An Alternating Direction Method of Multipliers for the Optimization Problem Constrained with a Stationary Maxwell System (Communications in Computational Physics, 2018)
This paper mainly focuses on an efficient numerical method for the optimizationproblem constrained with a stationary Maxwell system. Following the ideaof [32], the edge element is applied to approximate the state variable and the controlvariable, then the continuous optimal control problem is discretized into a finite dimensionalone. The novelty of this paper is the approach for solving the discretizedsystem. Based on the separable structure, an alternating direction method of multipliers(ADMM) is proposed. Furthermore, the global convergence analysis is establishedin the form of the objective function error, which includes the discretization error bythe edge element and the iterative error by ADMM. Finally, numerical simulations arepresented to demonstrate the efficiency of the proposed algorithm.
Keywords: Optimal control problem; stationary Maxwell's equations; Nédélec element; ADMM.