[R] optim seems to be finding a local minimum

[Dimitri Liakhovitski]

Bert,
that's exactly where I started. I found optim in the first paragraph
under "General Purpose Continuous Solvers" and used bounded BFGS for a
constrained optimization for a situation with more than 1 parameters.
Again, not being an engineer / mathematician - would greatly
appreciate any pointers.
Thank you, everyone!
Dimitri

On Thu, Nov 10, 2011 at 2:39 PM, Bert Gunter <gunter.berton at gene.com> wrote:
> Refer to the CRAN "Optimization" task view, please. That is a much more
> appropriate place to begin than posting a query here.
>
> All numerical optimizers only produce local optima.
>
> -- Bert
>
> On Thu, Nov 10, 2011 at 11:24 AM, Dimitri Liakhovitski
> <dimitri.liakhovitski at gmail.com> wrote:
>>
>> Just to add:
>>
>> I also experimented with the starting parameters (par) under optim,
>> especially with the second one. I tried 1, 10, 100, 1000, etc.
>> When I tried 100,000,000 then I got a somewhat better solution (but
>> still not as good as in Excel). However, under message it said:
>>
>> "ERROR: ABNORMAL_TERMINATION_IN_LNSRCH"
>>
>> Dimitri
>>
>> On Thu, Nov 10, 2011 at 1:50 PM, Dimitri Liakhovitski
>> <dimitri.liakhovitski at gmail.com> wrote:
>> > Hello!
>> >
>> > I am trying to create an R optimization routine for a task that's
>> > currently being done using Excel (lots of tables, formulas, and
>> > Solver).
>> > However, otpim seems to be finding a local minimum.
>> > Example data, functions, and comparison with the solution found in
>> > Excel are below.
>> > I am not experienced in optimizations so thanks a lot for your advice!
>> > Dimitri
>> >
>> > ### 2 Inputs:
>> >
>> > IV<-data.frame(IV=c(0,6672895.687,13345791.37,20018687.06,26691582.75,33364478.44,40037374.12,46710269.81,53383165.5,60056061.18,66728956.87,73401852.56,80074748.24,86747643.93,93420539.62,100093435.3,106766331,113439226.7,120112122.4,126785018.1,133457913.7,140130809.4,146803705.1,153476600.8,160149496.5,166822392.2,173495287.9,180168183.5,186841079.2,193513974.9,200186870.6))
>> >
>> > DV<-data.frame(DV=c(0,439.8839775,829.7360945,1176.968757,1487.732038,1767.147276,2019.49499,2248.366401,2456.78592,2647.310413,2822.109854,2983.033036,3131.661246,3269.352233,3397.276321,3516.446162,3627.741311,3731.928591,3829.679009,3921.581866,4008.156537,4089.862363,4167.106955,4240.253215,4309.625263,4375.513474,4438.178766,4497.856259,4554.75841,4609.077705,4660.988983))
>> >
>> > ## Function "transformIV" transforms a data frame column "IV" using
>> > parameters .alpha & .beta:
>> > ## It returns a data frame column IV_transf:
>> > transformIV = function(.alpha,.beta) {
>> >  IV_transf <- as.data.frame(1 - (1/exp((IV/.beta)^.alpha)))
>> >  return(IV_transf)
>> > }
>> >
>> > ### Function "mysum" calculates the sum of absolute residuals after a
>> > regression with a single predictor:
>> > mysum<- function(myIV,myDV){
>> >  regr<-lm(myDV[[1]] ~ 0 + myIV[[1]])
>> >  mysum<-sum(abs(regr$resid))
>> >  return(mysum)
>> > }
>> >
>> > ### Function to be optimized;
>> > ### param is a vector of 2 values (.alpha and .beta)
>> > myfunc <- function(param){
>> >  myalpha<-param[1]
>> >  mybeta<-param[2]
>> >  IVtransf<-transformIV(myalpha, mybeta)
>> >  sumofdevs<-mysum(myIV=IVtransf,myDV=DV)
>> >  return(sumofdevs)
>> > }
>> >
>> > # Optimizing using optim:
>> > myopt <- optim(fn=myfunc, par=c(0.1,max(IV)), method="L-BFGS-B",
>> > lower=0)
>> > (myopt)
>> > myfunc(myopt$par)
>> > ## Comparing this solution to Excel Solver solution:
>> > myfunc(c(0.888452533990788,94812732.0897449))
>> >
>> > --
>> > Dimitri Liakhovitski
>> > marketfusionanalytics.com
>> >
>>
>>
>>
>> --
>> Dimitri Liakhovitski
>> marketfusionanalytics.com
>>
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>> and provide commented, minimal, self-contained, reproducible code.
>
>
>
> --
>
> Bert Gunter
> Genentech Nonclinical Biostatistics
>
> Internal Contact Info:
> Phone: 467-7374
> Website:
> http://pharmadevelopment.roche.com/index/pdb/pdb-functional-groups/pdb-biostatistics/pdb-ncb-home.htm
>
>



-- 
Dimitri Liakhovitski
marketfusionanalytics.com