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

Tue, 17 Jun 2008 13:06:09 -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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