Robust nonlinear least squares via consecutive LMI optimizations

An algorithm is developed for robust nonlinear least-squares optimization in which the function to be minimized has dependence on an uncertain parameter. The goal is to minimize the worst-case norm-square of the function, under the assumption that the uncertain parameter can take any value from a given compact region. The algorithm simply replaces the quadratic optimization in the Gauss-Newton update scheme with a robust linear matrix inequality (LMI) optimization step.