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update optimtool
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@linjing-lab
linjing-lab committed Oct 19, 2023
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22 changes: 11 additions & 11 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, verbose: bool=False, 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, verbose: bool=False, 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, verbose: bool=False, 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 |
| barzilar_borwein(funcs: FuncArray, args: ArgArray, x_0: PointArray, verbose: bool=False, 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 @@ -134,7 +134,7 @@ 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, verbose: bool=False,, 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, verbose: bool=False, 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, epsk: float=1e-6, 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, verbose: bool=False, 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, epsk: float=1e-6, 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 @@ -144,7 +144,7 @@ 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, verbose: bool=False, 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, epsk: float=1e-6, 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, verbose: bool=False, 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, epsk: float=1e-6, 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 @@ -161,8 +161,8 @@ 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: FuncArray, cons: FuncArray, x_0: PointArray, verbose: bool=False, 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, verbose: bool=False, 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 |
| penalty_quadratice(funcs: FuncArray, args: FuncArray, cons: FuncArray, x_0: PointArray, verbose: bool=False, 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, verbose: bool=False, 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 @@ -172,8 +172,8 @@ 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, verbose: bool=False, 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 |
| lagrange_augmentedu(funcs: FuncArray, args: ArgArray, cons: FuncArray, x_0: PointArray, verbose: bool=False, 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 |
| penalty_quadraticu(funcs: FuncArray, args: ArgArray, cons: FuncArray, x_0: PointArray, verbose: bool=False, 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 |
| lagrange_augmentedu(funcs: FuncArray, args: ArgArray, cons: FuncArray, x_0: PointArray, verbose: bool=False, 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 @@ -183,9 +183,9 @@ 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, verbose: bool=False, 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, verbose: bool=False, 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, verbose: bool=False, 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, etak: 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, verbose: bool=False, 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, verbose: bool=False, 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, verbose: bool=False, 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., etak: 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）

Expand All @@ -201,7 +201,7 @@ oe.Lasso.[函数名]([矩阵A], [矩阵b], [因子mu], [参数表], [初始迭

| 方法头 | 解释 |
| ------------------------------------------------------------------------------------------------------- | ---------------- |
| gradient(A: NDArray, b: NDArray, mu: float, args: ArgArray, x_0: PointArray, verbose: bool=False, draw: bool=True, output_f: bool=False, delta: float=10, alp: float=1e-3, epsilon: float=1e-2, k: int=0) -> OutputType | 光滑化Lasso函数法 |
| gradient(A: NDArray, b: NDArray, mu: float, args: ArgArray, x_0: PointArray, verbose: bool=False, draw: bool=True, output_f: bool=False, delta: float=10., alp: float=1e-3, epsilon: float=1e-2, k: int=0) -> OutputType | 光滑化Lasso函数法 |
| subgradient(A: NDArray, b: NDArray, mu: float, args: ArgArray, x_0: PointArray, verbose: bool=False, draw: bool=True, output_f: bool=False, alphak: float=2e-2, epsilon: float=1e-3, k: int=0) -> OutputType | 次梯度法Lasso避免一阶不可导 |
| approximate_point(A: NDArray, b: NDArray, mu: float, args: ArgArray, x_0: PointArray, verbose: bool=False, draw: bool=True, output_f: bool=False, epsilon: float=1e-4, k: int=0) -> OutputType | 邻近算子更新 |

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