Robust regression modelling: interior point methods, simplex method, descent along nodal straight lines

Implementation of the least absolute deviations method for robust estimation of linear regression dependencies by means of interior point algorithms is considered. Two affine scaling interior point algorithms for robust regression estimation are implemented. A comparative analysis of these algorithms with simplex method and descent along nodal straightlinesis carried out. Their computational complexity is found to be comparable to the simplex method, but they lose to the latter in terms of computation time. It is also found that the interior point algorithms significantly lose to the modified descent along nodal straight lines, both in terms of computational complexity and actual computation time. Examples of using interior point algorithms for practical problems are given.