01252627

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01252627 Madsen, Kaj Nielsen, Hans Bruun Pinar, Mustafa \c{C}elebi A finite continuation algorithm for bound constrained quadratic programming. SIAM J. Optim. 9, No.1, 62-83 (1998). 1998 Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA EN bound constrained quadratic programming Lagrangian duality linear $\ell_1$ estimation Huber's M-estimator robust regression

doi:10.1137/S1052623495297820

Summary: The dual of the strictly convex quadratic programming problem with unit bounds is posed as a linear $\ell_1$ minimization problem with quadratic terms. A smooth approximation to the linear $\ell_1$ function is used to obtain a parametric family of piecewise-quadratic approximation problems. The unique path generated by the minimizers of these problems yields the solution to the original problem for finite values of the approximation parameter. Thus, a finite continuation algorithm is designed. Results of extensive computational experiments are reported.