带约束的R线性模型 [英] R linear model with constraints

问题描述

我想拟合线性模型

y ~ a_1 * x_1 + ... + a_n * x_n

具有参数约束

a_1,...,a_n >=0 

和

a_1 + ... + a_n <= 1 

在R.

是否有一种优雅而又快速的方法来执行此操作，而无需使用quadprog软件包的Solve.QP. 如果为建议的解决方案概述一个简短而详细的用例，那将是很棒的事情.

Is there an elegant and fast way to do that and without using solve.QP of the quadprog package. It would be wonderful if a short but detailed use case would be outlined for a proposed solution.

推荐答案

您可以将constrOptim与成本函数最小二乘和约束定义为ui %*% a >= ci一起使用.

You can use constrOptim with cost function least square and contraints defined such that ui %*% a >= ci.

假设n=3.您需要以下约束:

Suppose n=3. You want constraints such as:

 a1         >=  0
     a2     >=  0
         a3 >=  0
-a1 -a2 -a3 >= -1

因此，您必须提供constrOptim以下参数:

Thus you have to provide constrOptim the following parameters:

ui = rbind(c(1,0,0),
           c(0,1,0),
           c(0,0,1),
           c(-1,-1,-1))

ci = c(0,0,0,-1)

如果不使用渐变，也请在constrOptim中明确设置grad=NULL.

Set also explicitely grad=NULL in constrOptim if you do not use the gradient.

希望有帮助.

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