Hi R-list,
I am new to optimization in R and would appreciate help on the following
question. I would like to minimize the following function using two
constraints:
######
fn <- function(par,H,F){
fval <- 0.5 * t(par) %*% H %*% par + F%*% par
fval
}
# matrix H is (n by k)
# matrix F is (n by 1)
# par is a (n by 1) set of weights
# I need two constraints:
# 1. each element in par needs to be between 0 and 1
# 2. sum(par)=1 i.e. the elements in par need to sum to 1
## I try to use optim
res <- optim(c(runif(16),fn, method="L-BFGS-B", H=H, F=f
,control=list(fnscale=-1), lower=0, upper=1)
######
If I understand this correctly, using L-BFGS-B with lower=0 and upper=1
should take care of constraint 1 (box constraints). What I am lacking is the
skill to include constraint no 2.
I guess I could solve this by reparametrization but I am not sure how
exactly. I could not find (i.e. wasn't able to infer) the answer to this in
the archives despite the many comments on optim and constrained optimization
(sorry if I missed it there). I am using version 2.1.1 under windows XP.
Thank you very much.
Jens
This is actually quadratic programming, so why do you want to use optim()? There are packages specifically for QP, e.g. quadprog. A more general approach is to eliminate one variable, which gives you an inequality constrained problem in n-1 variables to which you could apply contrOptim(). Other re-parametrizations (e.g. of weights as a log-linear model) will work provided none of the parameters are going to be zero at the optimum (one cannot be one without all the others being zero). On Wed, 12 Oct 2005, Jens Hainmueller wrote:> Hi R-list, > > I am new to optimization in R and would appreciate help on the following > question. I would like to minimize the following function using two > constraints: > > ###### > fn <- function(par,H,F){ > > fval <- 0.5 * t(par) %*% H %*% par + F%*% par > fval > > } > > # matrix H is (n by k) > # matrix F is (n by 1) > # par is a (n by 1) set of weights > > # I need two constraints: > # 1. each element in par needs to be between 0 and 1 > # 2. sum(par)=1 i.e. the elements in par need to sum to 1 > > ## I try to use optim > res <- optim(c(runif(16),fn, method="L-BFGS-B", H=H, F=f > ,control=list(fnscale=-1), lower=0, upper=1) > ###### > > If I understand this correctly, using L-BFGS-B with lower=0 and upper=1 > should take care of constraint 1 (box constraints). What I am lacking is the > skill to include constraint no 2. > > I guess I could solve this by reparametrization but I am not sure how > exactly. I could not find (i.e. wasn't able to infer) the answer to this in > the archives despite the many comments on optim and constrained optimization > (sorry if I missed it there). I am using version 2.1.1 under windows XP. > > Thank you very much. > > Jens > > ______________________________________________ > R-help at stat.math.ethz.ch mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html >-- Brian D. Ripley, ripley at stats.ox.ac.uk Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272866 (PA) Oxford OX1 3TG, UK Fax: +44 1865 272595
Hello, I have a follow-up from Jens's question and Professor Ripley's response. Jens wants to do quadratic optimization with 2 constraints:> > > # I need two constraints: > > > # 1. each element in par needs to be between 0 and 1 > > > # 2. sum(par)=1, i.e. the elements in par need to sum to 1how does one set both constraints in quadprog, per Prof. Ripley's suggestion? i know how to get quadprog to handle the second constraint, but not BOTH, since quadprog only takes as inputs the constraint matrix "A" and constraint vector "b"-- unlike in "ipop" (kernlab), there is no additional option for box constraints. apologies if i am not seeing something obvious here. thanks in advance, alexis On 10/19/05, Jens Hainmueller <jhainm at fas.harvard.edu> wrote:> > > > -----Urspr??ngliche Nachricht----- > > Von: Prof Brian Ripley [mailto:ripley at stats.ox.ac.uk] > > Gesendet: Thursday, October 13, 2005 2:46 AM > > An: Jens Hainmueller > > Cc: r-help at stat.math.ethz.ch > > Betreff: Re: [R] Optim with two constraints > > > > This is actually quadratic programming, so why do you want to > > use optim()? > > There are packages specifically for QP, e.g. quadprog. > > > > A more general approach is to eliminate one variable, which > > gives you an inequality constrained problem in n-1 variables > > to which you could apply contrOptim(). Other > > re-parametrizations (e.g. of weights as a log-linear model) > > will work provided none of the parameters are going to be > > zero at the optimum (one cannot be one without all the others > > being zero). > > > > On Wed, 12 Oct 2005, Jens Hainmueller wrote: > > > > > Hi R-list, > > > > > > I am new to optimization in R and would appreciate help on the > > > following question. I would like to minimize the following function > > > using two > > > constraints: > > > > > > ###### > > > fn <- function(par,H,F){ > > > > > > fval <- 0.5 * t(par) %*% H %*% par + F%*% par > > > fval > > > > > > } > > > > > > # matrix H is (n by k) > > > # matrix F is (n by 1) > > > # par is a (n by 1) set of weights > > > > > > # I need two constraints: > > > # 1. each element in par needs to be between 0 and 1 # 2. > > sum(par)=1 > > > i.e. the elements in par need to sum to 1 > > > > > > ## I try to use optim > > > res <- optim(c(runif(16),fn, method="L-BFGS-B", H=H, F=f > > > ,control=list(fnscale=-1), lower=0, upper=1) ###### > > > > > > If I understand this correctly, using L-BFGS-B with lower=0 and > > > upper=1 should take care of constraint 1 (box constraints). > > What I am > > > lacking is the skill to include constraint no 2. > > > > > > I guess I could solve this by reparametrization but I am > > not sure how > > > exactly. I could not find (i.e. wasn't able to infer) the answer to > > > this in the archives despite the many comments on optim and > > > constrained optimization (sorry if I missed it there). I am > > using version 2.1.1 under windows XP. > > > > > > Thank you very much. > > > > > > Jens > > > > > > ______________________________________________ > > > R-help at stat.math.ethz.ch mailing list > > > https://stat.ethz.ch/mailman/listinfo/r-help > > > PLEASE do read the posting guide! > > > http://www.R-project.org/posting-guide.html > > > > > > > -- > > Brian D. Ripley, ripley at stats.ox.ac.uk > > Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ > > University of Oxford, Tel: +44 1865 272861 (self) > > 1 South Parks Road, +44 1865 272866 (PA) > > Oxford OX1 3TG, UK Fax: +44 1865 272595 > > > >
Alexis, WIKI: You create the box constraints with two inequality constraints for each element. Suppose that you have five elements, and your upper bound is .33, and your lower bound is 0. Then quadprog would require constraints as: A[1,]=(1,0,0,0,0) b=(0) A[2,]=(-1,0,0,0,0) b=(-.33) A[3,]=(0,1,0,0,0) b=(0) A[4,]=(0,-1,0,0,0) b=(-.33) .....and so on. The syntax is not quite correct but you get the picture. Remember that quadprog distinguishes between equality and inequality constraints, and these must be inequality constraints. The trick to the upper bound is to multiply the constraint by -1 (as indicated), which effectively translates the constraint from a <= constraint into the >= type of constraint required by quadprog. Regards, Tom Alexis Diamond wrote: I have a follow-up from Jens's question and Professor Ripley's response. Jens wants to do quadratic optimization with 2 constraints:> > > # I need two constraints: > > > # 1. each element in par needs to be between 0 and 1 > > > # 2. sum(par)=1, i.e. the elements in par need to sum to 1how does one set both constraints in quadprog, per Prof. Ripley's suggestion? i know how to get quadprog to handle the second constraint, but not BOTH, since quadprog only takes as inputs the constraint matrix "A" and constraint vector "b"-- unlike in "ipop" (kernlab), there is no additional option for box constraints. apologies if i am not seeing something obvious here. thanks in advance, alexis -- Tom Wood Fort Mason Capital 456 Montgomery Street 22nd Floor San Francisco, CA 94104 Direct: 415-249-3387 Fax: 415-249-3389 [1]twood at fortmasoncapital.com References 1. mailto:twood at fortmasoncapital.com