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ConstrainedLasso

ConstrainedLasso solves the following problem

$$\begin{split} & \text{minimize} \hspace{1em} \frac 12||\boldsymbol{y}-\boldsymbol{X\beta}||^2_2 + \rho||\boldsymbol{\beta}||_1 \\ & \text{ subject to} \hspace{0.5em} \boldsymbol{A\beta}=\boldsymbol{b} \text{ and } \boldsymbol{C\beta} \leq \boldsymbol{d} \end{split}$$

where

• $\boldsymbol{y} \in \mathbb{R}^n$: the response vector
• $\boldsymbol{X}\in \mathbb{R}^{n\times p}$: the design matrix of predictor or covariates
• $\boldsymbol{\beta} \in \mathbb{R}^p$: the vector of unknown regression coefficients,
• $\rho \geq 0$: a tuning parameter that controls the amount of regularization.

Installation

Within Julia, use the package manager to install ConstrainedLasso:

Pkg.clone("git://github.com/Hua-Zhou/ConstrainedLasso.git")

This package supports Julia v0.6.

Citation

Original method paper on the constrained lasso is

G.M. James, C. Paulson and P. Rusmevichientong. (2013) Penalized and constrained regression. http://www-bcf.usc.edu/~gareth/research/PAC.pdf

If you use ConstrainedLasso package in your research, please cite the following paper on the algorithms:

B.R. Gaines, H. Zhou. (2016) Algorithms for Fitting the Constrained Lasso. https://arxiv.org/abs/1611.01511