scipy.optimize.minimize中的逐元素约束 [英] Element-wise constraints in scipy.optimize.minimize

问题描述

我正在使用scipy.optimize.minimize的COBYLA方法来查找用于分类分布的参数矩阵.我需要施加一个约束，即每个参数都大于零，并且参数矩阵的行之和是一列.

I'm using scipy.optimize.minimize's COBYLA method to find a matrix of parameters for a categorical distribution. I need to impose the constraint that each parameter is greater than zero, and that the sum of the rows of the parameter matrix is a column of ones.

我不清楚如何在scipy.minimize中实现这一点，因为检查了约束的非负性而不是真实性.如果仅将数组作为约束，则最小化会引发异常.

It's not clear to me how to implement this in scipy.minimize, because the constraints are checked for non-negativity rather than truth. The minimization raises an exception if I just pass the arrays as the constraint.

有人知道如何实施这些约束吗?

Does anyone know how to go about implementing these kinds of constraints?

推荐答案

第一个约束x > 0可以非常简单地表示:

The first constraint x > 0 can be expressed very simply:

{'type':'ineq', 'fun': lambda x: x}

第二个约束是等式约束，COBYLA本身不支持该约束.但是，您可以将其表示为两个单独的不等式约束:

The second constraint is an equality constraint, which COBYLA doesn't natively support. However, you could express it as two separate inequality constraints instead:

{'type':'ineq', 'fun': lambda x: np.sum(x, 0) - 1}  # row sum >= 1
{'type':'ineq', 'fun': lambda x: 1 - np.sum(x, 0)}  # row sum <= 1

否则，您可以尝试使用SLSQP，它确实支持相等性约束.

Otherwise you could try SLSQP instead, which does support equality constraints.

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