Stochastic Primal–Dual Hybrid Gradient Algorithm with Adaptive Step Sizes

IF 1.3 4区数学 Q4 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Journal of Mathematical Imaging and Vision Pub Date : 2024-03-16 DOI:10.1007/s10851-024-01174-1

引用次数: 0

Abstract

In this work, we propose a new primal–dual algorithm with adaptive step sizes. The stochastic primal–dual hybrid gradient (SPDHG) algorithm with constant step sizes has become widely applied in large-scale convex optimization across many scientific fields due to its scalability. While the product of the primal and dual step sizes is subject to an upper-bound in order to ensure convergence, the selection of the ratio of the step sizes is critical in applications. Up-to-now there is no systematic and successful way of selecting the primal and dual step sizes for SPDHG. In this work, we propose a general class of adaptive SPDHG (A-SPDHG) algorithms and prove their convergence under weak assumptions. We also propose concrete parameters-updating strategies which satisfy the assumptions of our theory and thereby lead to convergent algorithms. Numerical examples on computed tomography demonstrate the effectiveness of the proposed schemes.

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自适应步长的随机原始-双重混合梯度算法

摘要在这项工作中，我们提出了一种新的具有自适应步长的初等双梯度算法。具有恒定步长的随机主双混合梯度（SPDHG）算法因其可扩展性，已在许多科学领域的大规模凸优化中得到广泛应用。为了确保收敛性，原始步长和二元步长的乘积受制于一个上限值，而步长比例的选择在应用中至关重要。迄今为止，还没有一种系统而成功的方法来选择 SPDHG 的原始步长和对偶步长。在这项研究中，我们提出了一类自适应 SPDHG（A-SPDHG）算法，并证明了它们在弱假设条件下的收敛性。我们还提出了具体的参数更新策略，这些策略满足我们理论中的假设，从而导致算法收敛。计算断层扫描的数值示例证明了所提方案的有效性。

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

Journal of Mathematical Imaging and Vision 工程技术-计算机：人工智能

CiteScore

4.30

自引率

5.00%

发文量

审稿时长

3.3 months

期刊介绍： The Journal of Mathematical Imaging and Vision is a technical journal publishing important new developments in mathematical imaging. The journal publishes research articles, invited papers, and expository articles. Current developments in new image processing hardware, the advent of multisensor data fusion, and rapid advances in vision research have led to an explosive growth in the interdisciplinary field of imaging science. This growth has resulted in the development of highly sophisticated mathematical models and theories. The journal emphasizes the role of mathematics as a rigorous basis for imaging science. This provides a sound alternative to present journals in this area. Contributions are judged on the basis of mathematical content. Articles may be physically speculative but need to be mathematically sound. Emphasis is placed on innovative or established mathematical techniques applied to vision and imaging problems in a novel way, as well as new developments and problems in mathematics arising from these applications. The scope of the journal includes: computational models of vision; imaging algebra and mathematical morphology mathematical methods in reconstruction, compactification, and coding filter theory probabilistic, statistical, geometric, topological, and fractal techniques and models in imaging science inverse optics wave theory. Specific application areas of interest include, but are not limited to: all aspects of image formation and representation medical, biological, industrial, geophysical, astronomical and military imaging image analysis and image understanding parallel and distributed computing computer vision architecture design.

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