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凸优化

Convex Optimization
课程网址: http://videolectures.net/mlss2011_vandenberghe_convex/  
主讲教师: Lieven Vandenberghe
开课单位: 加州大学
开课时间: 2011-10-12
课程语种: 英语
中文简介:
这些讲座将介绍凸优化的理论和应用,并概述算法的最新发展。第一讲将介绍凸分析的基础知识,重点关注对凸建模最有用的结果,即识别和制定应用中的凸优化问题。我们将介绍二次曲线优化,以及两种最广泛研究的圆锥优化问题类型,二阶锥和半定规划。该材料将用于鲁棒优化,非凸优化中的凸松弛和稀疏优化的凸技术。第2讲将介绍圆锥优化的内点法,包括路径跟踪法和对称原始对偶法,以及数值实现。内点法。第3讲将重点介绍大规模凸优化的一阶算法,包括近端梯度法领域的最新发展,以及双重分解和乘法方法。
课程简介: The lectures will give an introduction to the theory and applications of convex optimization, and an overview of recent developments in algorithms. The first lecture will cover the basics of convex analysis, focusing on the results that are most useful for convex modeling, i.e., recognizing and formulating convex optimization problems in applications. We will introduce conic optimization, and the two most widely studied types of conic optimization problems, second-order cone and semidefinite programs. The material will be illustrated with applications to robust optimization, convex relaxations in nonconvex optimization, and convex techniques for sparse optimization. Lecture 2 will cover interior-point methods for conic optimization, including path-following methods and symmetric primal-dual methods, and the numerical implementation of interior-point methods. Lecture 3 will focus on first-order algorithms for large-scale convex optimization, including recent developments in the area of proximal gradient methods, and on dual decomposition and multiplier methods.
关 键 词: 凸优化; 算法; 圆锥优化
课程来源: 视频讲座网
最后编审: 2020-10-28:zyk
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