Scipy.optimize 不等式约束 - 考虑不等式的哪一侧? [英] Scipy.optimize Inequality Constraint - Which side of the inequality is considered?

问题描述

我正在使用 scipy.optimize 模块来寻找可以最小化我的输出的最佳输入权重.从我看到的例子中，我们用单边方程定义了约束；然后我们创建一个不等式"类型的变量.我的问题是优化包如何知道我的约束中变量的总和需要小于 1 还是大于 1?

...

def 约束 1(x):返回 x[0]+x[1]+x[2]+x[3]-1

....

con1 = {'type':'ineq','fun':constraint1}

链接到我在示例中使用的完整解决方案:

其中不等式的形式为 C_j(x) >= 0.

所以当你将约束定义为

def 约束 1(x):返回 x[0]+x[1]+x[2]+x[3]-1

并指定约束类型为

con1 = {'type':'ineq','fun':constraint1}

它自动假定约束采用标准形式 x[0]+x[1]+x[2]+x[3]-1>=0 即，x[0]+x[1]+x[2]+x[3]>=1

I am using the scipy.optimize module to find optimal input weights that would minimize my output. From the examples I've seen, we define the constraint with a one-sided equation; then we create a variable that's of the type 'inequality'. My question is how does the optimization package know whether the sum of the variables in my constraint need to be smaller than 1 or larger than 1?

...

def constraint1(x):
    return x[0]+x[1]+x[2]+x[3]-1

....

con1 = {'type': 'ineq', 'fun': constraint1}

link to full solution I'm using in my example: http://apmonitor.com/che263/index.php/Main/PythonOptimization

Thank you.

解决方案

If you refer to https://docs.scipy.org/doc/scipy-0.18.1/reference/tutorial/optimize.html and scrool down to Constrained minimization of multivariate scalar functions (minimize), you can find that

This algorithm allows to deal with constrained minimization problems of the form:

where the inequalities are of the form C_j(x) >= 0.

So when you define the constraint as

def constraint1(x):
    return x[0]+x[1]+x[2]+x[3]-1

and specify the type of the constraint as

con1 = {'type': 'ineq', 'fun': constraint1}

it automatically assumes that the constraint is in the standard form x[0]+x[1]+x[2]+x[3]-1>=0 i.e., x[0]+x[1]+x[2]+x[3]>=1

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