Set constraints in a Matrix - OPTIM in R

Question

I have a vector of integers as input values (starting values for optim par)

my.data.var <- c(10,0.25,0.25,0.25,0.25,0.25,
             10,0.25,0.25,0.25,0.25,0.25,
             10,0.25,0.25,0.25,0.25,0.25,
             10,0.25,0.25,0.25,0.25,0.25)

Optimization problem is a min. problem.
The error function calculates sum of square root of diff in values between TWO MATRICES (Given Values Matrix vs Calculated Matrix)
The calculated matrix is the one that uses above integer vector.
Hence, in the error function, I stack the integer vector into a matrix as my.data.var.mat <- matrix(my.data.var,nrow = 4,ncol = 6,byrow = TRUE)

The constraint that I must introduce is that colSum(my.data.var.mat) <=1

The optim is defined as

sols<-optim(my.data.var,Error.func,method="L-BFGS-B",upper=c(Inf,1,1,1,1,1,Inf,1,1,1,1,1,Inf,1,1,1,1,1,Inf,1,1,1,1,1),
  lower=c(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))

Error Function is defined as

Error.func <- function(my.data.var){


my.data.var.mat <- matrix(my.data.var,nrow = ncol(my.data.matrix.prod),ncol = ncol(my.data.matrix.inj)+1,byrow = TRUE)

  Calc.Qjk.Value <- Qjk.Cal.func(my.data.timet0,my.data.qo,my.data.matrix.time,
                                 my.data.matrix.inj, my.data.matrix.prod,my.data.var,my.data.var.mat)

  diff.values <- my.data.matrix.prod-Calc.Qjk.Value    #FIND DIFFERENCE BETWEEN CAL. MATRIX AND ORIGINAL MATRIX

  Error <- ((colSums ((diff.values^2), na.rm = FALSE, dims = 1))/nrow(my.data.matrix.inj))^0.5    #sum of square root of the diff

  Error_total <- sum(Error,na.rm=FALSE)/ncol(my.data.matrix.prod)   # total avg error

  Error_total
}

Given Dataset: my.data.matrix.prod , my.data.timet0, my.data.qo, my.data.matrix.time, my.data.matrix.inj

So, my question is how and where should I introduce the matrix col sum constraint? Or the other way to put it as how would OPTIM vary integer vector under Matrix col sum constraint?

@ZheyuanLi: Solved it. Instead of using Optim, I used nloptr solver. It allows for inequality constraints. have a look here..http://stackoverflow.com/questions/37951719/multiple-inequality-constraints-minimization-with-r-nloptr-package — Modi, Jun 22 '16 at 18:45

score 1 · Accepted Answer · edited May 23 '17 at 10:28

1

I realized that nloptr is a better option than optim since my problem consisted of "inequality constraints".

I modified the implementation as I explain in this post here. "multiple inequality constraints" - Minimization with R nloptr package

Hence, closing this thread.

edited May 23 '17 at 10:28

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answered Jun 22 '16 at 18:47

Modi

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Set constraints in a Matrix - OPTIM in R

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