Affine algorithms for L-minimization

Abstract

Summary form only given, as follows. L/sub 2/-minimization problems are commonly solved using one of the following methods: (i) variants of the simplex method, used to solve the L/sub 1/-minimization problem formulated as a linear programming (LP) problem, and (ii) the iteratively reweighted least-squares (IRLS) method, a method favored in some signal processing applications. Interior-point methods (primal affine and Karmarkar's dual affine methods) are considerably faster than the simplex method for solving large LP problems. The principles of affine algorithms and their implementation strongly resemble the IRLS method. However, an efficient implementation is essential to obtain good performances from the interior-point methods. The implementation details for dense and sparse L/sub 1/-minimization problems with and without linear inequality constraints are discussed. A number of examples are worked out, and comparisons are made with existing algorithms wherever possible. >