of the approach. An application of the dynamic inversion approach to time-varying distributed optimization problems is considered. A simulation study is conducted to assess the performance of the proposed technique.