A direct approach for L1-norm minimisation

A straightforward algorithm is proposed for L1-norm minimisation. The proposed algorithm is based on grey wolf optimisation which is a meta-heuristic method. Although L1-norm is an efficient tool for robust estimation and outlier detection, the complexity of its implementation made it less useful than L2-norm since after formulation of the L1-norm minimisation for a certain problem one must solve a linear programming problem by a search method while here we only need to set the corresponding L1-norm target function. Two geodetic examples approve the efficiency of the proposed approach.