# Solving quadratic programming using R

I would like to solve the following quadratic programming equation using ipop function from kernlab :

min 0.5*x'*H*x + f'*x subject to: A*x <= b Aeq*x = beq LB <= x <= UB

where in our example H 3x3 matrix, f is 3x1, A is 2x3, b is 2x1, LB and UB are both 3x1.

**edit 1**
My R code is :

library(kernlab) H <- rbind(c(1,0,0),c(0,1,0),c(0,0,1)) f = rbind(0,0,0) A = rbind(c(1,1,1), c(-1,-1,-1)) b = rbind(4.26, -1.73) LB = rbind(0,0,0) UB = rbind(100,100,100) > ipop(f,H,A,b,LB,UB,0) Error in crossprod(r, q) : non-conformable arguments

I know from matlab that is something like this :

H = eye(3); f = [0,0,0]; nsamples=3; eps = (sqrt(nsamples)-1)/sqrt(nsamples); A=ones(1,nsamples); A(2,:)=-ones(1,nsamples); b=[nsamples*(eps+1); nsamples*(eps-1)]; Aeq = []; beq = []; LB = zeros(nsamples,1); UB = ones(nsamples,1).*1000; [beta,FVAL,EXITFLAG] = quadprog(H,f,A,b,Aeq,beq,LB,UB);

and the answer is a vector of 3x1 equals to [0.57,0.57,0.57];

However when I try it on R, using ipop function from kernlab library
ipop(f,H,A,b,LB,UB,0)) and I am facing *Error in crossprod(r, q) : non-conformable arguments*

I appreciate any comment

## Answers

The original question asks about the error message *Error in crossprod(r, q) : non-conformable arguments*. The answer is that r must be specified with the same dimensions as b. So if b is 2x1 then r must also be 2x1.

A secondary question (from the comments) asks about why the system presented in the original question works in Matlab but not in R. The answer is that R and Matlab specify the problems differently. Matlab allows for inequality constraints to be entered separately from the equality constraints. However in R the constraints must all be of the form b<=Ax<=b+r (at least within the kernlab function ipop). So how may we mimic the original inequality constraints? The simple way is to make b very negative and to make r'=-b+r, where r' is your new r vector. Now we still have the same upper bound on the constraints because r'+b=-b+r+b=r. However we have put a lower bound on the constraints, too. My suggestion is to try solving the system with a few different values for b to see if the solution is consistent.

EDIT:

This is probably a better way to handle solving the program:

library(quadprog); dvec <- -f; Dmat <- H; Amat <- -t(A); bvec <- -rbind(4.26,-1.73); solve.QP(Dmat, dvec, Amat, bvec)

where these definitions depend on the previously defined R code.