Jiajia Wang, Chengjing Wang, Peipei Tang, Aimin Xu, Wenhan Jia, A primal alternating direction method of multipliers for the cost-sensitive constrained Lasso problem

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DOI: 10.23952/jano.8.2026.1.07
Volume 8, Issue 1, 1 April 2026, Pages 115-126

Abstract. In this paper, we investigate the cost-sensitive constrained Lasso model, a novel extension of the traditional Lasso framework that incorporates a quadratic performance constraint. This innovative approach enables simultaneous optimization of overall prediction error while rigorously maintaining prediction accuracy for designated subgroups. To address the inherent complexity arising from the nonsmooth $l_1$ -norm regularization term in the objective function coupled with the additional quadratic performance constraint, we introduce a primal alternating direction method of multipliers (pADMM). Furthermore, we establish that pADMM achieves global convergence under mild conditions. Comprehensive numerical experiments demonstrate the effectiveness and robustness of our proposed algorithm.

How to Cite this Article:
J. Wang, C. Wang, P. Tang, A. Xu, W. Jia, A primal alternating direction method of multipliers for the cost-sensitive constrained Lasso problem, J. Appl. Numer. Optim. 8 (2026), 115-126.