Optimization Solvers with Linear Constraints in R

Optimization Solvers with Linear Constraints in R - nonlinear-optimization

Does anyone know of any R packages that allow you to maximize a function according to a linear constraint? I have been recommended ipoptr but I cannot figure out how to install it so that I can use the R interface.
For some background, I am trying to allocate 80M of investment (x) between 114 products in a way that maximizes revenue (y). Predicted revenue for each product and investment level is based off a two-part model i.e. it is the result of multiplying the predicted probability of any revenue being generated, by the predicted level of revenue, conditional on revenue being generated. Each line of the objective function represents the fitted model for each product.
I have tried using nloptr but it seems to be unable to find global maximums - it always gives me the same values as my starting values.
I am including the functions I am using below.
# Objective function
function(x){
return(-((plogis(-0.17283 + 0.0000471*x[1])*exp(9.53643)*(x[1])^0.468)+
(plogis(-0.17283 + 0.0000471*x[2])*exp(9.53643)*(x[2])^0.468)+
(plogis(-0.17283 + 0.0000471*x[3])*exp(9.53643)*(x[3])^0.468)+
(plogis(-0.17283 + 0.0000471*x[4])*exp(9.53643)*(x[4])^0.468)+
(plogis(-0.17283 + 0.0000471*x[5])*exp(9.53643)*(x[5])^0.468)+
(plogis(-0.17283 + 0.0000471*x[6])*exp(9.53643)*(x[6])^0.468)+
(plogis(-0.17283 + 0.0000471*x[7])*exp(9.53643)*(x[7])^0.468)+
(plogis(-0.17283 + 0.0000471*x[8])*exp(9.53643)*(x[8])^0.468)+
(plogis(-0.17283 + 0.0000471*x[9])*exp(9.53643)*(x[9])^0.468)+
(plogis(-0.17283 + 0.0000471*x[10])*exp(9.53643)*(x[10])^0.468)+
(plogis(-0.17283 + 0.0000471*x[11])*exp(9.53643)*(x[11])^0.468)+
(plogis(-0.17283 + 0.0000471*x[12])*exp(9.53643)*(x[12])^0.468)+
(plogis(-0.17283 + 0.0000471*x[13])*exp(9.53643)*(x[13])^0.468)+
(plogis(-0.17283 + 0.0000471*x[14])*exp(9.53643)*(x[14])^0.468)+
(plogis(-0.17283 + 0.0000471*x[15])*exp(9.53643)*(x[15])^0.468)+
(plogis(-0.17283 + 0.0000471*x[16])*exp(9.53643)*(x[16])^0.468)+
(plogis(-0.17283 + 0.0000471*x[17])*exp(9.53643)*(x[17])^0.468)+
(plogis(-0.17283 + 0.0000471*x[18])*exp(9.53643)*(x[18])^0.468)+
(plogis(-0.17283 + 0.0000471*x[19])*exp(9.53643)*(x[19])^0.468)+
(plogis(-0.17283 + 0.0000471*x[20])*exp(9.53643)*(x[20])^0.468)+
(plogis(-0.17283 + 0.0000471*x[21])*exp(9.53643)*(x[21])^0.468)+
(plogis(-0.17283 + 0.0000471*x[22])*exp(9.53643)*(x[22])^0.468)+
(plogis(-0.17283 + 0.0000471*x[23])*exp(9.53643)*(x[23])^0.468)+
(plogis(-0.17283 + 0.0000471*x[24])*exp(9.53643)*(x[24])^0.468)+
(plogis(-0.17283 + 0.0000471*x[25])*exp(9.53643)*(x[25])^0.468)+
(plogis(-0.17283 + 0.0000471*x[26])*exp(9.53643)*(x[26])^0.468)+
(plogis(-0.17283 + 0.0000471*x[27])*exp(9.53643)*(x[27])^0.468)+
(plogis(-0.17283 + 0.0000471*x[28])*exp(9.53643)*(x[28])^0.468)+
(plogis(-0.17283 + 0.0000471*x[29])*exp(9.53643)*(x[29])^0.468)+
(plogis(-0.17283 + 0.0000471*x[30])*exp(9.53643)*(x[30])^0.468)+
(plogis(-0.17283 + 0.0000471*x[31])*exp(9.53643)*(x[31])^0.468)+
(plogis(-0.17283 + 0.0000471*x[32])*exp(9.53643)*(x[32])^0.468)+
(plogis(-0.17283 + 0.0000471*x[33])*exp(9.53643)*(x[33])^0.468)+
(plogis(-0.17283 + 0.0000471*x[34])*exp(9.53643)*(x[34])^0.468)+
(plogis(-0.17283 + 0.0000471*x[35])*exp(9.53643)*(x[35])^0.468)+
(plogis(-0.17283 + 0.0000471*x[36])*exp(9.53643)*(x[36])^0.468)+
(plogis(-0.17283 + 0.0000471*x[37])*exp(9.53643)*(x[37])^0.468)+
(plogis(-0.17283 + 0.0000471*x[38])*exp(9.53643)*(x[38])^0.468)+
(plogis(0.11617 + 0.0000471*x[39])*exp(8.70643)*(x[39])^0.468)+
(plogis(0.11617 + 0.0000471*x[40])*exp(8.70643)*(x[40])^0.468)+
(plogis(0.11617 + 0.0000471*x[41])*exp(8.70643)*(x[41])^0.468)+
(plogis(0.11617 + 0.0000471*x[42])*exp(8.70643)*(x[42])^0.468)+
(plogis(0.11617 + 0.0000471*x[43])*exp(8.70643)*(x[43])^0.468)+
(plogis(0.11617 + 0.0000471*x[44])*exp(8.70643)*(x[44])^0.468)+
(plogis(0.11617 + 0.0000471*x[45])*exp(8.70643)*(x[45])^0.468)+
(plogis(0.11617 + 0.0000471*x[46])*exp(8.70643)*(x[46])^0.468)+
(plogis(0.11617 + 0.0000471*x[47])*exp(8.70643)*(x[47])^0.468)+
(plogis(0.11617 + 0.0000471*x[48])*exp(8.70643)*(x[48])^0.468)+
(plogis(0.11617 + 0.0000471*x[49])*exp(8.70643)*(x[49])^0.468)+
(plogis(0.11617 + 0.0000471*x[50])*exp(8.70643)*(x[50])^0.468)+
(plogis(0.11617 + 0.0000471*x[51])*exp(8.70643)*(x[51])^0.468)+
(plogis(0.11617 + 0.0000471*x[52])*exp(8.70643)*(x[52])^0.468)+
(plogis(0.11617 + 0.0000471*x[53])*exp(8.70643)*(x[53])^0.468)+
(plogis(0.11617 + 0.0000471*x[54])*exp(8.70643)*(x[54])^0.468)+
(plogis(0.11617 + 0.0000471*x[55])*exp(8.70643)*(x[55])^0.468)+
(plogis(0.11617 + 0.0000471*x[56])*exp(8.70643)*(x[56])^0.468)+
(plogis(0.11617 + 0.0000471*x[57])*exp(8.70643)*(x[57])^0.468)+
(plogis(0.11617 + 0.0000471*x[58])*exp(8.70643)*(x[58])^0.468)+
(plogis(0.11617 + 0.0000471*x[59])*exp(8.70643)*(x[59])^0.468)+
(plogis(0.11617 + 0.0000471*x[60])*exp(8.70643)*(x[60])^0.468)+
(plogis(0.11617 + 0.0000471*x[61])*exp(8.70643)*(x[61])^0.468)+
(plogis(0.11617 + 0.0000471*x[62])*exp(8.70643)*(x[62])^0.468)+
(plogis(0.11617 + 0.0000471*x[63])*exp(8.70643)*(x[63])^0.468)+
(plogis(0.11617 + 0.0000471*x[64])*exp(8.70643)*(x[64])^0.468)+
(plogis(0.11617 + 0.0000471*x[65])*exp(8.70643)*(x[65])^0.468)+
(plogis(0.11617 + 0.0000471*x[66])*exp(8.70643)*(x[66])^0.468)+
(plogis(0.11617 + 0.0000471*x[67])*exp(8.70643)*(x[67])^0.468)+
(plogis(0.11617 + 0.0000471*x[68])*exp(8.70643)*(x[68])^0.468)+
(plogis(0.11617 + 0.0000471*x[69])*exp(8.70643)*(x[69])^0.468)+
(plogis(0.11617 + 0.0000471*x[70])*exp(8.70643)*(x[70])^0.468)+
(plogis(0.11617 + 0.0000471*x[71])*exp(8.70643)*(x[71])^0.468)+
(plogis(0.11617 + 0.0000471*x[72])*exp(8.70643)*(x[72])^0.468)+
(plogis(0.90817 + 0.0000471*x[73])*exp(8.89943)*(x[73])^0.468)+
(plogis(0.90817 + 0.0000471*x[74])*exp(8.89943)*(x[74])^0.468)+
(plogis(0.90817 + 0.0000471*x[75])*exp(8.89943)*(x[75])^0.468)+
(plogis(0.90817 + 0.0000471*x[76])*exp(8.89943)*(x[76])^0.468)+
(plogis(0.90817 + 0.0000471*x[77])*exp(8.89943)*(x[77])^0.468)+
(plogis(0.90817 + 0.0000471*x[78])*exp(8.89943)*(x[78])^0.468)+
(plogis(0.90817 + 0.0000471*x[79])*exp(8.89943)*(x[79])^0.468)+
(plogis(0.90817 + 0.0000471*x[80])*exp(8.89943)*(x[80])^0.468)+
(plogis(0.90817 + 0.0000471*x[81])*exp(8.89943)*(x[81])^0.468)+
(plogis(0.90817 + 0.0000471*x[82])*exp(8.89943)*(x[82])^0.468)+
(plogis(0.90817 + 0.0000471*x[83])*exp(8.89943)*(x[83])^0.468)+
(plogis(0.90817 + 0.0000471*x[84])*exp(8.89943)*(x[84])^0.468)+
(plogis(0.90817 + 0.0000471*x[85])*exp(8.89943)*(x[85])^0.468)+
(plogis(0.90817 + 0.0000471*x[86])*exp(8.89943)*(x[86])^0.468)+
(plogis(0.90817 + 0.0000471*x[87])*exp(8.89943)*(x[87])^0.468)+
(plogis(0.90817 + 0.0000471*x[88])*exp(8.89943)*(x[88])^0.468)+
(plogis(0.90817 + 0.0000471*x[89])*exp(8.89943)*(x[89])^0.468)+
(plogis(0.90817 + 0.0000471*x[90])*exp(8.89943)*(x[90])^0.468)+
(plogis(0.90817 + 0.0000471*x[91])*exp(8.89943)*(x[91])^0.468)+
(plogis(0.90817 + 0.0000471*x[92])*exp(8.89943)*(x[92])^0.468)+
(plogis(0.90817 + 0.0000471*x[93])*exp(8.89943)*(x[93])^0.468)+
(plogis(0.90817 + 0.0000471*x[94])*exp(8.89943)*(x[94])^0.468)+
(plogis(0.90817 + 0.0000471*x[95])*exp(8.89943)*(x[95])^0.468)+
(plogis(0.90817 + 0.0000471*x[96])*exp(8.89943)*(x[96])^0.468)+
(plogis(0.90817 + 0.0000471*x[97])*exp(8.89943)*(x[97])^0.468)+
(plogis(0.90817 + 0.0000471*x[98])*exp(8.89943)*(x[98])^0.468)+
(plogis(0.90817 + 0.0000471*x[99])*exp(8.89943)*(x[99])^0.468)+
(plogis(0.90817 + 0.0000471*x[100])*exp(8.89943)*(x[100])^0.468)+
(plogis(0.90817 + 0.0000471*x[101])*exp(8.89943)*(x[101])^0.468)+
(plogis(0.90817 + 0.0000471*x[102])*exp(8.89943)*(x[102])^0.468)+
(plogis(0.90817 + 0.0000471*x[103])*exp(8.89943)*(x[103])^0.468)+
(plogis(0.90817 + 0.0000471*x[104])*exp(8.89943)*(x[104])^0.468)+
(plogis(0.90817 + 0.0000471*x[105])*exp(8.89943)*(x[105])^0.468)+
(plogis(0.90817 + 0.0000471*x[106])*exp(8.89943)*(x[106])^0.468)+
(plogis(0.90817 + 0.0000471*x[107])*exp(8.89943)*(x[107])^0.468)+
(plogis(0.90817 + 0.0000471*x[108])*exp(8.89943)*(x[108])^0.468)+
(plogis(0.90817 + 0.0000471*x[109])*exp(8.89943)*(x[109])^0.468)+
(plogis(0.90817 + 0.0000471*x[110])*exp(8.89943)*(x[110])^0.468)+
(plogis(-2.15083 + 0.0000471*x[111])*exp(9.87243)*(x[111])^0.468)+
(plogis(-2.15083 + 0.0000471*x[112])*exp(9.87243)*(x[112])^0.468)+
(plogis(-2.15083 + 0.0000471*x[113])*exp(9.87243)*(x[113])^0.468)+
(plogis(-2.15083 + 0.0000471*x[114])*exp(9.87243)*(x[114])^0.468)+
(plogis(-1.86183 + 0.0000471*x[115])*exp(9.04243)*(x[115])^0.468)+
(plogis(-1.86183 + 0.0000471*x[116])*exp(9.04243)*(x[116])^0.468)+
(plogis(-1.86183 + 0.0000471*x[117])*exp(9.04243)*(x[117])^0.468)+
(plogis(-1.86183 + 0.0000471*x[118])*exp(9.04243)*(x[118])^0.468)+
(plogis(-1.06983 + 0.0000471*x[119])*exp(9.23543)*(x[119])^0.468)+
(plogis(-1.06983 + 0.0000471*x[120])*exp(9.23543)*(x[120])^0.468)+
(plogis(-1.06983 + 0.0000471*x[121])*exp(9.23543)*(x[121])^0.468)+
(plogis(-1.06983 + 0.0000471*x[122])*exp(9.23543)*(x[122])^0.468)))
}
# Inequality constraint function
eval_g0_ineq <- function(x)
{
return(x[1]+x[2]+x[3]+x[4]+x[5]+x[6]+x[7]+x[8]+x[9]+x[10]+x[11]+x[12]+x[13]+x[14]+x[15]+x[16]+x[17]+x[18]+x[19]+x[20]+x[21]+x[22]+x[23]+x[24]+x[25]+x[26]+x[27]+x[28]+x[29]+x[30]+x[31]+x[32]+x[33]+x[34]+x[35]+x[36]+x[37]+x[38]+x[39]+x[40]+x[41]+x[42]+x[43]+x[44]+x[45]+x[46]+x[47]+x[48]+x[49]+x[50]+x[51]+x[52]+x[53]+x[54]+x[55]+x[56]+x[57]+x[58]+x[59]+x[60]+x[61]+x[62]+x[63]+x[64]+x[65]+x[66]+x[67]+x[68]+x[69]+x[70]+x[71]+x[72]+x[73]+x[74]+x[75]+x[76]+x[77]+x[78]+x[79]+x[80]+x[81]+x[82]+x[83]+x[84]+x[85]+x[86]+x[87]+x[88]+x[89]+x[90]+x[91]+x[92]+x[93]+x[94]+x[95]+x[96]+x[97]+x[98]+x[99]+x[100]+x[101]+x[102]+x[103]+x[104]+x[105]+x[106]+x[107]+x[108]+x[109]+x[110]+x[111]+x[112]+x[113]+x[114]+x[115]+x[116]+x[117]+x[118]+x[119]+x[120]+x[121]+x[122]-80000)
}
# Lower bounds
lb = c(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0)
# Upper bounds
ub = c(30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000,30000),

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At line:57 char:22
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+ ~~~~~~~~~~~~~~~~~~~~~~~~~~
+ CategoryInfo : InvalidArgument: (:) [], RuntimeException
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At line:3 char:1
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**********************
Windows PowerShell transcript start
Start time: 20180207113151
Username :
Machine : (Microsoft Windows NT 6.1.7601 Service Pack 1)
**********************
Transcript started, output file is OneSourceUsers-2018-02-07_11-31.txt Enumerating group membership. This may take some time...
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At E:\OneSource\get_OneSourceUsers.ps1:19 char:215
+ ... neSource\Output($strTimestamp + "_" + $group + ".csv") -NoType
+ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+ CategoryInfo : InvalidArgument: (:) [Export-Csv], ParameterBindingException
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At E:\OneSource\get_OneSourceUsers.ps1:19 char:215
+ ... neSource\Output($strTimestamp + "_" + $group + ".csv") -NoType
+ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+ CategoryInfo : InvalidArgument: (:) [Export-Csv], ParameterBindingException
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Error: "String must be exactly one character long."
At E:\OneSource\get_OneSourceUsers.ps1:19 char:215
+ ... neSource\Output($strTimestamp + "_" + $group + ".csv") -NoType
+ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+ CategoryInfo : InvalidArgument: (:) [Export-Csv], ParameterBindingException
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At E:\OneSource\get_OneSourceUsers.ps1:19 char:215
+ ... neSource\Output($strTimestamp + "_" + $group + ".csv") -NoType
+ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+ CategoryInfo : InvalidArgument: (:) [Export-Csv], ParameterBindingException
+ FullyQualifiedErrorId : CannotConvertArgumentNoMessage,Microsoft.PowerShell.Commands.ExportCsvCommand
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"String must be exactly one character long."
At E:\OneSource\get_OneSourceUsers.ps1:19 char:215
+ ... neSource\Output($strTimestamp + "_" + $group + ".csv") -NoType
+ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+ CategoryInfo : InvalidArgument: (:) [Export-Csv], ParameterBindingException
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At E:\OneSource\get_OneSourceUsers.ps1:19 char:215
+ ... neSource\Output($strTimestamp + "_" + $group + ".csv") -NoType
+ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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Error: "String must be exactly one character long."
At E:\OneSource\get_OneSourceUsers.ps1:19 char:215
+ ... neSource\Output($strTimestamp + "_" + $group + ".csv") -NoType
+ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+ CategoryInfo : InvalidArgument: (:) [Export-Csv], ParameterBindingException
+ FullyQualifiedErrorId : CannotConvertArgumentNoMessage,Microsoft.PowerShell.Commands.ExportCsvCommand
Execution Complete 2018-02-07T11:31:51
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Windows PowerShell transcript end
End time: 20180207113151
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When you run something like
... | Export-Csv \\server\share($strTimestamp + "_" + $group + ".csv") -NoType
PowerShell sees \\server\share as one argument, and ("something" + ".csv") as another argument (due to the grouping expression). The second positional parameter is passed to the parameter -Delimiter, which expects a single character. Hence the error you observed.
To create a path string from several variables just use a string with nested variables:
... | Export-Csv "\\server\share\${strTimestamp}_${group}.csv" -NoType

What does this Powershell command mean in English?

In Exchange Management Shell, you can write a query to display administrator activities.
Search-AdminAuditLog -Startdate ((get-date).AddDays(-5)) -EndDate (get-date) | where{$_.caller -ne "NT AUTHORITY\SYSTEM (MSExchangeHMWorker)"} |select Caller, Rundate, ObjectModified, CmdLetName, #{n="Parameters"; e={$e=$null;$_.CmdLetParameters|%{$e += ( " -" + $_.name.tostring() + " '" + $_.value + "'")};$e}} | ft -autosize
Most of the commands make sense but can anyone explain the #... part in English? Specifically this part:
#{n="Parameters"; e={$e=$null; $_.CmdLetParameters | %{$e += ( " -" + $_.name.tostring() + " '" + $_.value + "'")};$e}}

That's called a "Calculated property". It's a way to add a property in your selected object with the name specified by n= and having the value resulting from expression e=.
http://technet.microsoft.com/en-us/library/ff730948.aspx

Convert accountExpires to DateTime in powershell commandline (last step, help needed)

I have the following piece of code that works fine to output the user's displayname and the accountExpires attribute from AD. I am running them on commandline because of restricted mode at work:
$objSearch.findall() | %{" " + $_.properties.displayname + "| " + $_.properties.accountexpires}
Now I need to convert this output, specifically the accountExpires attribute to a humanly readable date.
After googling I figured that I can use something like the below to convert between the accountExpires and a datetime.
[datetime]::fromfiletime(129138320987173880)
But I am having issues combining the two. I tried the following:
$objSearch.findall() | %{" "+ $_.properties.displayname + " " + [datetime]::fromfiletime($_.properties.accountexpires)}
Cannot convert argument "0", with value: "System.DirectoryServices.ResultPropertyValueCollection", for "FromFileTime" to type "System.Int64": "Cannot convert the "System.DirectoryServices.ResultPropertyValueCollection" value of type "System.DirectoryServices.ResultPropertyValueCollection" to type "System.Int64"."
At line:1 char:96
+ $objSearch.findall() | %{" "+ $.properties.displayname + " " + [datetime]::fromfiletime <<<< ($.properties.accountexpires)}
+ CategoryInfo : NotSpecified: (:) [], MethodException
+ FullyQualifiedErrorId : MethodArgumentConversionInvalidCastArgument
$objSearch.findall() | %{" "+ $_.properties.displayname + " " + [datetime]::fromfiletime $_.properties.accountexpires}
Unexpected token '' in expression or statement.
At line:1 char:99
+ $objSearch.findall() | %{"This is "+ $.properties.displayname + " " + [datetime]::fromfiletime $_ <<<< .properties.accountexpires}
+ CategoryInfo : ParserError: (_:String) [], ParentContainsErrorRecordException
+ FullyQualifiedErrorId : UnexpectedToken
How can I convert the accountExpires to a humanly readable date?

You just miss that the underlying ADSI COM object presents properties as arrays here is a way to get the accountexpires property, just use $_.properties.accountexpires[0].
$search = [ADSISearcher]"OU=MonOu,DC=dom,DC=fr"
$search.Filter = "(cn=Jean Paul Blanc)"
$user = $search.FindOne()
$user | %{" "+ $_.properties.displayname + " " + [datetime]::fromfiletime($_.properties.accountexpires[0])}
This give for me :
Jean Paul Blanc 12/07/2012 00:00:00