A globally convergent proximal Newton-type method in nonsmooth convex optimization
A globally convergent proximal Newton-type method in nonsmooth convex optimization
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DOI：
10.1007/s10107-022-01797-5
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发表时间：
2020-11
影响因子：
2.7
通讯作者：
B. Mordukhovich;Xiaoming Yuan;Shangzhi Zeng;Jin Zhang
中科院分区：
文献类型：
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作者：
B. Mordukhovich;Xiaoming Yuan;Shangzhi Zeng;Jin Zhang
本文提出并证明了一种新的近似牛顿型算法，以解决广泛的非光滑复合凸优化问题没有强凸性假设。基于先进的变分分析的概念和技术，我们建立了可实现的结果，所提出的算法的全局收敛性，以及其局部收敛的超线性和二次率。对于某些结构化问题，所得到的局部收敛条件不需要相应的Hessian映射的局部Lipschitz连续性，这是文献中使用的一个重要假设，以确保超线性收敛的邻近牛顿型的其他算法。通过求解正则化逻辑回归模型的数值实验，说明了该算法应用于实际问题的可行性。
The paper proposes and justifies a new algorithm of the proximal Newton type to solve a broad class of nonsmooth composite convex optimization problems without strong convexity assumptions. Based on advanced notions and techniques of variational analysis, we establish implementable results on the global convergence of the proposed algorithm as well as its local convergence with superlinear and quadratic rates. For certain structured problems, the obtained local convergence conditions do not require the local Lipschitz continuity of the corresponding Hessian mappings that is a crucial assumption used in the literature to ensure a superlinear convergence of other algorithms of the proximal Newton type. The conducted numerical experiments of solving theregularized logistic regression model illustrate the possibility of applying the proposed algorithm to deal with practically important problems.