An extrapolated proximal iteratively reweighted method for nonconvex composite optimization problems
An extrapolated proximal iteratively reweighted method for nonconvex composite optimization problems
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DOI：
10.1007/s10898-023-01299-4
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发表时间：
2023-06
影响因子：
1.8
通讯作者：
Zhili Ge;Zhongming Wu;Xin Zhang;Q. Ni
中科院分区：
文献类型：
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作者：
Zhili Ge;Zhongming Wu;Xin Zhang;Q. Ni
我们考虑一类问题，其中目标函数是一个光滑函数和一个非凸非光滑函数的合成。这类优化问题在机器学习和数据处理中经常出现。最近的迭代重加权方法在解决这些问题中得到了广泛的应用和推广。在这篇文章中，我们发展了一种外推的近端迭代重加权方法，它在每次迭代中包含两个不同的灵活惯性步长。我们首先证明了该方法在参数约束下的子序列收敛性质。此外，如果目标函数满足Kurdyka-Łojasiewicz性质，则证明了新方法的全局收敛。此外，通过对目标函数的Kurdyka-Łojasiewicz指数作假设，分析了算法的局部收敛速度。最后，给出了极小化和特征选择问题的数值结果，表明了该算法的有效性和优越性。
We consider a class of problems where the objective function is the sum of a smooth function and a composition of nonconvex and nonsmooth functions. Such optimization problems arise frequently in machine learning and data processing. The proximal iteratively reweighted method has been widely used and popularized in solving these problems. In this paper, we develop an extrapolated proximal iteratively reweighted method that incorporates two different flexible inertial steps at each iteration. We first prove the subsequential convergence of the proposed method under parameter constraints. Moreover, if the objective function satisfies the Kurdyka-Łojasiewicz property, the global convergence of the new method is established. In addition, we analyze the local convergence rate by making assumptions on the Kurdyka-Łojasiewicz exponent of the objective function. Finally, numerical results onminimization and feature selection problems are reported to show the effectiveness and superiority of the proposed algorithm.