A Novel Path-Following Method for Time-Varying Optimizations with Optimal Parametric Functions

We address a broad category of nonlinear constrained optimization problems. We then reformulate it as a time-varying optimization using continuous-time parametric functions and derive a dynamical system to track the respective optimal solution. We then re-parameterize the dynamical system according to a linear combination of parametric functions. By applying the calculus of variations, we optimize these parametric functions to minimize the optimality distance. Consequently, we develop an iterative dynamic algorithm, termed as OP-TVO, to achieve efficient convergence to the solution. We compare the performance of the proposed algorithm with the prediction correction method (PCM) in terms of optimality and computational complexity. The results demonstrate that OP-TVO effectively competes with PCM for the given class of optimization problems, suggesting a promising alternative to PCM. This work also introduces a novel paradigm for solving parametric dynamic systems.