# constraining parameters during optimization
**URL:** https://discourse.itk.org/t/constraining-parameters-during-optimization/2848
**Category:** Beginner Questions
**Created:** [March 18, 2020, 3:03pm UTC](https://discourse.itk.org/t/constraining-parameters-during-optimization/2848 "2020-03-18T15:03:55Z")
**Posts on this page:** 8
**Page:** 1
### Author:  [@reox](https://discourse.itk.org/u/reox)
#### Post date: [March 18, 2020, 3:03pm UTC](https://discourse.itk.org/t/constraining-parameters-during-optimization/2848/1 "2020-03-18T15:03:55Z")
For example, I’m using the Similarity2DTransform. Here, I would like to enforce that the scale must be non-zero and positive, however I would like to allow for negative translation.
Is it correct, that the only optimizer which can handle constraints is the LBFGSBOptimizer?
But, it looks like that I can only constraint all parameters with the same bounds - is this correct?
So I tried something like this:
```
R = sitk.ImageRegistrationMethod()
R.SetInitialTransform(sitk.Similarity2DTransform())
R.SetOptimizerAsLBFGSB(lowerBound=0.1, upperBound=10)
```
But in that case all four parameters of the Similarity2DTransform are constraint. From the C++ documentation of ITK, it looks like that you could pass an array to the LBFGSB Optimizer, and this is not implemented in SimpleITK right now? Or is there some other method I’m not aware of?
Thanks in advance!
---
### Author:  [@dzenanz](https://discourse.itk.org/u/dzenanz)
#### Post date: [March 18, 2020, 5:02pm UTC](https://discourse.itk.org/t/constraining-parameters-during-optimization/2848/2 "2020-03-18T17:02:49Z")
> [@reox](#):
>
> scale must be non-zero and positive
Are you running into a case which violates this? Because this might already be implemented.
---
### Author:  [@reox](https://discourse.itk.org/u/reox)
#### Post date: [March 18, 2020, 5:33pm UTC](https://discourse.itk.org/t/constraining-parameters-during-optimization/2848/3 "2020-03-18T17:33:42Z")
Yes, I have a case were the scale is set to -0.7, which flips the image around.
```
>>> sitk.Version_VersionString()
'1.2.4'
>>> sitk.Version_ITKVersionString()
'4.13'
```
But in any case, is it possible to constraint certain parameters? Or can I only constraint all with one integer?
---
### Author:  [@blowekamp](https://discourse.itk.org/u/blowekamp)
#### Post date: [March 18, 2020, 5:42pm UTC](https://discourse.itk.org/t/constraining-parameters-during-optimization/2848/4 "2020-03-18T17:42:44Z")
The SimpleITK interface for the LBFGSB Optimizer is designed to work with the uniform parameter spaces such as the b-spline transform.
With C++, in the past I have tried to use the LBFGS(B) optimizers on non-uniform parameter spaces with mix rotation, scale and translation without success.
---
### Author:  [@reox](https://discourse.itk.org/u/reox)
#### Post date: [March 18, 2020, 6:34pm UTC](https://discourse.itk.org/t/constraining-parameters-during-optimization/2848/5 "2020-03-18T18:34:41Z")
Ah okay, good to know.
Yes, for b-splines it seems quite good.
---
### Author:  [@reox](https://discourse.itk.org/u/reox)
#### Post date: [March 19, 2020, 11:59am UTC](https://discourse.itk.org/t/constraining-parameters-during-optimization/2848/6 "2020-03-19T11:59:21Z")
I tested now with SimpleITK 2.0r1 and I get the same thing - the scale gets negative and the image flips around.
However, I can prevent it by setting the lineSearchUpperLimit to something like 2.0 instead of 5.0 in the ConjugateGradientLineSearch.
---
### Author:  [@blowekamp](https://discourse.itk.org/u/blowekamp)
#### Post date: [March 19, 2020, 12:06pm UTC](https://discourse.itk.org/t/constraining-parameters-during-optimization/2848/7 "2020-03-19T12:06:11Z")
As I recall going from ITK 4 to ITK 5 there should be a nice performance improvement with the line search optimizers.
I recently has a similar problem which required reducing the lineSearchUpperLimit. I should have also tried setting the `estimateLearningRate` parameter to `EachIteration`. If if have time please share the results.
---
### Author:  [@reox](https://discourse.itk.org/u/reox)
#### Post date: [March 19, 2020, 12:55pm UTC](https://discourse.itk.org/t/constraining-parameters-during-optimization/2848/8 "2020-03-19T12:55:07Z")
Just setting it to EachIteration does not work. For me the upperLimit must be less than 4.8 to work…
This is my iteration output with EachIteration and upperLimit=default:
```
0 = 63225.35480: (0.9417236641686194, -0.002710882030060366, 0.8318583144239113, 0.4403867697114576)
1 = 24769.04467: (0.8193635679960766, -0.00806438148396374, 1.4708275792215932, 0.9126646303280062)
2 = 1767.91351: (-0.7590296165364513, -0.0729438940676933, 5.470181184104698, 6.600428933823899)
3 = 13756.57000: (-0.7659270933004365, -0.0731529783270789, 5.452503302655331, 6.608979898210135)
4 = 13736.14770: (-0.768255924423802, -0.07284864593329286, 5.26900889478838, 6.514027014632924)
5 = 13441.74994: (-0.7684237804039744, -0.07101113472142932, 4.441187056947582, 6.013047016875679)
6 = 12250.67285: (-0.7771872535221632, -0.06321687611669763, 1.8315534893073226, 3.985288601825094)
7 = 10609.89473: (-0.8121235582069708, -0.04965874076607467, 2.23606855339464, 0.9635690675693827)
8 = 9056.59000: (-0.8125653109713288, -0.04284474209336353, 2.99296637371436, 1.1378312713558225)
9 = 8879.27372: (-0.8136129653985188, -0.022699197350708775, 3.1357057410231066, 1.612590588916469)
10 = 8773.04976: (-0.8135741278665546, -0.010558835438296896, 2.8956102643952506, 1.6573513625957272)
11 = 8735.90026: (-0.811643162579073, -0.009135066951720481, 2.7770013051208857, 1.138088712794068)
12 = 8694.28999: (-0.812168851724825, -0.008694164360242599, 2.812388135976882, 1.118838263678742)
13 = 8693.64139: (-0.8124058125952398, -0.008334040773027964, 2.81696398489521, 1.1103428072832422)
14 = 8693.55494: (-0.8123499948450742, -0.0076758323348522966, 2.7855202798384577, 1.1094840570836944)
15 = 8693.23957: (-0.8119820121293603, -0.006968355987709816, 2.779354293222849, 1.1091571368946627)
16 = 8693.07748: (-0.8118681080825537, -0.00670457643779322, 2.7929565747861345, 1.1069767734546279)
17 = 8693.00478: (-0.8120219163519984, -0.0067023357717718385, 2.796942887223431, 1.1059202723531565)
18 = 8692.98036: (-0.8120314496176448, -0.006702709889591167, 2.797055148813363, 1.105881984756556)
19 = 8692.98026: (-0.8120267059637083, -0.006704935770477283, 2.796420117201529, 1.106019114958926)
20 = 8692.98008: (-0.8120260062327926, -0.006705173062985829, 2.7963733472433963, 1.106030409581191)
21 = 8692.98005: (-0.8120236434686153, -0.0067059900652930785, 2.796218697008211, 1.1060680706710344)
SIMILARITY finished after 22 metric 1767.913507049963 param (-0.7590296165364513, -0.0729438940676933, 5.470181184104698, 6.600428933823899)
```
Using EachIteration and upperLimit=4.8:
```
0 = 63225.35480: (0.9440497130545455, -0.002602679548968489, 0.7986554186359417, 0.42280911764308055)
1 = 25850.19966: (0.8206294588975955, -0.008022046595299665, 1.514568822644362, 0.9199073072495313)
2 = 1814.59713: (0.8187457259455184, -0.008099258407641155, 1.5197085229633467, 0.9269372766024895)
3 = 1811.08426: (0.818653795478708, -0.008076694980941069, 1.492367347124886, 0.9246892483926054)
4 = 1785.67003: (0.8185732377151316, -0.007955043505412658, 1.363403933217665, 0.9125857590736595)
5 = 1672.19161: (0.8181608274396125, -0.00738645060923019, 0.7981358788324328, 0.8533063442635993)
6 = 1281.99700: (0.8163800232208098, -0.005900265984633511, -0.20465544868203256, 0.666351040391283)
7 = 1006.89600: (0.8103944606886667, -0.003366207607840059, -0.20516253289142863, 0.336790773308636)
8 = 962.20778: (0.8100575564958342, 0.004954745462649816, -0.42594213936184366, 0.18496877660497926)
9 = 938.80399: (0.8098298647815174, 0.005849897334587465, -0.24354708038403497, 0.17819897896596495)
10 = 928.99950: (0.8113208593766895, 0.008969101509811141, -0.23320375350858244, 0.19634801636209162)
11 = 924.32931: (0.8116036904031729, 0.01093351824316089, -0.22643254122091977, 0.18103902497958455)
12 = 923.56114: (0.8099247706128822, 0.012822934766515613, -0.21575698032430035, 0.08663447156407175)
13 = 920.32931: (0.8094925838062388, 0.013393909218753258, -0.23243313373910182, 0.05882734414525096)
14 = 920.11439: (0.8097127884418852, 0.013440776205586433, -0.25893936479197244, 0.06346169879332969)
15 = 919.80532: (0.8097553217003186, 0.013456662073142521, -0.260020528847502, 0.06393092465554676)
16 = 919.80259: (0.8097845307160055, 0.013471196967725894, -0.2600766540332024, 0.06422811307493391)
17 = 919.80174: (0.8098022562670975, 0.013481817719600438, -0.2598698801030021, 0.06440154705876333)
18 = 919.80142: (0.8098025038945809, 0.013494394778774836, -0.25849005039563466, 0.06436680385329568)
19 = 919.79789: (0.8097703555151784, 0.013523894965600402, -0.25846175362705154, 0.06394991474796959)
20 = 919.79591: (0.8097710511099022, 0.013524156837837531, -0.258497151628061, 0.06393588908119192)
21 = 919.79591: (0.8097720811681713, 0.013524558875546072, -0.25854793660592784, 0.06391445860762386)
22 = 919.79593: (0.8097732312458021, 0.01352503444526458, -0.2586017317688072, 0.06388934265827186)
SIMILARITY finished after 23 metric 919.7959106749754 param (0.8097710511099022, 0.013524156837837531, -0.258497151628061, 0.06393588908119192)
```
Subjectively, it feels faster now actually - but for proper results I would had to record the timing as well 😃