A Data-Driven Line Search Rule for Support Recovery in High-dimensional Data Analysis

In this work, we consider the algorithm to the (nonlinear) regression problems with ℓ0 penalty. The existing algorithms for ℓ0 based optimization problem are often carried out with a fixed step size, and the selection of an appropriate step size depends on the restricted strong convexity and smoothness for the loss function, hence it is difficult to compute in practical calculation. In sprite of the ideas of support detection and root finding citeHJK2020, we proposes a novel and efficient data-driven line search rule to adaptively determine the appropriate step size. We prove the ℓ2 error bound to the proposed algorithm without much restrictions for the cost functional. A large number of numerical comparisons with state-of-the-art algorithms in linear and logistic regression problems show the stability, effectiveness and superiority of the proposed algorithms.