R中不等式系统的求解

Question

我有以下不等式系统：Ay＆gt; = 0，其中A是9x3矩阵，y = (y1, y2, y3)是3个元素的向量。不平等的解决方案是一个区域，但我想返回一个可能解决这个不等式的元组（y1，y2，y3）。注意，y的所有元素都必须是> 0

有没有办法在R？中做到这一点？

由于

 A = matrix(runif(27, -0.5, 0.5), nc = 3)

 ### The system to solve is:    A %*% y >= as.matrix(rep(0,9))    Solve for y. Do not return region, but rather any possible tuple that solves the inequalities

Answer 1

尝试线性编程：

library(Rglpk)
rhs <- rep(c(0, 1e-3), c(9, 3))
ge <- rep(">=", 12)

# an example with no feasible solution (status = 1)
set.seed(123)
A <- rbind(matrix(runif(27, -0.5, 0.5), nc = 3), diag(3))
Rglpk_solve_LP(obj = numeric(3), mat = A, dir = ge, rhs = rhs)

# an example with a feasible solution (status = 0)
A2 <- rbind(cbind(numeric(9), 1, -1), diag(3))
Rglpk_solve_LP(obj = numeric(3), mat = A2, dir = ge, rhs = rhs)