Playing with Duality
Playing with Duality
复制标题
DOI：
10.1109/msp.2014.2377273
复制
发表时间：
2015-11-01
影响因子：
14.9
通讯作者：
Pesquet, Jean-Christophe
中科院分区：
文献类型：
--
作者：
Komodakis, Nikos;Pesquet, Jean-Christophe
优化方法是信号/图像处理、计算机视觉和机器学习中许多问题的核心。很长一段时间以来，人们已经认识到，查看优化问题的对偶可以极大地简化其解决方案。然而，导出有效的策略来共同发挥原始问题和双重问题是一个较新的想法，近年来产生了许多重要的新贡献。这些新的发展是基于凸分析、离散优化、并行处理和强调稀疏性问题的非光滑优化的最新进展。在本文中，我们旨在介绍原始对偶方法的原理，同时概述在不同背景下提出的数值方法。最后但并非最不重要的是，原始对偶方法导致算法易于并行化。如今，这种并行算法对于高效处理高维问题变得越来越重要。
Optimization methods are at the core of many problems in signal/image processing, computer vision, and machine learning. For a long time, it has been recognized that looking at the dual of an optimization problem may drastically simplify its solution. However, deriving efficient strategies that jointly bring into play the primal and dual problems is a more recent idea that has generated many important new contributions in recent years. These novel developments are grounded in the recent advances in convex analysis, discrete optimization, parallel processing, and nonsmooth optimization with an emphasis on sparsity issues. In this article, we aim to present the principles of primal-dual approaches while providing an overview of the numerical methods that have been proposed in different contexts. Last but not least, primal-dual methods lead to algorithms that are easily parallelizable. Today, such parallel algorithms are becoming increasingly important for efficiently handling high-dimensional problems.