MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
Home // Instances // Documentation // Download // Statistics
Instance kriging_peaks-full030
Gaussian process regression for the peaks functions using 30 datapoints. This is the full-space formulation where intermediate variables are defined by additional constraints.
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | -1.58660398 (ANTIGONE) -1.58674659 (BARON) -1.58658792 (LINDO) -1.58659973 (SCIP) |
| Referencesⓘ | Schweidtmann, Artur M., Bongartz, Dominik, Grothe, Daniel, Kerkenhoff, Tim, Lin, Xiaopeng, Najman, Jaromil, and Mitsos, Alexander, Deterministic global optimization with Gaussian processes embedded, Mathematical Programming Computation, 13:3, 2021, 553-581. |
| Applicationⓘ | Kriging |
| Added to libraryⓘ | 11 Dec 2020 |
| Problem typeⓘ | NLP |
| #Variablesⓘ | 66 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 32 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 1 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 64 |
| #Linear Constraintsⓘ | 4 |
| #Quadratic Constraintsⓘ | 30 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 30 |
| Operands in Gen. Nonlin. Functionsⓘ | exp mul sqrt |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 187 |
| #Nonlinear Nonzeros in Jacobianⓘ | 90 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 32 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 32 |
| #Blocks in Hessian of Lagrangianⓘ | 32 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 1 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 1 |
| Average blocksize in Hessian of Lagrangianⓘ | 1.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 9.2316e-03 |
| Maximal coefficientⓘ | 3.2718e+01 |
| Infeasibility of initial pointⓘ | 53.64 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 65 65 0 0 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 67 67 0 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 189 99 90 0
*
* Solve m using NLP minimizing objvar;
Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19
,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36
,x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51,x52,x53
,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65,x66,objvar;
Positive Variables x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,x20
,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36,x37
,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51,x52,x53,x54
,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64;
Equations e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18,e19
,e20,e21,e22,e23,e24,e25,e26,e27,e28,e29,e30,e31,e32,e33,e34,e35,e36
,e37,e38,e39,e40,e41,e42,e43,e44,e45,e46,e47,e48,e49,e50,e51,e52,e53
,e54,e55,e56,e57,e58,e59,e60,e61,e62,e63,e64,e65;
e1.. - x66 + objvar =E= 0;
e2.. 0.166666666666667*x1 - x3 =E= -0.5;
e3.. 0.166666666666667*x2 - x4 =E= -0.5;
e4.. 28.8031207707063*sqr(0.111229942702413 - x3) + 32.7180515537385*sqr(
0.59541072256986 - x4) - x5 =E= 0;
e5.. 0.267663478098588*(1 + 2.23606797749979*sqrt(x5) + 1.66666666666667*x5)*
exp(-2.23606797749979*sqrt(x5)) - x6 =E= 0;
e6.. 28.8031207707063*sqr(0.863858827199432 - x3) + 32.7180515537385*sqr(
0.683898783136516 - x4) - x7 =E= 0;
e7.. 0.267663478098588*(1 + 2.23606797749979*sqrt(x7) + 1.66666666666667*x7)*
exp(-2.23606797749979*sqrt(x7)) - x8 =E= 0;
e8.. 28.8031207707063*sqr(0.0951907195096362 - x3) + 32.7180515537385*sqr(
0.987881605457913 - x4) - x9 =E= 0;
e9.. 0.267663478098588*(1 + 2.23606797749979*sqrt(x9) + 1.66666666666667*x9)*
exp(-2.23606797749979*sqrt(x9)) - x10 =E= 0;
e10.. 28.8031207707063*sqr(0.730646280982898 - x3) + 32.7180515537385*sqr(
0.241742586444198 - x4) - x11 =E= 0;
e11.. 0.267663478098588*(1 + 2.23606797749979*sqrt(x11) + 1.66666666666667*x11)
*exp(-2.23606797749979*sqrt(x11)) - x12 =E= 0;
e12.. 28.8031207707063*sqr(0.320238787378679 - x3) + 32.7180515537385*sqr(
0.218296935351353 - x4) - x13 =E= 0;
e13.. 0.267663478098588*(1 + 2.23606797749979*sqrt(x13) + 1.66666666666667*x13)
*exp(-2.23606797749979*sqrt(x13)) - x14 =E= 0;
e14.. 28.8031207707063*sqr(0.87059458573363 - x3) + 32.7180515537385*sqr(
0.801085894330831 - x4) - x15 =E= 0;
e15.. 0.267663478098588*(1 + 2.23606797749979*sqrt(x15) + 1.66666666666667*x15)
*exp(-2.23606797749979*sqrt(x15)) - x16 =E= 0;
e16.. 28.8031207707063*sqr(0.0415641459792807 - x3) + 32.7180515537385*sqr(
0.659793606686887 - x4) - x17 =E= 0;
e17.. 0.267663478098588*(1 + 2.23606797749979*sqrt(x17) + 1.66666666666667*x17)
*exp(-2.23606797749979*sqrt(x17)) - x18 =E= 0;
e18.. 28.8031207707063*sqr(0.801433475166551 - x3) + 32.7180515537385*sqr(
0.402392282692781 - x4) - x19 =E= 0;
e19.. 0.267663478098588*(1 + 2.23606797749979*sqrt(x19) + 1.66666666666667*x19)
*exp(-2.23606797749979*sqrt(x19)) - x20 =E= 0;
e20.. 28.8031207707063*sqr(0.419134454621807 - x3) + 32.7180515537385*sqr(
0.520974338874469 - x4) - x21 =E= 0;
e21.. 0.267663478098588*(1 + 2.23606797749979*sqrt(x21) + 1.66666666666667*x21)
*exp(-2.23606797749979*sqrt(x21)) - x22 =E= 0;
e22.. 28.8031207707063*sqr(0.917201570287689 - x3) + 32.7180515537385*sqr(
0.84457790520867 - x4) - x23 =E= 0;
e23.. 0.267663478098588*(1 + 2.23606797749979*sqrt(x23) + 1.66666666666667*x23)
*exp(-2.23606797749979*sqrt(x23)) - x24 =E= 0;
e24.. 28.8031207707063*sqr(0.452550488432341 - x3) + 32.7180515537385*sqr(
0.465470910341813 - x4) - x25 =E= 0;
e25.. 0.267663478098588*(1 + 2.23606797749979*sqrt(x25) + 1.66666666666667*x25)
*exp(-2.23606797749979*sqrt(x25)) - x26 =E= 0;
e26.. 28.8031207707063*sqr(0.381086148033683 - x3) + 32.7180515537385*sqr(
0.0284410867012327 - x4) - x27 =E= 0;
e27.. 0.267663478098588*(1 + 2.23606797749979*sqrt(x27) + 1.66666666666667*x27)
*exp(-2.23606797749979*sqrt(x27)) - x28 =E= 0;
e28.. 28.8031207707063*sqr(0.664445710060874 - x3) + 32.7180515537385*sqr(
0.715687166073911 - x4) - x29 =E= 0;
e29.. 0.267663478098588*(1 + 2.23606797749979*sqrt(x29) + 1.66666666666667*x29)
*exp(-2.23606797749979*sqrt(x29)) - x30 =E= 0;
e30.. 28.8031207707063*sqr(0.35783709395474 - x3) + 32.7180515537385*sqr(
0.557803528332154 - x4) - x31 =E= 0;
e31.. 0.267663478098588*(1 + 2.23606797749979*sqrt(x31) + 1.66666666666667*x31)
*exp(-2.23606797749979*sqrt(x31)) - x32 =E= 0;
e32.. 28.8031207707063*sqr(0.290737438310084 - x3) + 32.7180515537385*sqr(
0.784795849934872 - x4) - x33 =E= 0;
e33.. 0.267663478098588*(1 + 2.23606797749979*sqrt(x33) + 1.66666666666667*x33)
*exp(-2.23606797749979*sqrt(x33)) - x34 =E= 0;
e34.. 28.8031207707063*sqr(0.184545159482649 - x3) + 32.7180515537385*sqr(
0.071764872448536 - x4) - x35 =E= 0;
e35.. 0.267663478098588*(1 + 2.23606797749979*sqrt(x35) + 1.66666666666667*x35)
*exp(-2.23606797749979*sqrt(x35)) - x36 =E= 0;
e36.. 28.8031207707063*sqr(0.52271755235026 - x3) + 32.7180515537385*sqr(
0.337358966433907 - x4) - x37 =E= 0;
e37.. 0.267663478098588*(1 + 2.23606797749979*sqrt(x37) + 1.66666666666667*x37)
*exp(-2.23606797749979*sqrt(x37)) - x38 =E= 0;
e38.. 28.8031207707063*sqr(0.245628297893699 - x3) + 32.7180515537385*sqr(
0.10677814322697 - x4) - x39 =E= 0;
e39.. 0.267663478098588*(1 + 2.23606797749979*sqrt(x39) + 1.66666666666667*x39)
*exp(-2.23606797749979*sqrt(x39)) - x40 =E= 0;
e40.. 28.8031207707063*sqr(0.948138629452501 - x3) + 32.7180515537385*sqr(
0.382163884479295 - x4) - x41 =E= 0;
e41.. 0.267663478098588*(1 + 2.23606797749979*sqrt(x41) + 1.66666666666667*x41)
*exp(-2.23606797749979*sqrt(x41)) - x42 =E= 0;
e42.. 28.8031207707063*sqr(0.556510835307559 - x3) + 32.7180515537385*sqr(
0.272182954878091 - x4) - x43 =E= 0;
e43.. 0.267663478098588*(1 + 2.23606797749979*sqrt(x43) + 1.66666666666667*x43)
*exp(-2.23606797749979*sqrt(x43)) - x44 =E= 0;
e44.. 28.8031207707063*sqr(0.022380181406173 - x3) + 32.7180515537385*sqr(
0.610730424339593 - x4) - x45 =E= 0;
e45.. 0.267663478098588*(1 + 2.23606797749979*sqrt(x45) + 1.66666666666667*x45)
*exp(-2.23606797749979*sqrt(x45)) - x46 =E= 0;
e46.. 28.8031207707063*sqr(0.497905175502968 - x3) + 32.7180515537385*sqr(
0.0602044467956143 - x4) - x47 =E= 0;
e47.. 0.267663478098588*(1 + 2.23606797749979*sqrt(x47) + 1.66666666666667*x47)
*exp(-2.23606797749979*sqrt(x47)) - x48 =E= 0;
e48.. 28.8031207707063*sqr(0.792485426296966 - x3) + 32.7180515537385*sqr(
0.151938325910849 - x4) - x49 =E= 0;
e49.. 0.267663478098588*(1 + 2.23606797749979*sqrt(x49) + 1.66666666666667*x49)
*exp(-2.23606797749979*sqrt(x49)) - x50 =E= 0;
e50.. 28.8031207707063*sqr(0.670655556838736 - x3) + 32.7180515537385*sqr(
0.876936461235205 - x4) - x51 =E= 0;
e51.. 0.267663478098588*(1 + 2.23606797749979*sqrt(x51) + 1.66666666666667*x51)
*exp(-2.23606797749979*sqrt(x51)) - x52 =E= 0;
e52.. 28.8031207707063*sqr(0.207973182236053 - x3) + 32.7180515537385*sqr(
0.331173292175481 - x4) - x53 =E= 0;
e53.. 0.267663478098588*(1 + 2.23606797749979*sqrt(x53) + 1.66666666666667*x53)
*exp(-2.23606797749979*sqrt(x53)) - x54 =E= 0;
e54.. 28.8031207707063*sqr(0.966799636494498 - x3) + 32.7180515537385*sqr(
0.903623280335378 - x4) - x55 =E= 0;
e55.. 0.267663478098588*(1 + 2.23606797749979*sqrt(x55) + 1.66666666666667*x55)
*exp(-2.23606797749979*sqrt(x55)) - x56 =E= 0;
e56.. 28.8031207707063*sqr(0.73547573937596 - x3) + 32.7180515537385*sqr(
0.750945430575571 - x4) - x57 =E= 0;
e57.. 0.267663478098588*(1 + 2.23606797749979*sqrt(x57) + 1.66666666666667*x57)
*exp(-2.23606797749979*sqrt(x57)) - x58 =E= 0;
e58.. 28.8031207707063*sqr(0.610566185432721 - x3) + 32.7180515537385*sqr(
0.198845982666349 - x4) - x59 =E= 0;
e59.. 0.267663478098588*(1 + 2.23606797749979*sqrt(x59) + 1.66666666666667*x59)
*exp(-2.23606797749979*sqrt(x59)) - x60 =E= 0;
e60.. 28.8031207707063*sqr(0.141944660623143 - x3) + 32.7180515537385*sqr(
0.489288865821674 - x4) - x61 =E= 0;
e61.. 0.267663478098588*(1 + 2.23606797749979*sqrt(x61) + 1.66666666666667*x61)
*exp(-2.23606797749979*sqrt(x61)) - x62 =E= 0;
e62.. 28.8031207707063*sqr(0.578558541443415 - x3) + 32.7180515537385*sqr(
0.962551216897219 - x4) - x63 =E= 0;
e63.. 0.267663478098588*(1 + 2.23606797749979*sqrt(x63) + 1.66666666666667*x63)
*exp(-2.23606797749979*sqrt(x63)) - x64 =E= 0;
e64.. - 0.141170866470016*x6 - 0.0410227184433634*x8 + 0.00923158102538404*x10
+ 0.0322471218273555*x12 + 0.159305500449696*x14 - 0.123117661099077*x16
+ 0.0380530713899642*x18 + 0.889594746101726*x20 + 0.514139990210469*x22
- 0.0738007765330698*x24 + 1.44710982730193*x26 + 0.132568049860004*x28
+ 1.32552100239566*x30 - 0.880281256081741*x32 + 0.67317507860953*x34
+ 0.0699447658622974*x36 - 0.180419508821865*x38 + 0.114486082175227*x40
+ 0.0157657511439586*x42 - 2.42272624857116*x44 + 0.0619293699366356*x46
- 0.102616266190338*x48 + 0.236512593081257*x50 + 0.39189121299016*x52
+ 0.0949736077002411*x54 - 0.013659007622883*x56 + 0.408191007714036*x58
- 1.79436698216086*x60 - 0.393018856049253*x62 + 0.140369132198771*x64
- x65 =E= 0;
e65.. 1.70327473357547*x65 - x66 =E= 0.104337166479966;
* set non-default bounds
x1.lo = -3; x1.up = 3;
x2.lo = -3; x2.up = 3;
x3.lo = -1; x3.up = 1;
x4.lo = -1; x4.up = 1;
x5.up = 10000000;
x6.up = 10000000;
x7.up = 10000000;
x8.up = 10000000;
x9.up = 10000000;
x10.up = 10000000;
x11.up = 10000000;
x12.up = 10000000;
x13.up = 10000000;
x14.up = 10000000;
x15.up = 10000000;
x16.up = 10000000;
x17.up = 10000000;
x18.up = 10000000;
x19.up = 10000000;
x20.up = 10000000;
x21.up = 10000000;
x22.up = 10000000;
x23.up = 10000000;
x24.up = 10000000;
x25.up = 10000000;
x26.up = 10000000;
x27.up = 10000000;
x28.up = 10000000;
x29.up = 10000000;
x30.up = 10000000;
x31.up = 10000000;
x32.up = 10000000;
x33.up = 10000000;
x34.up = 10000000;
x35.up = 10000000;
x36.up = 10000000;
x37.up = 10000000;
x38.up = 10000000;
x39.up = 10000000;
x40.up = 10000000;
x41.up = 10000000;
x42.up = 10000000;
x43.up = 10000000;
x44.up = 10000000;
x45.up = 10000000;
x46.up = 10000000;
x47.up = 10000000;
x48.up = 10000000;
x49.up = 10000000;
x50.up = 10000000;
x51.up = 10000000;
x52.up = 10000000;
x53.up = 10000000;
x54.up = 10000000;
x55.up = 10000000;
x56.up = 10000000;
x57.up = 10000000;
x58.up = 10000000;
x59.up = 10000000;
x60.up = 10000000;
x61.up = 10000000;
x62.up = 10000000;
x63.up = 10000000;
x64.up = 10000000;
x65.lo = -10000000; x65.up = 10000000;
x66.lo = -10000000; x66.up = 10000000;
Model m / all /;
m.limrow=0; m.limcol=0;
m.tolproj=0.0;
$if NOT '%gams.u1%' == '' $include '%gams.u1%'
$if not set NLP $set NLP NLP
Solve m using %NLP% minimizing objvar;
Last updated: 2025-08-07 Git hash: e62cedfc