An asynchronous proximal bundle method
成果类型：
Article
署名作者：
Fischer, Frank
署名单位：
Johannes Gutenberg University of Mainz
刊物名称：
MATHEMATICAL PROGRAMMING
ISSN/ISSBN：
0025-5610
DOI：
10.1007/s10107-024-02088-x
发表日期：
2025
页码：
825-857
关键词：
摘要：
We develop a fully asynchronous proximal bundle method for solving non-smooth, convex optimization problems. The algorithm can be used as a drop-in replacement for classic bundle methods, i.e., the function must be given by a first-order oracle for computing function values and subgradients. The algorithm allows for an arbitrary number of master problem processes computing new candidate points and oracle processes evaluating functions at those candidate points. These processes share information by communication with a single supervisor process that resembles the main loop of a classic bundle method. All processes run in parallel and no explicit synchronization step is required. Instead, the asynchronous and possibly outdated results of the oracle computations can be seen as an inexact function oracle. Hence, we show the convergence of our method under weak assumptions very similar to inexact and incremental bundle methods. In particular, we show how the algorithm learns important structural properties of the functions to control the inaccuracy induced by the asynchronicity automatically such that overall convergence can be guaranteed.