完成一维和多维无约束非线性优化的功能，并添加文档

doc/rmvl.bib

@@ -1,8 +1,9 @@
-@misc{opencv,
+@software{opencv,
   author = {opencv},
   title = {opencv},
-  year = {2001},
-  url = {https://github.com/matheecs/ICRA-2019-DJI-RoboMaster}
+  license = {Apache-2.0},
+  url = {https://github.com/matheecs/ICRA-2019-DJI-RoboMaster},
+  year = {2001}
 }
 @misc{icra2019,
   author = {matheecs},
@@ -19,13 +20,13 @@ @article{kalman
   pages = {35--45},
   year = {1960}
 }
-@misc{onnx-rt,
+@software{onnx-rt,
   author = {microsoft},
   title = {onnx runtime inference},
   year = {2021},
   url = {https://github.com/microsoft/onnxruntime}
 }
-@misc{apriltag,
+@software{apriltag,
   author = {AprilRobotics},
   title = {AprilTag 3},
   year = {2023},
@@ -62,4 +63,50 @@ @book{numerical_analysis
   year = {2008},
   publisher = {华南理工大学出版社},
   address = {广州}
-}
+}
+@software{Agarwal_Ceres_Solver_2022,
+  author = {Agarwal, Sameer and Mierle, Keir and The Ceres Solver Team},
+  title = {{Ceres Solver}},
+  license = {Apache-2.0},
+  url = {https://github.com/ceres-solver/ceres-solver},
+  version = {2.2},
+  year = {2023},
+  month = {10}
+}
+@article{ConjGrad,
+  author = {Hestenes, Magnus R. and Stiefel, Eduard},
+  title = {Methods of Conjugate Gradients for Solving Linear Systems},
+  journal = {Journal of Research of the National Bureau of Standards},
+  volume = {49},
+  number = {6},
+  pages = {409},
+  year = {1952},
+  month = {12},
+  doi = {10.6028/jres.049.044},
+  url = {https://nvlpubs.nist.gov/nistpubs/jres/049/jresv49n6p409_A1b.pdf}
+}
+@article{Ridders,
+  author = {C. J. F. Ridders},
+  title = {Accurate computation of F'(x) and F'(x) F"(x)},
+  journal = {Advances in Engineering Software},
+  volume = {4},
+  number = {2},
+  pages = {75--76},
+  year = {1978}
+}
+@article{NelderMead,
+    author = {Nelder, J. A. and Mead, R.},
+    title = "{A Simplex Method for Function Minimization}",
+    journal = {The Computer Journal},
+    volume = {7},
+    number = {4},
+    pages = {308-313},
+    year = {1965},
+    month = {01},
+    abstract = "{A method is described for the minimization of a function of n variables, which depends on the comparison of function values at the (n + 1) vertices of a general simplex, followed by the replacement of the vertex with the highest value by another point. The simplex adapts itself to the local landscape, and contracts on to the final minimum. The method is shown to be effective and computationally compact. A procedure is given for the estimation of the Hessian matrix in the neighbourhood of the minimum, needed in statistical estimation problems.}",
+    issn = {0010-4620},
+    doi = {10.1093/comjnl/7.4.308},
+    url = {https://doi.org/10.1093/comjnl/7.4.308},
+    eprint = {https://academic.oup.com/comjnl/article-pdf/7/4/308/1013182/7-4-308.pdf},
+}
+

doc/tutorials/modules/algorithm/auto_differential.md

@@ -0,0 +1,168 @@
+自动求导、数值微分 {#tutorial_modules_auto_differential}
+============
+
+@author 赵曦
+@date 2024/05/06
+@version 1.0
+@brief 包含中心差商以及 Richardson 外推原理的介绍
+
+@prev_tutorial{tutorial_modules_runge_kutta}
+
+@next_tutorial{tutorial_modules_fminbnd}
+
+@tableofcontents
+
+------
+
+\f[
+\def\red#1{\color{red}{#1}}
+\def\teal#1{\color{teal}{#1}}
+\def\green#1{\color{green}{#1}}
+\def\transparent#1{\color{transparent}{#1}}
+\def\orange#1{\color{orange}{#1}}
+\def\fml#1{\text{(#1)}}
+\f]
+
+### 1. 基于 Taylor 公式的数值微分
+
+利用以下两个 2 阶 Taylor 公式：
+
+\f[\begin{align}f(x+h)&=f(x)+f'(x)h+\frac{f''(x)}2h^2+\frac{f'''(x)}{3!}h^3\tag{1-1a}\\
+f(x-h)&=f(x)-f'(x)h+\frac{f''(x)}2h^2-\frac{f'''(x)}{3!}h^3\tag{1-1b}\end{align}\f]
+
+可以得到两个数值微分公式及其对应的截断误差（余项）\f$R\f$：
+
+\f[\begin{align}f'(x)&\approx\frac{f(x+h)-f(x)}h,\qquad R=-\frac{f''(\xi)}2h+o(h^2)\tag{1-2a}\\
+f'(x)&\approx\frac{f(x)-f(x-h)}h,\qquad R=\frac{f''(\eta)}2h+o(h^2)\tag{1-2b}\end{align}\f]
+
+其中\f$\fml{1-2a}\f$称为<span style="color: red">前向差商</span>，\f$\fml{1-2b}\f$称为<span style="color: red">后向差商</span>。由于截断误差的存在，差商法的精度不高，因此我们可以考虑使用更高阶的差商法。我们将\f$\fml{1-1a}\f$和\f$\fml{1-1b}\f$相减，得到：
+
+\f[f(x+h)-f(x-h)=2f'(x)h+\frac2{3!}f'''(\xi)h^3+o(h^3)\tag{1-3a}\f]
+
+整理得到
+
+\f[f'(x)=\frac{f(x+h)-f(x-h)}{2h},\qquad R=-\frac{f'''(\xi)}{3!}h^2+o(h^2)\tag{1-3b}\f]
+
+如果导数\f$f'(x)\f$用\f$\fml{1-3b}\f$计算，那么截断误差为\f$o(h^2)\f$，比\f$\fml{1-2a}\f$和\f$\fml{1-2b}\f$的截断误差\f$O(h)\f$更小。这种方法称为<span style="color: red">中心差商</span>。
+
+### 2. Richardson 外推原理
+
+#### 2.1 公式推导
+
+将公式\f$\fml{1-3b}\f$扩展，可以得到更完全的写法：
+
+\f[f'(x)=\green{\frac{f(x+h)-f(x-h)}{2h}}-\left[\frac1{3!}f^{(3)}(x)h^2+\frac1{5!}f^{(5)}(x)h^4+\frac1{7!}f^{(7)}(x)h^6+\cdots\right]\tag{2-1}\f]
+
+一般的，可以记作
+
+\f[L=\green{\varphi(h)}+\left[a_2h^2+a_4h^4+a_6h^6+\cdots\right]\tag{2-2}\f]
+
+正如上一节所说，如果\f$L\f$用\f$\varphi(h)\f$来近似表示，则截断误差是按\f$h^2\f$展开的幂级数，误差阶为\f$o\left(h^2\right)\f$。
+
+事实上，对于公式\f$\fml{2-2}\f$，求解\f$L\f$的过程还可以继续向前推进（外推），不妨以\f$\frac h2\f$替换\f$\fml{2-2}\f$中的\f$h\f$，可得
+
+\f[L=\varphi\left(\frac h2\right)+\left[a_2\frac{h^2}4+a_4\frac{h^4}{16}+a_6\frac{h^6}{64}+\cdots\right]\tag{2-3}\f]
+
+由\f$4\times\fml{2-3}-\fml{2-2}\f$可以得到
+
+\f[L=\left[\frac43\varphi\left(\frac h2\right)-\frac13\varphi(h)\right]-\left[a_4\frac{h^4}4+5a_6\frac{h^6}{16}+\cdots\right]\tag{2-4}\f]
+
+上式表达了外推过程的第 1 步，说明\f$\varphi(h)\f$和\f$\varphi\left(\frac h2\right)\f$的一个线性组合提供了导数即\f$L\f$的新的计算公式，其<span style="color: red">精度提高</span>至了\f$o\left(h^4\right)\f$
+
+继续进行第 2 步，令
+
+\f[\psi(h)=\frac43\varphi\left(\frac h2\right)-\frac13\varphi(h)=\frac1{4^1-1}\left[4^1\varphi\left(\frac h2\right)-\varphi(h)\right]\tag{2-5}\f]
+
+那么\f$\fml{2-4}\f$可以改写成
+
+\f[L=\psi(h)+\left[b_4h^4+b_6h^6+\cdots\right]\tag{2-6}\f]
+
+与第 1 步的外推过程类似，以\f$\frac h2\f$替换\f$\fml{2-6}\f$中的\f$h\f$，可得
+
+\f[L=\psi\left(\frac h2\right)+\left[b_4\frac{h^4}{16}+b_6\frac{h^6}{64}+\cdots\right]\tag{2-7}\f]
+
+由\f$4^2\times\fml{2-7}-\fml{2-6}\f$可以得到
+
+\f[L=\left[\frac{16}{15}\psi\left(\frac h2\right)-\frac1{15}\psi(h)\right]-\left[b_6\frac{h^6}{20}+\cdots\right]\tag{2-8}\f]
+
+此式表达了外推过程的第 2 步，说明\f$\psi(h)\f$和\f$\psi\left(\frac h2\right)\f$的一个线性组合提供了导数即\f$L\f$的新的计算公式，其<span style="color: red">精度提高</span>至了\f$o\left(h^6\right)\f$
+
+如果我们令
+
+\f[\theta(h)=\frac{16}{15}\psi\left(\frac h2\right)-\frac1{15}\psi(h)\tag{2-9}\f]
+
+不难猜出，新的导数计算公式为
+
+\f[L\approx\frac{64}{63}\theta\left(\frac h2\right)-\frac1{63}\theta(h)\tag{2-10}\f]
+
+读者可以自行验证，按照这个思路可以进一步外推，可执行任意多步得到精度不断提高的新公式，这就是 <span style="color: red">Richardson 外推原理</span>。
+
+#### 2.2 外推算法总结
+
+令\f$\varphi(h)=\frac{f(x+h)-f(x-h)}{2h}\f$，外推\f$M\f$步，则外推算法的步骤如下
+
+① 选取一个适当的\f$h\f$值，计算\f$M+1\f$个数，记为\f$T(*,*)\f$
+
+\f[T(n,0)=\varphi\left(\frac h{2^n}\right),\qquad n=0,1,2,\cdots,M\tag{2-11}\f]
+
+② 按公式计算
+
+\f[T(n,k)=\frac1{4^k-1}\left[4^kT(n,k-1)-T(n-1,k-1)\right],\qquad\left\{\begin{align}
+k&=1,2,\cdots,M\\n&=k,k+1,\cdots,M
+\end{align}\right.\tag{2-12}\f]
+
+按照以上步骤计算得到的\f$T(n,k)\f$，满足等式
+
+\f[L=T(n,k)+o(h^{2k+2})\qquad(h\to0)\tag{2-13}\f]
+
+即\f$T(n,k)\f$具备\f$2k+2\f$阶的精度。
+
+### 3. 如何使用
+
+RMVL 中提供了一元函数以及多元函数的微分工具，求解一元函数导数时可使用 rm::derivative ，求解多元函数梯度是需要使用 rm::grad 。
+
+以下展示了使用自动求导、数值微分的例子。
+
+#### 3.1 创建项目
+
+1. 添加源文件 `main.cpp`
+   ```cpp
+   #include <cstdio>
+   #include <rmvl/core/numcal.hpp>
+
+   // 自定义函数 f(x)=x²+4x-3
+   inline double quadratic(double x) { return x * x + 4 * x - 3; }
+
+   int main()
+   {
+       double dydx = rm::derivative(quadratic, 1);
+       printf("f'(1) = %f\n", dydx);
+   }
+   ```
+
+2. 添加 `CMakeLists.txt`
+   ```cmake
+   cmake_minimum_required(VERSION 3.10)
+   project(DerivativeDemo)
+   find_package(RMVL COMPONENTS core REQUIRED)
+   add_executable(demo main.cpp)
+   target_link_libraries(demo PRIVATE rmvl_core)
+   ```
+
+#### 3.2 构建、运行
+
+在项目根目录打开终端，输入
+
+```bash
+mkdir build
+cd build
+cmake ..
+make -j2
+./demo
+```
+
+可以看到运行结果
+
+```
+f'(1) = 6
+```

doc/tutorials/modules/algorithm/ew_topsis.md

@@ -4,7 +4,7 @@
 @author RoboMaster Vision Community
 @date 2023/01/11
 
-@prev_tutorial{tutorial_modules_runge_kutta}
+@prev_tutorial{tutorial_modules_fminunc}
 
 @next_tutorial{tutorial_modules_kalman}