Time-Varying Optimization with Optimal Parametric Function

In this paper, we consider a class of nonlinear constrained optimization problems. We formulate this problem as a time-varying optimization using continuous-time parametric functions and derive a dynamical system for tracking the optimal solution. We then re-parameterize the dynamical system to express it as a linear combination of the parametric functions. Calculus of variations is applied to optimize the parametric functions, such that the optimality distance of the solution is minimized. Accordingly, an iterative dynamic algorithm is devised to find the solution with an efficient convergence rate. We benchmark the performance of the proposed algorithm with the prediction-correction method from the optimality and computational complexity point-of-views.