Nonconvex truncated conditional value at risk-based sparse linear regression

Conditional value at risk (CVaR) is a widely recognized risk measure used to manage data uncertainty within risk management. In this paper, we study a class of sparse linear regression models based on truncated CVaR measure and ℓ0-norm regularization. Due to the nonconvexity and nonsmoothness of the...

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Vydáno v:European journal of operational research Ročník 328; číslo 1; s. 246 - 257
Hlavní autoři: Xie, Boyi, Wu, Zhongming, Li, Min
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 01.01.2026
Témata:
Capped ℓ1-norm
Conditional value at risk
Risk management
Semismooth Newton method
Sparse linear regression
Risk management
Semismooth Newton method
Sparse linear regression
Conditional value at risk
Capped ℓ1-norm
ISSN:0377-2217
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Shrnutí:Conditional value at risk (CVaR) is a widely recognized risk measure used to manage data uncertainty within risk management. In this paper, we study a class of sparse linear regression models based on truncated CVaR measure and ℓ0-norm regularization. Due to the nonconvexity and nonsmoothness of the objective functions, as well as the NP-hardness of the problem with the ℓ0-norm regularization, we propose an approximation model that employs a tight relaxation of the ℓ0-norm. The solution equivalence between the proposed model and its approximation model is explored. To efficiently solve the approximation model, we develop a semismooth Newton-based proximal majorization-minimization algorithm. Furthermore, the convergence analysis of the proposed algorithm is presented, and the convergence rate for the reduced CVaR-based sparse linear regression model is established. Moreover, extensive numerical experiments conducted on both synthetic and real datasets validate the stability and effectiveness of the proposed algorithm, demonstrating significant improvements in both sparsity and accuracy compared to existing state-of-the-art methods. •A truncated conditional value at risk-based sparse regression model is proposed.•An approximation model with a novel regularization is introduced.•A semismooth Newton-based proximal majorization-minimization algorithm is developed.•A theoretical analysis of the solution equivalence and convergence is provided.•Numerical experiments are conducted on both synthetic and real datasets.
ISSN:0377-2217
DOI:10.1016/j.ejor.2025.06.004