Re: [R] constrOptim with method = "L-BFGS-B"

From: Spencer Graves <spencer.graves_at_pdf.com>
Date: Tue, 17 Jun 2008 12:34:27 -0700

I believe that 'optim' will not accept equality constraints.

However, you do not need the generality of 'optim' to "minimize a quadratic function with boundary conditions and one equality condition". This type of problem is called "quadratic programming", and RSiteSearch("quadratic programming", "fun") just returned 29 hits for me. The first 3 cite functions in the "LowRankQP", "kernlab", and "quadprog" packages. I don't know if any of these will solve your problem, but I suspect that at least one might. If not, can you recast the problem to remove the equality constraint?

If the above does not work for you, I suggest you try a much simpler version, e.g., with 'mat' = a 3 x 3 array with one inequality and one equality, as suggested in the famous book by Polya on "How to Solve It" (http://en.wikipedia.org/wiki/How_to_Solve_It). This has the added advantage of giving you a simpler example to send to this list if you can't make it work. You are to be commended for providing a self-contained example. Unfortunately, your example is so large that it is slightly intimidating. A simpler example might elicit more (and more useful) replies -- if it doesn't lead you to the solution, as Polya suggested that it might.

```      Hope this helps,
Spencer

```

lhaba wrote:
> Hi,
> i need to minimize a quadratic function with boundary condidtions and one
> equality condition.
> In order to do that i converted the equality constraint into 2 inequality
> constaints and passed everything cia constrOptim, as the manual said:
> everything included in the ... will be passed to Optim that will pass it
> back to fn in case it does not need it.
>
> My code is the following:
>
> mat <- array( c(0.0001088799073581, 0.0000136029502036, 0.0000060430384243,
> 0.0000847097879033, 0.0000115053365822, 0.0000216245975292,
> 0.0000483253391811, 0.0000787580901352, 0.0000186474817658,
> 0.0000312260571354, 0.0000217594093734, 0.0000536298150897,
> 0.0000166202592455, 0.0000451975061637, -0.0000120364862228,
> 0.0000497117714376,
> 0.0000136029502036, 0.0001537319301276, 0.0000226518408080,
> 0.0000591480002102, 0.0000797128619950, 0.0000091332643423,
> 0.0000693354260457, 0.0000825217915015, 0.0000229122227269,
> 0.0000297662414650, 0.0000334443258658, 0.0000273254534933,
> 0.0000202062301763, 0.0000026260702295, 0.0000558975248740,
> 0.0000953647537111,
> 0.0000060430384243, 0.0000226518408080, 0.0005971325756834,
> -0.0000762583321100, -0.0000246005202071, -0.0000300982253054,
> 0.0000299178429478, 0.0000135672602503, 0.0001735431064391,
> -0.0000133347388414, 0.0001387582890571, 0.0000964898243724,
> -0.0000149571346672, 0.0000104437939143, 0.0001246900353191,
> -0.0000171884354549,
> 0.0000847097879033, 0.0000591480002102, -0.0000762583321100,
> 0.0004968467836203, 0.0002303499425964, 0.0000992731601466,
> 0.0002685466918035, 0.0002580180069951, 0.0000725833959653,
> 0.0000525639940758, 0.0001785049461665, 0.0001781339191317,
> 0.0000597631329497, 0.0000201160486244, 0.0002582267884874,
> 0.0002473268250781,
> 0.0000115053365822, 0.0000797128619950, -0.0000246005202071,
> 0.0002303499425964, 0.0002945009393242, -0.0000426583313588,
> 0.0002067711081561, 0.0002695894499975, 0.0001312519434236,
> -0.0000079156628396, 0.0001423655606105, 0.0000044733483182,
> 0.0000303832556655, 0.0000577624190434, 0.0001193435284164,
> 0.0002422477575812,
> 0.0000216245975292, 0.0000091332643423, -0.0000300982253054,
> 0.0000992731601466, -0.0000426583313588, 0.0001641146317929,
> 0.0000311621614693, -0.0000147821020927, -0.0000767394607354,
> 0.0000619936562782, -0.0000306228761064, 0.0001495752154579,
> 0.0000389317919640, -0.0000714551280935, -0.0000564616194935,
> 0.0000384367900903,
> 0.0000483253391811, 0.0000693354260457, 0.0000299178429478,
> 0.0002685466918035, 0.0002067711081561, 0.0000311621614693,
> 0.0003176493360736, 0.0002575792630182, 0.0001371966488704,
> 0.0000436833885846, 0.0001442516276721, 0.0001075447728937,
> 0.0000371155448252, 0.0000475873370276, 0.0002162409964174,
> 0.0002870514043081,
> 0.0000787580901352, 0.0000825217915015, 0.0000135672602503,
> 0.0002580180069951, 0.0002695894499975, -0.0000147821020927,
> 0.0002575792630182, 0.0006217963583393, 0.0002368375072233,
> 0.0000078625467985, 0.0002054774387807, -0.0000066572248626,
> 0.0000485854317294, 0.0002802199677114, 0.0001676465030622,
> 0.0003028775764026,
> 0.0000186474817658, 0.0000229122227269, 0.0001735431064391,
> 0.0000725833959653, 0.0001312519434236, -0.0000767394607354,
> 0.0001371966488704, 0.0002368375072233, 0.0004475645060339,
> -0.0000030389778729, 0.0001706183643212, -0.0000017789896670,
> 0.0000722657436668, 0.0001664088523103, 0.0001220193496918,
> 0.0001641280878243,
> 0.0000312260571354, 0.0000297662414650, -0.0000133347388414,
> 0.0000525639940758, -0.0000079156628396, 0.0000619936562782,
> 0.0000436833885846, 0.0000078625467985, -0.0000030389778729,
> 0.0000822356406019, -0.0000226786278360, 0.0000752056105897,
> 0.0000399801889185, -0.0000441549693477, 0.0000047887593401,
> 0.0000352165734549,
> 0.0000217594093734, 0.0000334443258658, 0.0001387582890571,
> 0.0001785049461665, 0.0001423655606105, -0.0000306228761064,
> 0.0001442516276721, 0.0002054774387807, 0.0001706183643212,
> -0.0000226786278360, 0.0004304869804941, 0.0001566983136020,
> 0.0000332770114864, 0.0000012432094922, 0.0002491186667930,
> 0.0001285479414542,
> 0.0000536298150897, 0.0000273254534933, 0.0000964898243724,
> 0.0001781339191317, 0.0000044733483182, 0.0001495752154579,
> 0.0001075447728937, -0.0000066572248626, -0.0000017789896670,
> 0.0000752056105897, 0.0001566983136020, 0.0005292416268831,
> 0.0000893358436932, -0.0001009559617338, 0.0000888461032129,
> 0.0000714719761291,
> 0.0000166202592455, 0.0000202062301763, -0.0000149571346672,
> 0.0000597631329497, 0.0000303832556655, 0.0000389317919640,
> 0.0000371155448252, 0.0000485854317294, 0.0000722657436668,
> 0.0000399801889185, 0.0000332770114864, 0.0000893358436932,
> 0.0001844874143317, 0.0000549019705905, -0.0000117658984941,
> 0.0000394986211508,
> 0.0000451975061637, 0.0000026260702295, 0.0000104437939143,
> 0.0000201160486244, 0.0000577624190434, -0.0000714551280935,
> 0.0000475873370276, 0.0002802199677114, 0.0001664088523103,
> -0.0000441549693477, 0.0000012432094922, -0.0001009559617338,
> 0.0000549019705905, 0.0006686123611712, -0.0001115788528761,
> 0.0000151312169512,
> -0.0000120364862228, 0.0000558975248740, 0.0001246900353191,
> 0.0002582267884874, 0.0001193435284164, -0.0000564616194935,
> 0.0002162409964174, 0.0001676465030622, 0.0001220193496918,
> 0.0000047887593401, 0.0002491186667930, 0.0000888461032129,
> -0.0000117658984941, -0.0001115788528761, 0.0014937840813054,
> 0.0001299625832782,
> 0.0000497117714376, 0.0000953647537111, -0.0000171884354549,
> 0.0002473268250781, 0.0002422477575812, 0.0000384367900903,
> 0.0002870514043081, 0.0003028775764026, 0.0001641280878243,
> 0.0000352165734549, 0.0001285479414542, 0.0000714719761291,
> 0.0000394986211508, 0.0000151312169512, 0.0001299625832782,
> 0.0004355778955394), c(16,16))
>
> covar <- function(x) return (t(x) %*%mat %*% (x))
> covargr <- function(x) return ( 2*mat %*% (x))
>
> upper1 = c(1, 0, 0, 0, 0, 0, 0,0 ,0 , 0, 0, 0, 0, 0, 0, 0)
> lower1 = c(1, -0.25, -0.25, -0.25, -0.25, -0.25, -0.25, -0.25, -0.25, -0.25,
> -0.25, -0.25, -0.25, -0.25, -0.25, -0.25)
> lower[1] = 1
> init = upper1- 1/15.0
> init[1] = 1
>
> optim( init, covar, covargr, method = "L-BFGS-B", lower = lower1, upper =
> upper1)
> u1 <- c(0, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 0,
> -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1)
> u2<- array(u1, c(16, 2))
> u2[,2] <- -u2[,2]
>
> u1<- t(u1)
> c1<- array(c(-1, -1),c(2,1))
> constrOptim (init, covar, covargr, t(u2), c1, mu = 1e-054, method =
> "L-BFGS-B", lower = lower1, upper = upper1, outer.iterations = 100,
> outer.eps = 1e-05)
>
>
> The problem I face is an error message telling me that the method "L-BFGS-B"
> needs finite values of fn...
> while everything works well in the optim case without the inequalities.
>
> Does anybody have any clue about what might have gone wrong?
>
> THank you for your help
>
>
> Georges
>
>

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