A Set of Linearized Partially-Parallel Splitting Methods for Separable Convex Programs

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IIMB Management Review Pub Date : 2024-03-12 DOI:10.1016/j.iimb.2024.03.001

Jitamitra Desai, Kai Wang

引用次数: 0

Abstract

The proximal partially-parallel splitting method (PPSM), originally proposed in Wang et al. (2017), is a hybrid mechanism that inherits the nice properties of both Gauss-Seidel and Jacobian substitution procedures for solving the multiple-block convex minimization problem, whose objective function is the sum of individual (separable) functions without any shared variables, subject to a linear coupling constraint. In this paper, we extend this work and present some of the PPSM, which fully utilize the separable structure and result in subproblems that either have closed-form solutions or are relatively easy to solve as compared to their original nonlinear versions. Global convergence of these linearized methods under the projection contraction algorithmic framework is proven, and furthermore, detailed remarks that serve to clarify the interconnections between these linearized variants are highlighted. Finally, the worst-case convergence rate of these methods under ergodic conditions is also established.

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可分离凸程序的线性化部分并行分割方法集

近似部分并行分割法（PPSM）最初由 Wang 等人（2017）提出，它是一种混合机制，继承了高斯-赛德尔程序和雅各布替代程序的优良特性，用于求解多块凸最小化问题，该问题的目标函数是没有任何共享变量的单个（可分离）函数之和，受线性耦合约束。在本文中，我们对这一工作进行了扩展，提出了一些 PPSM，这些方法充分利用了可分离结构，所产生的子问题要么具有闭式解，要么与其原始非线性版本相比相对容易求解。这些线性化方法在投影收缩算法框架下的全局收敛性得到了证明，此外，还强调了有助于澄清这些线性化变体之间相互联系的详细说明。最后，还确定了这些方法在遍历条件下的最坏收敛率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

IIMB Management Review MANAGEMENT-

CiteScore

3.20

自引率

5.90%

发文量

审稿时长

68 days

期刊介绍： IIMB Management Review (IMR) is a quarterly journal brought out by the Indian Institute of Management Bangalore. Addressed to management practitioners, researchers and academics, IMR aims to engage rigorously with practices, concepts and ideas in the field of management, with an emphasis on providing managerial insights, in a reader friendly format. To this end IMR invites manuscripts that provide novel managerial insights in any of the core business functions. The manuscript should be rigorous, that is, the findings should be supported by either empirical data or a well-justified theoretical model, and well written. While these two requirements are necessary for acceptance, they do not guarantee acceptance. The sole criterion for publication is contribution to the extant management literature.Although all manuscripts are welcome, our special emphasis is on papers that focus on emerging economies throughout the world. Such papers may either improve our understanding of markets in such economies through novel analyses or build models by taking into account the special characteristics of such economies to provide guidance to managers.