Sparsity-constraint optimization has wide applicability in signal processing, statistics, and machine learning. Existing fast algorithms must burdensomely tune parameters, such as the step size or the implementation of precise stop criteria, which may be challenging to determine in practice. To address this issue, we develop an algorithm named Sparsity-Constraint Optimization via sPlicing itEration (SCOPE) to optimize nonlinear differential objective functions with strong convexity and smoothness in low dimensional subspaces. Algorithmically, the SCOPE algorithm converges effectively without tuning parameters. Theoretically, SCOPE has a linear convergence rate and converges to a solution that recovers the true support set when it correctly specifies the sparsity. We also develop parallel theoretical results without restricted-isometry-property-type conditions. We apply SCOPE's versatility and power to solve sparse quadratic optimization, learn sparse classifiers, and recover sparse Markov networks for binary variables. The numerical results on these specific tasks reveal that SCOPE perfectly identifies the true support set with a 10--1000 speedup over the standard exact solver, confirming SCOPE's algorithmic and theoretical merits. Our open-source Python package skscope based on C++ implementation is publicly available on GitHub, reaching a ten-fold speedup on the competing convex relaxation methods implemented by the cvxpy library.

稀疏约束优化问题的研究中，通过开发名为SCOPE的算法，以强凸性和平滑性为特点的低维子空间中的非线性微分目标函数得到了有效收敛、无需参数调节以及能够正确恢复真实支撑集的解，同时在稀疏二次优化、稀疏分类器学习和二进制变量稀疏马尔科夫网络恢复等特定任务中显示出优越性能。

稀疏约束优化的分割迭代优化方法