Penalized and Constrained Lasso Optimization
Function to Randomly Generate Data (with Constraints)
Constrained LARS Coefficient Function (Equality Constraints)
Constrained LARS Coefficient Function with Inequality Constraints
Complete Run of Constrained LASSO Path Function (Equality Constraints)
Complete Run of Constrained LASSO Path Function with Inequality Constr...
Initialize Linear Programming Fit with Inequality Constraints
Initialize Linear Programming Fit (Equality Constraints)
Initialize Quadratic Programming Fit with Inequality Constraints
Initialize Quadratic Programming Fit (Equality Constraints)
Transform Data to Fit PaC Implementation for Inequality Constraints
Transform Data to Fit PaC Implementation (Equality Constraints)
An implementation of both the equality and inequality constrained lasso functions for the algorithm described in "Penalized and Constrained Optimization" by James, Paulson, and Rusmevichientong (Journal of the American Statistical Association, 2019; see <http://www-bcf.usc.edu/~gareth/research/PAC.pdf> for a full-text version of the paper). The algorithm here is designed to allow users to define linear constraints (either equality or inequality constraints) and use a penalized regression approach to solve the constrained problem. The functions here are used specifically for constraints with the lasso formulation, but the method described in the PaC paper can be used for a variety of scenarios. In addition to the simple examples included here with the corresponding functions, complete code to entirely reproduce the results of the paper is available online through the Journal of the American Statistical Association.