R Constrained Optimization Error

Question

Please note that I am not very familiar with R and I am trying to solve the following optimization (minimization). Any inputs would be greatly appreciated. The issue seems to be with the initial values; am unsure how to pick valid initial values. Though it seems to satisfy the criteria given in the documentation.

  thetaImp = 5*(10^-5);
  eps1 = -0.23;
  eps2 = 0.31;
  minFunc <- function(x) {
    x1 <- x[1];
    x2 <- x[2];
    -1*(max(thetaImp*x1+eps1,0)*(x1) + max(thetaImp*x2+eps2,0)*(x1+x2))
  }
  ui = rbind(c(1,1), c(1,0), c(0,1));
  ci = c(10000,0,0);
  initValues = c(5000,5000);
  constrOptim(initValues, minFunc, NULL, ui, ci);
  ui %*% initValues - ci

Please note that this is also posted on the statistics website with the full description of the problem. The above is only a sample.

https://stats.stackexchange.com/questions/355166/constrained-minimization-closed-form-if-available-or-r-suggestions

Stéphane Laurent · Accepted Answer · 2018-07-09 18:53:47Z

1

For optimization with an equality constraint, there is the Rsolnp package.

library(Rsolnp)

thetaImp = 5*(10^-5);
eps1 = -0.23;
eps2 = 0.31;
W = 10000

f <- function(x) { # function to minimize
  x1 <- x[1];
  x2 <- x[2];
  max(thetaImp*x1+eps1,0)*x1 + max(thetaImp*x2+eps2,0)*W
}

eqfun <- function(x){ # function defining the equality
  x[1] + x[2]
}

solnp(c(5000, 5000), # starting values 
      f, 
      eqfun = eqfun, 
      eqB = W, # the equality constraint
      LB=c(0,0) # lower bounds
)

Output:

Iter: 1 fn: 5435.5000    Pars:  7300.06425 2699.93575
Iter: 2 fn: 5435.5000    Pars:  7300.06425 2699.93575
solnp--> Completed in 2 iterations
$pars
[1] 7300.064 2699.936
......

In this case K=2, we can equivalently solve the problem with an unidimensional optimization, to check:

g <- function(t) { # function to minimize
  x1 <- t
  x2 <- W-t;
  max(thetaImp*x1+eps1,0)*x1 + max(thetaImp*x2+eps2,0)*W
}
optim(5000, g, method="L-BFGS-B", lower=0, upper=W) 


> optim(5000, g, lower=0, upper=W)
$par
[1] 7300
......

We get almost the same result.

edited Jul 9, 2018 at 18:53

answered Jul 9, 2018 at 18:44

Stéphane Laurent

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8 Comments

texmex Over a year ago

thanks for this detailed answer (and your other suggestions on the stats website). I will try it out. Also, in case later I need to change the constraints to inequalities, how would I make it work in the above case using constrOptim? Also, I suppose closed form solutions are to be ruled out?

Stéphane Laurent Over a year ago

@user249613 You mean you need an inequality constraint on $\sum S_i$ ?

texmex Over a year ago

Thanks Stephane,appreciate your time to provide these suggestions. The constraints would be on the sum (currently in your eqfun <- function(x)) and also on the individual $$S_{i}$$ as you mention.

Stéphane Laurent Over a year ago

@user249613 There's a uneqfun argument in the solnp function which is exactly for dealing with this kind of constraints.

texmex Over a year ago

@stehaneLaurent, Thanks for your suggestions thus far. solnp seems to be working fine for the most part. A couple of issues. Issue One: Sometimes it seems to go into an infinite loop and never returns. Anything we can do in such situations.

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