Algorithms for Fitting the Constrained Lasso

Abstract

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 ConstrainedLasso. Supplementary materials for this article are available online.

An Efficient Augmented Lagrangian-Based Method for Linear Equality-Constrained Lasso

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“…When rank(D) = p and p ≤ n, Tibshirani (2011) has derived that (2) can be transformed into a Lasso problem. In fact, (2) is a special case of constrained Lasso with d = 0 (Gaines et al, 2018;James et al, 2013) when p ≥ n and D has full column rank n and we elaborate on this in section 6.…”

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An Efficient Reactive Power Control Method for Power Network Systems with Solar Photovoltaic Generators Using Sparse Optimization

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“…Based on the constrained linear model, the study objective is formulated as an optimization problem to find the best reactive power injection that minimizes the system voltage variation. Two types of formulations are compared: the first one is the conventional least-square optimization, while the second one is adopted from a sparse optimization technique, called the constrained least absolute shrinkage and selection operator (LASSO) method [18,19]. The constrained LASSO method is characterized by a 1 -norm penalty on its regression coefficients, which is added to the reactive power change in this study.…”