线性等式约束广义Lasso问题的算法研究

Algorithm Research on Generalized Lasso Problems with Linear Equality Constraints

随着大数据时代的到来,众多研究领域都涉及到优化问题的求解,其中Lasso问题的求解尤其受到学者们的广泛研究。针对Lasso问题的求解,学者们研发出众多算法。随着应用的场景不同以及对数据的要求不同,带有约束的广义Lasso问题逐渐受到人们关注。本文将已有的快速邻近点算法结合半光滑牛顿算法,应用到对一类含线性等式约束的广义Lasso问题进行求解,并在一定的假设条件下证明了该算法的收敛性。最后,通过数值实验证实了该算法的高效性。

With the advent of the big data era,many research fields involve solving optimization problems,among which the solution of the Lasso problem has been widely studied by scholars.Scholars have developed numerous algorithms for solving the Lasso problem.As the application scenarios vary and the data requirements differ,the generalized Lasso problem with constraints has gradually attracted attention.This paper combines existing fast proximal point algorithms with a semi-smooth Newton algorithm to solve a class of generalized Lasso problems with linear equality constraints.The convergence of the algorithm is proved under certain assumptions.Finally,the efficiency of the algorithm is verified through numerical experiments.