Disciplined multi-convex programming
Disciplined multi-convex programming
复制标题
DOI：
10.1109/ccdc.2017.7978647
复制
发表时间：
2016-09
期刊：
影响因子：
--
通讯作者：
Xinyue Shen;Steven Diamond;Madeleine Udell;Yuantao Gu;Stephen P. Boyd
中科院分区：
文献类型：
--
作者：
Xinyue Shen;Steven Diamond;Madeleine Udell;Yuantao Gu;Stephen P. Boyd
多凸优化问题是在其他变量固定的情况下，将变量划分为若干个问题是凸的集合的问题。多凸问题一般用交替极小化或循环极小化的变化近似求解。多凸问题出现在许多应用中，例如非负矩阵分解、广义低秩模型和结构化控制综合，仅举几例。在迄今为止的大多数应用中，多重凸性很容易手工验证。本文利用正则凸规划的思想，研究了多凸性的自动检测与验证。我们描述了我们提出的方法的实现，该方法检测和验证多凸性，然后调用一个通用解方法。
A multi-convex optimization problem is one in which the variables can be partitioned into sets over which the problem is convex when the other variables are fixed. Multi-convex problems are generally solved approximately using variations on alternating or cyclic minimization. Multi-convex problems arise in many applications, such as nonnegative matrix factorization, generalized low rank models, and structured control synthesis, to name just a few. In most applications to date the multi-convexity is simple to verify by hand. In this paper we study the automatic detection and verification of multi-convexity using the ideas of disciplined convex programming. We describe an implementation of our proposed method that detects and verifies multi-convexity, and then invokes one of the general solution methods.