本文共 552 字，大约阅读时间需要 1 分钟。

1.$Min \frac{1}{2}x^TAx+x^Tb+c$

Equals to solve:

$$\frac{1}{2}(A+A^T)x = -b$$

2.$Min\frac{1}{2}x^TAx+x^Tb+c$

subject to: $A'x=b'$ Equals to solve:

$$\begin{bmatrix}\frac{1}{2}(A+A^T) &A'^T\\A' &0\end{bmatrix}\begin{bmatrix}x \\\lambda \end{bmatrix}=\begin{bmatrix}-b \\b'\end{bmatrix}$$

whose application can be seen in

3.$Min\lVert Ax + b\rVert^2$

Equals to solve:

$$Ax = -b$$

4.$Min\displaystyle\sum_{i=1}^{m}\lVert A_ix_i + b_i\rVert^2$

Equals to sovle:

$$A_ix_i=-b_i, \forall i=1,2,\cdots,m$$

$$\begin{bmatrix}A_1 &&&\\ &A_2&&\\ &&\ddots&\\ &&&A_m\end{bmatrix}\begin{bmatrix}x_1 \\x_2 \\\vdots \\x_m \end{bmatrix}=\begin{bmatrix}-b_1 \\-b_2 \\\vdots \\-b_m\end{bmatrix}$$

note:$\lVert v\rVert \geq0$

5.$Min\displaystyle\sum_{i=1}^{m}\lVert Rp_i - q_i\rVert^2$

where $R$ is a rotation matrix Equals to solve: the orthogonal part in polar decomposition of the matrix $q_ip_i^T$

[Meshless Deformations Based on Shape Matching]

[Example-Based skeleton Extraction]

转载地址：http://cnxdi.baihongyu.com/