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adding overall constraint in optim()

8 messages · Michael Ashton, Bert Gunter, David Winsemius +3 more

Michael Ashton
# 
Hi ?

This is giving me a headache. I?m trying to do a relatively simple optimization ? actually trying to approximate the output from the Excel Solver function but at roughly 1000x the speed. ?

The optimization parameters look like this. The only trouble is that I want to add a constraint that sum(wgt.vect)=1, and I can?t figure out how to do that in optim.

     Mo.vect <- as.vector(tail(head(mo,i),1))
     wgt.vect <- as.vector(tail(head(moWeightsMax,i),1))
     cov.mat <- cov(tail(head(morets,i+12),12))
     opt.fun <- function(wgt.vect) -sum(Mo.vect %*% wgt.vect) / (t(wgt.vect) %*% (cov.mat %*% wgt.vect))

     LowerBounds<-c(0.2,0.05,0.1,0,0,0)
     UpperBounds<-c(0.6,0.3,0.6,0.15,0.1,0.2)

     OptimSolution<-optim(wgt.vect, fn=opt.fun, method="L-BFGS-B",lower=LowerBounds,upper=UpperBounds)


Any thoughts are appreciated!

Mike

Michael Ashton, CFA
Managing Principal

Enduring Investments LLC
W: 973.457.4602
C: 551.655.8006
Bert Gunter
# 
You can't -- at least as I  read the docs for ?optim (but I'm pretty
ignorant about this, so maybe there's a way to tweak it so you can).

See here:   https://cran.r-project.org/web/views/Optimization.html
for other R optimization capabilities.

Also,  given your credentials, the r-sig-finance list might be a
better place for you to post your query.

Cheers,
Bert


Bert Gunter

"The trouble with having an open mind is that people keep coming along
and sticking things into it."
-- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )


On Thu, May 3, 2018 at 10:52 AM, Michael Ashton
<m.ashton at enduringinvestments.com> wrote:
Michael Ashton
# 
Thanks Bert. But everyone on that forum wants to use finance tools rather than general optimization stuff! And I am not optimizing a traditional Markowitz mean-variance problem. Plus, smarter people here. :-)
David Winsemius
# 
Have you reviewed the documentation for constrOptim {in pkg-stats}?
I was surprised that emoji made it through. Nonetheless it is usually much safer to posting in plain-text. Didn't seem to be a problem in this case but code and data are often mangled.


David Winsemius
Alameda, CA, USA

'Any technology distinguishable from magic is insufficiently advanced.'   -Gehm's Corollary to Clarke's Third Law
John C Nash
# 
This looks like what I call a sumscale problem i.e., some sort of simple
function of the parameters sums to a constant. I've done some work on
these, but don't have it with me just now. There are several approaches,
but they can be quite tricky. Will send some info in about a week or so
if you are still stuck and contact me offline.

JN
(you'll see my name on 3/5 of optim routines via ?optim)
On 2018-05-03 01:52 PM, Michael Ashton wrote:
Joshua Ulrich
# 
On Thu, May 3, 2018 at 2:03 PM, Michael Ashton
<m.ashton at enduringinvestments.com> wrote:
I'm very confused by these statements.  Most of the "finance tools"
use general-purpose global and/or stochastic optimization packages
(e.g. rugarch uses nloptr and Rsolnp, PortfolioAnalytics uses DEoptim,
pso, GenSA).  And most (all?) of those optimization packages have ways
to specify box, equality, and nonlinear inequality constraints.

And I can't recall the last time someone emailed the list about
optimizing a traditional Markowitz mean-variance problem... maybe 10
years ago?

  
    

      
      
    

  


  


      

    

    
2 days later

    

      
      

        


  

        

      Eric Berger
    

    

      
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Hi Michael,
A few comments
1. To add the constraint sum(wgt.vect=1) you would use the method of
Lagrange multipliers.
    What this means is that in addition to the w_i (the components of the
weight variables) you would add an additional variable, call it lambda.
    Then you would modify your optim.fun() function to add the term
 lambda * (sum(wgt.vect - 1)
2. Are you sure that you have defined Mo.vect correctly? It is a scalar the
way you have written it.
3. Similarly your definition of wgt.vect creates a scalar.

HTH,
Eric


On Fri, May 4, 2018 at 5:18 AM, Joshua Ulrich <josh.m.ulrich at gmail.com>
wrote:

            

      
      
      
    

        

      
      
    

            

      
      
      
    

        

      
      
    

        

      
      
    

            

      
      
      
    

        

      
      
    

            

      
      
      
    

        

      
      
    

        

  
  


  


      

    

    

      
      

        


  

        

      Eric Berger
    

    

      
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typo:  lambda * (sum(wgt.wect) - 1)

        
On Sun, May 6, 2018 at 10:51 AM, Eric Berger <ericjberger at gmail.com> wrote: