Dear List,
I'm trying to solve this simple optimization problem in R. The parameters
are the exponents to the matrix mm. The constraints specify that each row
of the parameter matrix should sum to 1 and their product to 0. I don't
understand why the constraints are not satisfied at the solution. I must be
misinterpreting how to specify the constrains somehow.
library(alabama)
ff <- function (x) {
mm <- matrix(c(10, 25, 5, 10), 2, 2)
matx <- matrix(x, 2, 2)
-sum(apply(mm ^ matx, 1, prod))
}
### constraints
heq <- function(x) {
h <- rep(NA, 1)
h[1] <- x[1] + x[3] -1
h[2] <- x[2] + x[4] -1
h[3] <- x[1] * x[3]
h[4] <- x[2] * x[4]
h
}
res <- constrOptim.nl(par = c(1, 1, 1, 1), fn = ff,
heq = heq)
res$convergence #why NULL?
matrix(round(res$par, 2), 2, 2) #why constraints are not satisfied?
Axel.
[[alternative HTML version deleted]]
Your constraints are non-sensical. The only way for these constraints to be
satisfied is for two of the parameters to be 0 and the other two to be 1.
Please spend time to formulate your problem correctly, before imposing on
others' time.
Ravi
________________________________
From: Axel Urbiz [axel.urbiz@gmail.com]
Sent: Sunday, February 10, 2013 3:16 PM
To: R-help@r-project.org; Ravi Varadhan
Subject: Constrained Optimization in R (alabama)
Dear List,
I'm trying to solve this simple optimization problem in R. The parameters
are the exponents to the matrix mm. The constraints specify that each row of the
parameter matrix should sum to 1 and their product to 0. I don't understand
why the constraints are not satisfied at the solution. I must be misinterpreting
how to specify the constrains somehow.
library(alabama)
ff <- function (x) {
mm <- matrix(c(10, 25, 5, 10), 2, 2)
matx <- matrix(x, 2, 2)
-sum(apply(mm ^ matx, 1, prod))
}
### constraints
heq <- function(x) {
h <- rep(NA, 1)
h[1] <- x[1] + x[3] -1
h[2] <- x[2] + x[4] -1
h[3] <- x[1] * x[3]
h[4] <- x[2] * x[4]
h
}
res <- constrOptim.nl(par = c(1, 1, 1, 1), fn = ff,
heq = heq)
res$convergence #why NULL?
matrix(round(res$par, 2), 2, 2) #why constraints are not satisfied?
Axel.
[[alternative HTML version deleted]]
Axel,
Your objective function has the wrong sign. The maximum is infinity, so it does
not make sense to maximize. YOu should be minimizing the product. So, remove
the negative sign and it works as you had expected.
ff <- function (x) {
mm <- matrix(c(10, 25, 5, 10), 2, 2)
matx <- matrix(x, 2, 2)
# - sum(apply(mm ^ matx, 1, prod)) # this is the problem
sum(apply(mm ^ matx, 1, prod))
}
### constraints
heq <- function(x) {
h <- rep(NA, 1)
h[1] <- x[1] + x[3] -1
h[2] <- x[2] + x[4] -1
h[3] <- x[1] * x[3]
h[4] <- x[2] * x[4]
h
}
res <- auglag(par = rep(1,4), fn = ff, heq = heq)
Ravi
________________________________
From: Axel Urbiz [axel.urbiz@gmail.com]
Sent: Sunday, February 10, 2013 3:16 PM
To: R-help@r-project.org; Ravi Varadhan
Subject: Constrained Optimization in R (alabama)
Dear List,
I'm trying to solve this simple optimization problem in R. The parameters
are the exponents to the matrix mm. The constraints specify that each row of the
parameter matrix should sum to 1 and their product to 0. I don't understand
why the constraints are not satisfied at the solution. I must be misinterpreting
how to specify the constrains somehow.
library(alabama)
ff <- function (x) {
mm <- matrix(c(10, 25, 5, 10), 2, 2)
matx <- matrix(x, 2, 2)
-sum(apply(mm ^ matx, 1, prod))
}
### constraints
heq <- function(x) {
h <- rep(NA, 1)
h[1] <- x[1] + x[3] -1
h[2] <- x[2] + x[4] -1
h[3] <- x[1] * x[3]
h[4] <- x[2] * x[4]
h
}
res <- constrOptim.nl(par = c(1, 1, 1, 1), fn = ff,
heq = heq)
res$convergence #why NULL?
matrix(round(res$par, 2), 2, 2) #why constraints are not satisfied?
Axel.
[[alternative HTML version deleted]]
On 10-02-2013, at 21:16, Axel Urbiz <axel.urbiz at gmail.com> wrote:> Dear List, > > I'm trying to solve this simple optimization problem in R. The parameters > are the exponents to the matrix mm. The constraints specify that each row > of the parameter matrix should sum to 1 and their product to 0. I don't > understand why the constraints are not satisfied at the solution. I must be > misinterpreting how to specify the constrains somehow. > > > library(alabama) > > ff <- function (x) { > mm <- matrix(c(10, 25, 5, 10), 2, 2) > matx <- matrix(x, 2, 2) > -sum(apply(mm ^ matx, 1, prod)) > } > > > ### constraints > > heq <- function(x) { > h <- rep(NA, 1) > h[1] <- x[1] + x[3] -1 > h[2] <- x[2] + x[4] -1 > h[3] <- x[1] * x[3] > h[4] <- x[2] * x[4] > h > } > > res <- constrOptim.nl(par = c(1, 1, 1, 1), fn = ff, > heq = heq) > res$convergence #why NULL? > matrix(round(res$par, 2), 2, 2) #why constraints are not satisfied?There is no need to use an optimization function in this case. You can easily find the optimum by hand. From the constraints : x[3] equals (1-x[1]) x[4] equals (1-x[2]) Therefore x[1] * (1-x[1]) equals 0 x[2] * (1-x[2]) equals 0 So you only need to calculate the function value for 4 vectors: x1 <- c(1,1,0,0) x2 <- c(0,0,1,1) x3 <- c(1,0,0,1) x4 <- c(0,1,1,0) Modifying your ff function in the way Ravi suggested: ff <- function (x) { mm <- matrix(c(10, 25, 5, 10), 2, 2) matx <- matrix(x, 2, 2) sum(apply(mm ^ matx, 1, prod)) } and running ff with x{1,2,3,4} as argument, one gets> ff(x1)[1] 35> ff(x2)[1] 15> ff(x3)[1] 20> ff(x4)[1] 30 So ff(x2) achieves the minimum, which corresponds to Ravi's result with auglag. Berend