ConstrainedLasso.jl: Algorithms for fitting the constrained Lasso. We compare alternative computing strategies for solving the constrained lasso problem. As its name suggests, the constrained lasso extends the widely used lasso to handle linear constraints, which allow the user to incorporate prior information into the model. In addition to quadratic programming, we employ the alternating direction method of multipliers (ADMM) and also derive an efficient solution path algorithm. Through both simulations and benchmark data examples, we compare the different algorithms and provide practical recommendations in terms of efficiency and accuracy for various sizes of data. We also show that, for an arbitrary penalty matrix, the generalized lasso can be transformed to a constrained lasso, while the converse is not true. Thus, our methods can also be used for estimating a generalized lasso, which has wide-ranging applications. Code for implementing the algorithms is freely available in both the Matlab toolbox SparseReg and the Julia package ConstrainedLass. Supplementary materials for this article are available online.

References in zbMATH (referenced in 13 articles , 1 standard article )

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  2. Wu, Xiaofei; Liang, Rongmei; Yang, Hu: Penalized and constrained LAD estimation in fixed and high dimension (2022)
  3. Benítez-Peña, Sandra; Carrizosa, Emilio; Guerrero, Vanesa; Jiménez-Gamero, M. Dolores; Martín-Barragán, Belén; Molero-Río, Cristina; Ramírez-Cobo, Pepa; Romero Morales, Dolores; Sillero-Denamiel, M. Remedios: On sparse ensemble methods: an application to short-term predictions of the evolution of COVID-19 (2021)
  4. Blanquero, Rafael; Carrizosa, Emilio; Ramírez-Cobo, Pepa; Sillero-Denamiel, M. Remedios: A cost-sensitive constrained Lasso (2021)
  5. Chen, Liang; Li, Xudong; Sun, Defeng; Toh, Kim-Chuan: On the equivalence of inexact proximal ALM and ADMM for a class of convex composite programming (2021)
  6. Jalilzadeh, Afrooz: Primal-dual incremental gradient method for nonsmooth and convex optimization problems (2021)
  7. Klopfenstein, Quentin; Vaiter, Samuel: Linear support vector regression with linear constraints (2021)
  8. James, Gareth M.; Paulson, Courtney; Rusmevichientong, Paat: Penalized and constrained optimization: an application to high-dimensional website advertising (2020)
  9. Jeon, Jong-June; Kim, Yongdai; Won, Sungho; Choi, Hosik: Primal path algorithm for compositional data analysis (2020)
  10. Zhao, Yaqing; Bondell, Howard: Solution paths for the generalized Lasso with applications to spatially varying coefficients regression (2020)
  11. Qin, Xiaolong; An, Nguyen Thai: Smoothing algorithms for computing the projection onto a Minkowski sum of convex sets (2019)
  12. Shi, Yue; Ng, Chi Tim; Feng, Zhiguo; Yiu, Ka-Fai Cedric: A descent algorithm for constrained LAD-Lasso estimation with applications in portfolio selection (2019)
  13. Gaines, Brian R.; Kim, Juhyun; Zhou, Hua: Algorithms for fitting the constrained Lasso (2018)