We propose a general formulation of nonconvex and nonsmooth sparse optimization problems with convex set constraint, which can take into account most existing types of nonconvex sparsity-inducing terms, bringing strong applicability to a wide range of applications. We design a general algorithmic framework of iteratively reweighted algorithms for solving the proposed nonconvex and nonsmooth sparse optimization problems, which solves a sequence of weighted convex regularization problems with adaptively updated weights. First-order optimality condition is derived and global convergence results are provided under loose assumptions, making our theoretical results a practical tool for analyzing a family of various reweighted algorithms. The effectiveness and efficiency of our proposed formulation and the algorithms are demonstrated in numerical experiments on various sparse optimization problems.

翻译：我们提出非convex和非moot smoot spolite probligation 问题的一般提法,采用convex 设置的制约,其中可以考虑到大多数现有的非convex sporsity-productive deservations deservations,使大量应用具有很强的适用性;我们设计了一个由迭代再加权算法组成的一般算法框架,以解决拟议的非convex 和非 smoot sporest point point sublications,解决一系列加权的convex 规范问题,并采用适应性更新的重量。 一级最佳性条件是产生,全球趋同结果是在松散的假设下提供的,使我们的理论结果成为分析各种重新加权算法系列的实用工具。我们提议的配法和算法的效力和效率在各种稀有优化问题的数字实验中得到了证明。