ArtMgn ArtMgn - 1 year ago 102
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)

I have found in this paper :
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.

Answer Source

A possible approach would be to make use of so-called Lagrange multipliers (cf., 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.

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