Browsing by Subject "Lagrangean duality"

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    Duality in robust linear regression using Huber's M-estimator
    (Elsevier, 1997-07) Pınar, M. Ç.
    The robust linear regression problem using Huber's piecewise-quadratic M-estimator function is considered. Without exception, computational algorithms for this problem have been primal in nature. In this note, a dual formulation of this problem is derived using Lagrangean duality. It is shown that the dual problem is a strictly convex separable quadratic minimization problem with linear equality and box constraints. Furthermore, the primal solution (Huber's M-estimate) is obtained as the optimal values of the Lagrange multipliers associated with the dual problem. As a result, Huber's M-estimate can be computed using off-the-shelf optimization software.