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linjing-lab committed Jun 1, 2023
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18 changes: 9 additions & 9 deletions README.md
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Expand Up @@ -100,7 +100,7 @@ ou.gradient_descent.[函数名]([目标函数], [参数表], [初始迭代点])
| ----------------------------------------------------------------------------------------------------------------------------------- | ------------------------------------ |
| solve(funcs: FuncArray, args: ArgArray, x_0: PointArray, draw: bool=True, output_f: bool=False, epsilon: float=1e-10, k: int=0) -> OutputType | 通过解方程的方式来求解精确步长 |
| 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 |
| 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, M: int=20, eta: 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）

Expand Down Expand Up @@ -162,8 +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="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 |
| penalty_quadratice(funcs: FuncArray, args: ArgArray, cons: FuncArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="newton", sigma: float=10, p: float=2, epsk: float=1e-4, 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="newton", 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 @@ -173,9 +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="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 |
| penalty_quadraticu(funcs: FuncArray, args: ArgArray, cons: FuncArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="newton", sigma: float=10, p: float=0.4, epsk: float=1e-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="newton", sigma: float=12, p: float=0.6, epsk: float=1e-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="newton", 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 @@ -185,9 +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="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 |
| penalty_quadraticm(funcs: FuncArray, args: ArgArray, cons_equal: FuncArray, cons_unequal: FuncArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="newton", sigma: float=10, p: float=0.6, epsk: float=1e-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="newton", sigma: float=1, p: float=0.6, epsk: float=1e-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="newton", 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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20 changes: 10 additions & 10 deletions README_en.md
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Original file line number Diff line number Diff line change
Expand Up @@ -100,9 +100,9 @@ ou.gradient_descent.[Function Name]([Target Function], [Parameters], [Initial Po
| ----------------------------------------------------------------------------------------------------------------------------------- | ------------------------------------ |
| solve(funcs: FuncArray, args: ArgArray, x_0: PointArray, draw: bool=True, output_f: bool=False, epsilon: float=1e-10, k: int=0) -> OutputType | Solve the exact step by solving the equation |
| 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 | Use line search method to solve imprecise step size (wolfe line search is used by default) |
| 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 | Update the step size using the nonmonotonic line search method proposed by Grippo and Zhang Hanger |
| 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, M: int=20, eta: float=0.6, alpha: float=1, epsilon: float=1e-10, k: int=0) -> OutputType | Update the step size using the nonmonotonic line search method proposed by Grippo and Zhang Hanger |

#### Newton Methods（newton)
#### Newton Methods（newton）

```python
ou.newton.[Function Name]([Target Function], [Parameters], [Initial Point])
Expand Down Expand Up @@ -162,8 +162,8 @@ oc.equal.[Function Name]([Target Function], [Parameters], [Equal Constraint Tabl

| head meathod | explain |
| ----------------------------------------------------------------------------------------------------------------------------------------------------- | --------- |
| 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 | Add secondary penalty |
| 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 | Augmented lagrange multiplier method |
| penalty_quadratice(funcs: FuncArray, args: ArgArray, cons: FuncArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="newton", sigma: float=10, p: float=2, epsk: float=1e-4, epsilon: float=1e-4, k: int=0) -> OutputType | Add secondary penalty |
| lagrange_augmentede(funcs: FuncArray, args: ArgArray, cons: FuncArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="newton", lamk: float=6, sigma: float=10, p: float=2, etak: float=1e-4, epsilon: float=1e-6, k: int=0) -> OutputType | Augmented lagrange multiplier method |

#### Unequal Constraint（unequal）

Expand All @@ -173,9 +173,9 @@ oc.unequal.[Function Name]([Target Function], [Parameters], [Unequal Constraint

| head meathod | explain |
| ------------------------------------------------------------------------------------------------------------------------------------------------------------------------ | --------- |
| 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 | Add secondary penalty |
| 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 | Increase penalty term of fractional function |
| 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 | Augmented lagrange multiplier method |
| penalty_quadraticu(funcs: FuncArray, args: ArgArray, cons: FuncArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="newton", sigma: float=10, p: float=0.4, epsk: float=1e-6, epsilon: float=1e-10, k: int=0) -> OutputType | Add secondary penalty |
| penalty_interior_fraction(funcs: FuncArray, args: ArgArray, cons: FuncArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="newton", sigma: float=12, p: float=0.6, epsk: float=1e-6, epsilon: float=1e-6, k: int=0) -> OutputType | Increase penalty term of fractional function |
| lagrange_augmentedu(funcs: FuncArray, args: ArgArray, cons: FuncArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="newton", 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 | Augmented lagrange multiplier method |

#### Mixequal Constraint（mixequal）

Expand All @@ -185,9 +185,9 @@ oc.mixequal.[Function Name]([Target Function], [Parameters], [Equal Constraint T

| head meathod | explain |
| ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | --------- |
| 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 | Add secondary penalty |
| 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 exact penalty function method |
| 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 | Augmented lagrange multiplier method |
| penalty_quadraticm(funcs: FuncArray, args: ArgArray, cons_equal: FuncArray, cons_unequal: FuncArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="newton", sigma: float=10, p: float=0.6, epsk: float=1e-4, epsilon: float=1e-10, k: int=0) -> OutputType | Add secondary penalty |
| penalty_L1(funcs: FuncArray, args: ArgArray, cons_equal: FuncArray, cons_unequal: FuncArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="newton", sigma: float=1, p: float=0.6, epsk: float=1e-6, epsilon: float=1e-10, k: int=0) -> OutputType | L1 exact penalty function method |
| lagrange_augmentedm(funcs: FuncArray, args: ArgArray, cons_equal: FuncArray, cons_unequal: FuncArray, x_0: PointArray, draw: bool=True, output_f: bool=False, method: str="newton", 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 | Augmented lagrange multiplier method |

### Application of Methods（example）

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