ABSTRACT
This chapter discusses algorithms for solving the nonlinear Lp-norm estimation problem. The solution to the Lp-norm problem can either be obtained directly by numerical minimization or by transformation of the original problem into the nonlinear programming problem. Although there are efficient numerical methods for solving problems in nonlinear constraints, see for example G. P. McCormick, this approach remains a cumbersome way of solving the original estimation problem in view of the number of nonlinear constraints and additional number of constrained variables. Algorithms which take the special structure of problem directly into account converge substantially faster than the general unconstrained procedures. The algorithm is due to Rene Gonin and is efficient in solving fairly well-behaved, small residual nonlinear Lp-norm estimation problems when 1 < p < ∞. It uses the structure of the Lp-norm estimation problem and is an extension of the Gauss-Newton method for solving nonlinear least squares problems.
