ArtMgn - 1 month ago 5x
R Question

# How to put mathematical constraints with GenSA function in R

I am currently trying to use Simulated Annealing package GenSA in order to minimize the function below :

``````efficientFunction <- function(v) {
t(v)  %*% Cov_Mat   %*%  v
}
``````

Where Cov_Mat is a covariance matrix obtained from 4 assets and v is a weight vector of dimension 4.

I'm trying to solve the Markowitz asset allocation approach this way and I would like to know how I could introduce mathematical constraint such as the sum of all coefficients have to equal 1 :

``````sum(v) = 1
``````

Moreover since I intend to rely on the GenSA function, I would like to use something like this with the constraint :

``````v <- c(0.25, 0.25, 0.25, 0.25)
dimension <- 4
lower <- rep(0, dimension)
upper <- rep(1, dimension)

out <- GenSA(v, lower = lower, upper = upper, fn = efficientFunction)
``````

how to handle such constraint within the Simulated Annealing Algorithm but I don't know how I could implement it in R.

I'd be very grateful for any advice. It is my first time using SO so don't hesitate to tell me if I have the wrong approach in the way I ask question.

``````efficientFunction <- function(v) {
, so that in order to minimize the objective function `efficientFunction` the resulting parameter also minimize the penalty term `lambda * abs( sum(v) - 1 )`. The Lagrange multiplier `lambda` is set to an arbitrary but sufficiently high level.