[R] question about constraint minimization

[dhacademic at gmail.com]

Hi, 

I am a beginner of R. There is a question about constraint minimization. A
function, y=f(x1,x2,x3....x12), needs to be minimized. There are 3
requirements for the minimization: 

(1) x2+x3+...+x12=1.5 (x1 is excluded);
(2) x1=x3=x4;
(3) x1, x3 and x5 are in the range of -1~0, respectively. The rest variables
(x2, x4, x6, x7, ...., x12) are in the range of 0~1, respectively.

The "optim" function is used. And part of my input is as follow, where
"xx1r" represents the x12:

xx1r=1.5-x[2]-x[1]-x[1]-x[3]-x[4]-x[5]-x[6]-x[7]-x[8]-x[9]
start=rnorm(9)
up=1:9/1:9*1
lo=1:9/1:9*-1
out=optim(start,f,lower=lo,upper=up,method="L-BFGS-B",hessian=TRUE,
control=list(trace=6,maxit=1000))

There are two problems in this input. the "up" and "lo" only define a range
of -1~1 for x1 to x11, which can not meet the requirement (3). In addition,
there is not any constraint imposed on x12. I have no idea how to specify a
matrix that can impose different constraints on individual variables in a
function. Any suggestion is highly appreciated.

Best,
Hao


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