Smoothing Strategies in Solving Inverse Electromagnetic Problems

Abstract

Many inverse and optimal design problems of electrical engineering are formulated in terms of least squares methodology (linear and nonlinear least squares). The objective function used makes a square-root deviation between prescribed and actual field distribution in a controlled subregion. In the paper some numerical methods that proved to be particularly useful in solving such problems of electrical engineering are presented. The common feature of these methods is the need of choosing a smoothing parameter controlling the solution quality. It is shown how this parameter may be chosen when using linear least squares (regularization) approach and the trust-region approach in nonlinear least squares method. For completeness we present the zeroth-order stochastic methods of optimization as well. As opposed to least squares approach, the latter do not require restrictive a priori assumptions about convexity and smoothness. Some electromagnetic optimal design problems solved by means of the above techniques are referred.