邻近点映射的性质下面这个定理讨论了邻近点映射和次梯度的关系 定理:假设 f:\mathbb{E}\to [-\infty,\infty] 是一个合理(proper:函数不恒等于正无穷且不取负无穷值)闭凸函数,那么以下三个命题是等价的( x,y…
邻近点映射 proximal mapping邻近点映射在非光滑凸优化的很多算法中至关重要,第一个研究它的人是Moreau,该映射定义为 \text{prox}_f(x)=\arg\min_{u\in\mathbb{E}}\{f(u)+\frac{1}{2}\|u-x\|^2\},\forall x\in\m…
对偶空间与双重对偶空间：向量空间上的线性泛函构成对偶空间，用符号表示。给定向量空间，其内积与对偶空间内积保持一致。对偶范数定义为线性泛函在单位球面上的最大内积值。引理证明了广义不等式成立。在有限维空间，双重对偶空间与原始空间同构，双重对偶范数与原始空间范数一致。伴随变换定义：给定向量空间与线...
comprehensive study of the main first-order methods that are frequently used in solving large-scale problems. First-order methods exploit information on values and gradients/subgradients (but not Hessians) of the functions composing the model under consideration. With the increase in the number of...
Springer Series in the Data Sciences(共11册),这套丛书还有 《Multivariate Data Analysis on Matrix Manifolds: (with Manopt)》《Cohesive Subgraph Computation over Large Sparse Graphs: Algorithms, Data Structures, and Programming Techniques》《Deep Learning Architectures》《Mathematical Foundations for Data An...
aFinally, the coordination of the foregoing optimization efforts at a supervisory level is discussed. The trade-off between pumping aid compressor power is discussed to arrive at the optimum temperature settings of chilled water and condenser water. The implementation of the optimization methods in dis...
Remarkably, the simplest X-configuration, while the simplest in terms of hardware implementation and computational time, appears an outlier, yielding considerably higher maximum retrieval errors when compared to all other configurations. We believe that our results are useful for the optimization of both...
A set of SW process - HW tile mapping candidates is generated by the holistic SW tool-chain using a combination of analytic and bio-inspired methods. The Hardware dependent Software is then generated, providing OS services with maximum efficiency/minimal overhead. The many-tile simulator collects...
\begin{equation*} S_{+}^n = \{A \in R^{n \times n}| A \ge O\} \end{equation*} (3)全体n \times n正定(positive \quad define)矩阵的集合S_{++}^n 所有n \times n维正定矩阵的全体构成的集合,记作S_{++}^n: \begin{equation*} S_{++}^n = \{A \in R^{n \times n}| A...
回顾: 支撑函数 σC(y)=maxx∈C⟨y,x⟩ 通俗来说是集合C的y法向切平面最大截距(集合的闭凸包可以由集合的超平面包络得到) 支撑函数是次线性函数 次梯度和次微分 f(y)≥f(x)+⟨g,y−x⟩,∀y∈E(次梯度) ∂f(x)={g∈E∗:f(y)≥f(x)+⟨g,y−x⟩,∀y∈E}(次微分是次...