Optimal correction of infeasible equations system as Ax + B|x|= b using ℓ p-norm regularization

Fakhrodin Hashemi; Saeed Ketabchi

doi:10.5269/bspm.44437

Fakhrodin Hashemi University of Guilan
Saeed Ketabchi University of Guilan

Resumen

Optimal correction of an infeasible equations system as Ax + B|x|= b leads into a non-convex fractional problem. In this paper, a regularization method(ℓp-norm, 0 < p < 1), is presented to solve mentioned fractional problem. In this method, the obtained problem can be formulated as a non-convex and nonsmooth optimization problem which is not Lipschitz. The objective function of this problem can be decomposed as a difference of convex functions (DC). For this reason, we use a special smoothing technique based on DC programming. The numerical results obtained for generated problem show high performance and the effectiveness of the proposed method.

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