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release: v2.4.1 -> v.2.4.2
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@linjing-lab
linjing-lab committed Apr 17, 2023
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Expand Up @@ -45,7 +45,6 @@ pip install -e . --verbose
```text
pip install optimtool --upgrade
```

## 项目结构

```textile
Expand Down Expand Up @@ -103,7 +102,7 @@ ou.gradient_descent.[函数名]([目标函数], [参数表], [初始迭代点])
| steepest(funcs: FuncArray, args: ArgArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="wolfe", epsilon: float=1e-10, k: int=0) -> OutputType | 使用线搜索方法求解非精确步长（默认使用wolfe线搜索） |
| barzilar_borwein(funcs: FuncArray, args: ArgArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="Grippo", c1: float=0.6, beta: float=0.6, alpha: float=1, epsilon: float=1e-10, k: int=0) -> OutputType | 使用Grippo与ZhangHanger提出的非单调线搜索方法更新步长 |

#### 牛顿法（newton)
#### 牛顿法（newton）

```python
ou.newton.[函数名]([目标函数], [参数表], [初始迭代点])
Expand All @@ -112,7 +111,7 @@ ou.newton.[函数名]([目标函数], [参数表], [初始迭代点])
| 方法头 | 解释 |
| ----------------------------------------------------------------------------------------------- | --------------------------------- |
| classic(funcs: FuncArray, args: ArgArray, x_0: PointArray, draw: bool=True, output_f: bool=False, epsilon: float=1e-10, k: int=0) -> OutputType | 通过直接对目标函数二阶导矩阵（海瑟矩阵）进行求逆来获取下一步的步长 |
| modified(funcs: FuncArray, args: ArgArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="wolfe", m: int=20, epsilon: float=1e-10, k: int=0) -> OutputType | 修正当前海瑟矩阵保证其正定性（目前只接入了一种修正方法） |
| modified(funcs: FuncArray, args: ArgArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="wolfe", epsilon: float=1e-10, k: int=0) -> OutputType | 修正当前海瑟矩阵保证其正定性（目前只接入了一种修正方法） |
| CG(funcs: FuncArray, args: ArgArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="wolfe", epsilon: float=1e-6, k: int=0) -> OutputType | 采用牛顿-共轭梯度法求解梯度（非精确牛顿法的一种） |

#### 拟牛顿法（newton_quasi）
Expand All @@ -123,8 +122,8 @@ ou.newton_quasi.[函数名]([目标函数], [参数表], [初始迭代点])

| 方法头 | 解释 |
| -------------------------------------------------------------------------------------------- | --------------- |
| bfgs(funcs: FuncArray, args: ArgArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="wolfe", m: float=20, epsilon: float=1e-10, k: int=0) -> OutputType | BFGS方法更新海瑟矩阵 |
| dfp(funcs: FuncArray, args: ArgArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="wolfe", m: float=20, epsilon: float=1e-4, k: int=0) -> OutputType | DFP方法更新海瑟矩阵 |
| bfgs(funcs: FuncArray, args: ArgArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="wolfe", epsilon: float=1e-10, k: int=0) -> OutputType | BFGS方法更新海瑟矩阵 |
| dfp(funcs: FuncArray, args: ArgArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="wolfe", epsilon: float=1e-4, k: int=0) -> OutputType | DFP方法更新海瑟矩阵 |
| L_BFGS(funcs: FuncArray, args: ArgArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="wolfe", m: float=6, epsilon: float=1e-10, k: int=0) -> OutputType | 双循环方法更新BFGS海瑟矩阵 |

#### 非线性最小二乘法（nonlinear_least_square）
Expand All @@ -136,7 +135,7 @@ ou.nonlinear_least_square.[函数名]([目标函数], [参数表], [初始迭代
| 方法头 | 解释 |
| ---------------------------------------------------------------------------------------------------------------------------------------------------- | -------------------------- |
| gauss_newton(funcr: FuncArray, args: ArgArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="wolfe", epsilon: float=1e-10, k: int=0) -> OutputType | 高斯-牛顿提出的方法框架，包括OR分解等操作 |
| levenberg_marquardt(funcr: FuncArray, args: ArgArray, x_0: PointArray, draw: bool=True, output_f: bool=False, m: float=100, lamk: float=1, eta: float=0.2, p1: float=0.4, p2: float=0.9, gamma1: float=0.7, gamma2: float=1.3, epsilon: float=1e-10, k: int=0) -> OutputType | Levenberg Marquardt提出的方法框架 |
| levenberg_marquardt(funcr: FuncArray, args: ArgArray, x_0: PointArray, draw: bool=True, output_f: bool=False, lamk: float=1, eta: float=0.2, p1: float=0.4, p2: float=0.9, gamma1: float=0.7, gamma2: float=1.3, epsilon: float=1e-10, k: int=0) -> OutputType | Levenberg Marquardt提出的方法框架 |

#### 信赖域方法（trust_region）

Expand All @@ -146,7 +145,7 @@ ou.trust_region.[函数名]([目标函数], [参数表], [初始迭代点])

| 方法头 | 解释 |
| ------------------------------------------------------------------------------------------------------------------------------------------------- | ------------------- |
| steihaug_CG(funcs: FuncArray, args: ArgArray, x_0: PointArray, draw: bool=True, output_f: bool=False, m: float=100, r0: float=1, rmax: float=2, eta: float=0.2, p1: float=0.4, p2: float=0.6, gamma1: float=0.5, gamma2: float=1.5, epsilon: float=1e-6, k: int=0) -> OutputType | 截断共轭梯度法在此方法中被用于搜索步长 |
| steihaug_CG(funcs: FuncArray, args: ArgArray, x_0: PointArray, draw: bool=True, output_f: bool=False, r0: float=1, rmax: float=2, eta: float=0.2, p1: float=0.4, p2: float=0.6, gamma1: float=0.5, gamma2: float=1.5, epsilon: float=1e-6, k: int=0) -> OutputType | 截断共轭梯度法在此方法中被用于搜索步长 |

### 约束优化算法（constrain）

Expand All @@ -163,8 +162,8 @@ oc.equal.[函数名]([目标函数], [参数表], [等式约束表], [初始迭

| 方法头 | 解释 |
| ----------------------------------------------------------------------------------------------------------------------------------------------------- | --------- |
| penalty_quadratice(funcs: FuncArray, args: ArgArray, cons: FuncArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="gradient_descent", sigma: float=10, p: float=2, epsilon: float=1e-4, k: int=0) -> OutputType | 增加二次罚项 |
| lagrange_augmentede(funcs: FuncArray, args: ArgArray, cons: FuncArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="gradient_descent", lamk: float=6, sigma: float=10, p: float=2, etak: float=1e-4, epsilon: float=1e-6, k: int=0) -> OutputType | 增广拉格朗日乘子法 |
| penalty_quadratice(funcs: FuncArray, args: ArgArray, cons: FuncArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="trust_region", sigma: float=10, p: float=2, epsilon: float=1e-4, k: int=0) -> OutputType | 增加二次罚项 |
| lagrange_augmentede(funcs: FuncArray, args: ArgArray, cons: FuncArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="trust_region", lamk: float=6, sigma: float=10, p: float=2, etak: float=1e-4, epsilon: float=1e-6, k: int=0) -> OutputType | 增广拉格朗日乘子法 |

#### 不等式约束（unequal）

Expand All @@ -174,9 +173,9 @@ oc.unequal.[函数名]([目标函数], [参数表], [不等式约束表], [初

| 方法头 | 解释 |
| ------------------------------------------------------------------------------------------------------------------------------------------------------------------------ | --------- |
| penalty_quadraticu(funcs: FuncArray, args: ArgArray, cons: FuncArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="gradient_descent", sigma: float=10, p: float=0.4, epsilon: float=1e-10, k: int=0) -> OutputType | 增加二次罚项 |
| penalty_interior_fraction(funcs: FuncArray, args: ArgArray, cons: FuncArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="gradient_descent", sigma: float=12, p: float=0.6, epsilon: float=1e-6, k: int=0) -> OutputType | 增加分式函数罚项 |
| lagrange_augmentedu(funcs: FuncArray, args: ArgArray, cons: FuncArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="gradient_descent", muk: float=10, sigma: float=8, alpha: float=0.2, beta: float=0.7, p: float=2, eta: float=1e-1, epsilon: float=1e-4, k: int=0) -> OutputType | 增广拉格朗日乘子法 |
| penalty_quadraticu(funcs: FuncArray, args: ArgArray, cons: FuncArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="trust_region", sigma: float=10, p: float=0.4, epsilon: float=1e-10, k: int=0) -> OutputType | 增加二次罚项 |
| penalty_interior_fraction(funcs: FuncArray, args: ArgArray, cons: FuncArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="trust_region", sigma: float=12, p: float=0.6, epsilon: float=1e-6, k: int=0) -> OutputType | 增加分式函数罚项 |
| lagrange_augmentedu(funcs: FuncArray, args: ArgArray, cons: FuncArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="trust_region", muk: float=10, sigma: float=8, alpha: float=0.2, beta: float=0.7, p: float=2, eta: float=1e-1, epsilon: float=1e-4, k: int=0) -> OutputType | 增广拉格朗日乘子法 |

#### 混合等式约束（mixequal）

Expand All @@ -186,9 +185,9 @@ oc.mixequal.[函数名]([目标函数], [参数表], [等式约束表], [不等

| 方法头 | 解释 |
| ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | --------- |
| penalty_quadraticm(funcs: FuncArray, args: ArgArray, cons_equal: FuncArray, cons_unequal: FuncArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="gradient_descent", sigma: float=10, p: float=0.6, epsilon: float=1e-10, k: int=0) -> OutputType | 增加二次罚项 |
| penalty_L1(funcs: FuncArray, args: ArgArray, cons_equal: FuncArray, cons_unequal: FuncArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="gradient_descent", sigma: float=1, p: float=0.6, epsilon: float=1e-10, k: int=0) -> OutputType | L1精确罚函数法 |
| lagrange_augmentedm(funcs: FuncArray, args: ArgArray, cons_equal: FuncArray, cons_unequal: FuncArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="gradient_descent", lamk: float=6, muk: float=10, sigma: float=8, alpha: float=0.5, beta: float=0.7, p: float=2, eta: float=1e-3, epsilon: float=1e-4, k: int=0) -> OutputType | 增广拉格朗日乘子法 |
| penalty_quadraticm(funcs: FuncArray, args: ArgArray, cons_equal: FuncArray, cons_unequal: FuncArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="trust_region", sigma: float=10, p: float=0.6, epsilon: float=1e-10, k: int=0) -> OutputType | 增加二次罚项 |
| penalty_L1(funcs: FuncArray, args: ArgArray, cons_equal: FuncArray, cons_unequal: FuncArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="trust_region", sigma: float=1, p: float=0.6, epsilon: float=1e-10, k: int=0) -> OutputType | L1精确罚函数法 |
| lagrange_augmentedm(funcs: FuncArray, args: ArgArray, cons_equal: FuncArray, cons_unequal: FuncArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="trust_region", lamk: float=6, muk: float=10, sigma: float=8, alpha: float=0.5, beta: float=0.7, p: float=2, eta: float=1e-3, epsilon: float=1e-4, k: int=0) -> OutputType | 增广拉格朗日乘子法 |

### 方法的应用（example）

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