chapter1.无约束优化基础

文档摘要

无约束优化基础知识向量和矩阵 A vector $x \in \mathbb{R}^{n}: x=\left(x{1}, \ldots, x{n}\right)^{T}$ Inner product: given $x, y \in \mathbb{R}^{n}, x^{T} y=\sum{i=1}^{n} x{i} y{i}$ A matrix $A \in \mathbb{R}^{m \times n}$ $A \in \mathbb{R}^{n \times n}$ is positive semidefinite, if $x^{T} A x \geq 0$ for any $x \in \mathbb{R}^{n}$ $Q \in \mathbb{R}^{n \times