[R] Optimization issue - Solution converges for any initial value

Paul Gilbert Fri, 30 Sep 2016 13:44:50 -0700

Narendra

You should check the definition of your objective function, somethingseems to be wrong. When you evaluate the objective function with yourinitial guess, and then with some different value, you should expect thereturned value will be different, but it is not:


> print(Koval.Error.func(vp.kval, n=1), digits=20)
[1] 2767.1357969742521163
> print(Koval.Error.func(2*vp.kval, n=1), digits=20)
[1] 2767.1357969742521163

So the objective function is flat. Optim converges with the message"CONVERGENCE: NORM OF PROJECTED GRADIENT <= PGTOL". Of course, thegradient is zero because the objective function is flat.

This would normally be considered a "user error" but perhaps John'snewer code can catch it?


Paul

Date: Thu, 29 Sep 2016 14:53:08 -0500
From: Narendra Modi <bjpmodi2...@gmail.com>
To: "r-help@r-project.org" <r-help@r-project.org>
Subject: [R] Optimization issue - Solution converges for any initial
        value
Message-ID:
        <CAPq=xqd983bacpvcyesfz-auxi1oyuykmdah1m36+zdu4kh...@mail.gmail.com>
Content-Type: text/plain; charset=UTF-8

I have put together a R snippet wherein I am trying to get optimum
values for which error is minimized. The error is the difference
between two matrices.
Every time I run the below code, I don't see any optimization
happening as in the final answer is the same as the initial estimate
regardless of what I mention as initial estimate.
Could you please advise on how can I improve it?
I have also tried using nloptr but to no avail.

To optimize vp.kval




my.data.matrix.prod <- matrix(a,nrow = length(a),1)
Estimated.Qt.mat <- matrix(b,nrow = nrow(my.data.matrix.prod), ncol = 1)
Cum.WInj.matrix <- matrix (c,nrow = nrow(my.data.matrix.prod), ncol = 1)
Koval.tD <- matrix(,nrow = nrow(my.data.matrix.prod), ncol = 1)  # tD Matrix
Koval.fw <- matrix(,nrow = nrow(my.data.matrix.prod), ncol = 1) # fw Matrix

Koval.Error.func <- function(vp.kval,n)
{
  #First convert vector(Koval.InitialData.list) to MATRIX and send it
to calculate estimated matrix

  Koval.InitialData.Matrix <- matrix(vp.kval,nrow = 2, 1,byrow = TRUE)
 # Define Koval Parameters Matrix for the "n"

  Qo.Koval <- Qo.Koval(Koval.InitialData.Matrix)  # Get Qo Estimation from Koval

  diff.values <- my.data.matrix.prod[,n] - Qo.Koval  #FIND DIFFERENCE
BETWEEN CAL. MATRIX AND ORIGINAL MATRIX

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

  Error   # return error value
}

Qo.Koval <- function(Koval.InitialData.Matrix)
{
  Qo.Koval.Est <- matrix(,nrow(my.data.matrix.prod), 1)
#ncol(my.data.matrix.prod)

  for(rowno in 1:nrow(my.data.matrix.prod)) #number of rows of data
  {
    Koval.tD[rowno,1] = Cum.WInj.matrix[rowno,1] *
Koval.InitialData.Matrix[1,1]   # Evaluate tD matrix

    if(Koval.tD[rowno,1] < (1/Koval.InitialData.Matrix[2,1]))
    {
      Koval.fw[rowno,1] = 0
    }
    else
    {
      if(Koval.tD[rowno,1] > Koval.InitialData.Matrix[2,1])
      {
        Koval.fw[rowno,1] = 1
      }else
      {
        Koval.fw[rowno,1] = (Koval.InitialData.Matrix[2,1] -
sqrt(Koval.InitialData.Matrix[2,1]/Koval.tD[rowno,1]))/(Koval.InitialData.Matrix[2,1]-1)
      }
    }

    Qo.Koval.Est[rowno,1] = Koval.fw[rowno,1] * Estimated.Qt.mat[rowno,1]
  }

  Qo.Koval.Est    # Return Estimated matrix
}

vp.kval <- c(100000,1)  #initial estimate
Koval.lb = c(0,0)
Koval.ub = c(Inf,Inf)
n <- 1
Koval.result <- optim(vp.kval,Koval.Error.func, method = "L-BFGS-B",
lower = Koval.lb,
                     upper = Koval.ub, n=n)
print(paste(Koval.result$convergence))
print(paste(Koval.result$par))


Here is the input data:

a:

structure(c(414, 40, 639, 616, 677, 598, 586, 494, 322, 351,
322, 213, 395, 358, 406, 384, 409, 404, 370, 376, 412, 404, 369,
391, 341, 350, 349, 313, 302, 196, 386, 330, 350, 323, 454, 465,
465, 399, 416, 396, 453, 388, 496, 379, 472, 491, 492, 503, 516,
454, 630, 547, 578, 312, 764, 672, 548, 611, 546, 552, 520, 486,
581, 559, 433, 262, 650, 615, 542, 571, 542, 529, 577, 469, 557,
540, 546, 519, 376, 605, 520, 435, 299, 531, 538, 475, 511, 487,
490, 494, 537, 482, 438, 498, 312, 476, 383, 382), .Dim = c(98L,
1L), .Dimnames = list(NULL, "Q2"))

b:

structure(c(2342.12883525675, 2595.06229039124, 2715.2774272809,
2742.14586849367, 2678.48814516156, 2769.17482063132, 2809.26904957691,
2647.26143288146, 2142.48588931211, 1986.26692938822, 2417.80180308667,
2539.99173834861, 2889.68696098066, 2949.03395956634, 3345.265659123,
3178.09552101488, 3202.97894028497, 3294.04615708455, 3273.96002181006,
3290.59294404149, 3074.57078080845, 2809.00966959208, 2870.20594457832,
2994.89960881099, 3031.51083818418, 2838.72778780229, 2779.83367818986,
2471.70302686638, 2277.52074079803, 2313.67080371772, 2415.57558854185,
2593.57170885689, 2579.65222779155, 2542.47630393453, 2610.16334633228,
2715.1622580481, 2680.04491562794, 2676.08878142995, 2890.5657368073,
2939.98447437336, 2932.41354171428, 2699.29100102243, 2748.9757584712,
2885.90115387751, 2841.03004973532, 3111.28842226602, 3293.09352655985,
3448.16679970445, 3470.58231818316, 3077.6191619663, 2892.81263635983,
2563.00601428125, 2410.40833201752, 2696.80369889632, 3250.95996536945,
3900.33363068933, 3571.89127039948, 3569.09158205254, 3718.94141619046,
3963.05018539626, 4317.67764180387, 4143.2306512351, 4482.33003541385,
4313.47162218783, 4162.58533919444, 4119.75974744111, 4080.01960112015,
4146.78116940934, 3848.98992961189, 3507.00912988581, 3336.3269842557,
3691.50683899193, 3616.0923981163, 3325.14304882807, 3471.79805853069,
3229.60965194249, 3106.05768279943, 3184.66721766981, 3140.79657087168,
3242.97205541341, 3090.78617601495, 3086.74973135927, 3317.74000570974,
3594.90929884806, 3716.02759860505, 3622.91307702134, 3793.8518218782,
3666.82966979173, 3779.4557494045, 3750.98605852729, 3333.45681985961,
3057.22984206785, 3395.04273620089, 3623.47886822009, 3690.34495906538,
3827.97665203175, 3933.61679986677, 3762.82354740958), .Dim = c(98L,
1L))

c:

structure(c(2854.17262019504, 91576.5893971961, 171680.262910889,
257565.867448752, 335812.78671975, 424624.296030534, 510229.898689908,
586994.432148103, 636896.230541501, 691311.784820203, 780382.614051205,
860628.109248455, 961649.745761829, 1055011.51571743, 1162113.22730208,
1255164.70993334, 1352077.97513698, 1457172.94644257, 1554726.68952114,
1657279.26732716, 1745523.14071769, 1821000.62788843, 1911979.2340704,
2005954.86455037, 2101129.54803795, 2182822.62676551, 2258661.15941603,
2325202.52364728, 2387098.71588595, 2460005.26984465, 2535846.63352407,
2622071.03988945, 2701584.84087477, 2776628.22472118, 2859757.87551639,
2944689.28669068, 3026621.7086177, 3109451.02390273, 3200463.68736646,
3293220.09008416, 3380941.82063061, 3456992.53009029, 3541106.87910663,
3635049.74483035, 3721653.58199201, 3823940.56521733, 3931974.7704047,
4040554.293988, 4148875.73758196, 4231424.94909108, 4306157.82023537,
4374820.38189491, 4442080.07977206, 4535051.28823047, 4650928.35668784,
4793084.92990124, 4893067.57046614, 5000047.61946087, 5120237.59556207,
5247211.61097682, 5392662.33159569, 5515394.91894634, 5652397.35652795,
5780590.26125026, 5900471.93425283, 6026783.31719041, 6147868.09782702,
6278602.62144284, 6388178.16489299, 6482065.35854026, 6579907.11054506,
6702412.42037957, 6812043.87236422, 6905604.01572694, 7007786.71329603,
7099980.68361161, 7189071.57372477, 7290368.20702837, 7383139.53472758,
7487014.64958016, 7577849.79802546, 7670318.64215094, 7780726.13033402,
7897750.56237753, 8016910.17077053, 8126173.95193153, 8241923.12215802,
8351438.92663496, 8468551.68021943, 8583900.77567578, 8670079.97000769,
8755816.49103472, 8872115.39013376, 8988383.34061776, 9104971.76148562,
9224368.08502439, 9349766.5439318, 9460826.05419725), .Dim = c(98L,
1L))


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[R] Optimization issue - Solution converges for any initial value

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