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 real 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 the
Matlab toolbox SparseReg.

本研究比较了在求解有约束的 Lasso 问题中的几种不同的计算策略（包括二次规划、交替方向乘子法、以及一种高效的求解路径算法）。在通过模拟和真实数据示例的比较之后，提出了适用于不同数据规模下的实际建议，同时也发现一般化 Lasso 可以转化为有约束的 Lasso 问题，但反之则不成立。因此，该研究的方法也可以用于估计具有广泛应用的一般化 Lasso。

拟合受限 Lasso 的算法

Algorithms for Fitting the Constrained Lasso

We consider a suboptimal solution path algorithm for the Support Vector
Machine. The solution path algorithm is an effective tool for solving a
sequence of a parametrized optimization problems in machine learning. The path
of the solutions provided by this algorithm are very accurate and they satisfy
the optimality conditions more strictly than other SVM optimization algorithms.
In many machine learning application, however, this strict optimality is often
unnecessary, and it adversely affects the computational efficiency. Our
algorithm can generate the path of suboptimal solutions within an arbitrary
user-specified tolerance level. It allows us to control the trade-off between
the accuracy of the solution and the computational cost. Moreover, We also show
that our suboptimal solutions can be interpreted as the solution of a
\emph{perturbed optimization problem} from the original one. We provide some
theoretical analyses of our algorithm based on this novel interpretation. The
experimental results also demonstrate the effectiveness of our algorithm.

本文介绍了一种支持向量机的次优解路径算法，该算法可以在任意用户指定的容忍度范围内生成次优解路径，并能够控制解的准确性和计算成本的平衡。