How to put mathematical constraints with GenSA function in R

Question

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

efficientFunction <- function(v) {
  t(v)  %*% Co         


        

Answer 1

A possible approach would be to make use of so-called Lagrange multipliers (cf., http://en.wikipedia.org/wiki/Lagrange_multiplier). For example, set

efficientFunction <- function(v) {
  lambda <- 100
  t(v)  %*% Cov_Mat   %*%  v + lambda * abs( sum(v) - 1 )
}

, 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.