介绍凸优化与非凸优化的基本概念,常用算法,主要的研究成果及其在机器视觉,压缩感知,深度学习和信息论中的应用。 Big picture of mathematical optimization 摘要:Basic concepts, optimality conditions, different types of optimization, algorithm design techniques阅读全文 posted @2020-06-29 20:47科研民工阅读(130)评...
the convex optimization methods provide theoretical support for AI model training, which can be viewed as a process of solving an optimization problem. In this chapter, we introduce the foundations of convex optimization algorithms. Particularly, the first- and second-order methods are specified for ...
这个list主要包括stochastic convex and non-convex optimization, 借鉴了Allen-Zhu在ICML上的那个workshop. 另外两个是blog: 孙举的 Provable Nonconvex Methods/Algorithms,和 Off the convex path ===请叫我, 分割线=== Paper List (by time order) Before 2010s 2004, Nesterov : textbook Introductory Lectu...
非凸优化的凸启发式算法Convex heuristics for nonconvex optimization 凸优化是求解非凸问题的几种启发式算法的基础。我们将看到的一个有趣的例子是找到一个满足某些约束的稀疏向量(即具有少量非零项的向量)的问题。虽然这是一个困难的组合问题,但有一些基于凸优化的简单启发式方法,通常可以找到相当稀疏的解决方案。
第四类是大规模分离非凸优化问题，通过Shapley-Folkman定理证明了当分离项趋于无穷时，对偶间隙趋于零，因此可以求解对偶问题得到原问题的最优解。在通信领域中，这有着重要的应用。最后，奇异值分解（Singular Value Decomposition）及其应用在通信和信号处理中极为关键。通过矩阵的奇异值分解，我们能够以曼若...
The functions which have the property that every level set is convex are precisely called quasi-convex functions. In the first section we give necessary and sufficient conditions for a point to be a solution to a minimization problem of a quasi-convex function under convex constraints....
The series Nonconvex Optimization and Its Applications publishes monographs and state-of-the-art expository works which focus on algorithms for solving ...
Convex Optimization & Euclidean Distance Geometryis about convex optimization,convex geometry(with particular attention todistance geometry), and nonconvex, combinatorial, and geometrical problems that can be relaxed or transformed into convex optimization problems. ...
Cone的定义 一个集合\(C\)中任意元素\(x\),如果满足\(\theta x∈C,\theta≥0\),则称\(C\)为cone或者nonnegative homogeneous(非负齐次) Convex Cone定义 如果一个集合\(C\)是凸的,而且是一个cone,也就是说如果\(\forall{x_1,x_2∈C},\theta_1,\theta_2≥0\),都有\[\theta_1 x_1+\thet...
and a review of non-convex single-objective optimization problems; this book moves on to cover multi-objective branch and bound algorithms, worst-case optimal algorithms (for Lipschitz functions and bi-objective problems), statistical models based algorithms, and probabilistic branch and bound approach...