Open AccessOptimal correction of infeasible equations system as Ax + B|x|= b using ℓ p-norm regularization
Author(s) -
Fakhrodin Hashemi,
Saeed Ketabchi
Publication year - 2022
Publication title -
boletim da sociedade paranaense de matemática
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.347
H-Index - 15
eISSN - 2175-1188
pISSN - 0037-8712
DOI - 10.5269/bspm.44437
Subject(s) - lipschitz continuity , smoothing , mathematics , convex function , regularization (linguistics) , regular polygon , norm (philosophy) , convex optimization , mathematical optimization , proximal gradient methods for learning , optimization problem , mathematical analysis , subderivative , computer science , statistics , geometry , artificial intelligence , political science , law
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.