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Instance kriging_peaks-full020
Gaussian process regression for the peaks functions using 20 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ⓘ | 0.37242684 (ANTIGONE) 0.37239130 (BARON) 0.37242854 (LINDO) 0.37241621 (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ⓘ | 46 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 22 |
| #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ⓘ | 44 |
| #Linear Constraintsⓘ | 4 |
| #Quadratic Constraintsⓘ | 20 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 20 |
| Operands in Gen. Nonlin. Functionsⓘ | exp mul sqrt |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 127 |
| #Nonlinear Nonzeros in Jacobianⓘ | 60 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 22 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 22 |
| #Blocks in Hessian of Lagrangianⓘ | 22 |
| 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ⓘ | 1.3648e-02 |
| Maximal coefficientⓘ | 9.8424e+00 |
| Infeasibility of initial pointⓘ | 9.52 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 45 45 0 0 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 47 47 0 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 129 69 60 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,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;
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;
e1.. - x46 + objvar =E= 0;
e2.. 0.166666666666667*x1 - x3 =E= -0.5;
e3.. 0.166666666666667*x2 - x4 =E= -0.5;
e4.. 0.73427818977281*sqr(0.203948432429007 - x3) + 9.84239329440621*sqr(
0.167077301047217 - x4) - x5 =E= 0;
e5.. 0.0409492741385585*(1 + 2.23606797749979*sqrt(x5) + 1.66666666666667*x5)*
exp(-2.23606797749979*sqrt(x5)) - x6 =E= 0;
e6.. 0.73427818977281*sqr(0.385865710218389 - x3) + 9.84239329440621*sqr(
0.710629474506774 - x4) - x7 =E= 0;
e7.. 0.0409492741385585*(1 + 2.23606797749979*sqrt(x7) + 1.66666666666667*x7)*
exp(-2.23606797749979*sqrt(x7)) - x8 =E= 0;
e8.. 0.73427818977281*sqr(0.736967756917555 - x3) + 9.84239329440621*sqr(
0.752652716266839 - x4) - x9 =E= 0;
e9.. 0.0409492741385585*(1 + 2.23606797749979*sqrt(x9) + 1.66666666666667*x9)*
exp(-2.23606797749979*sqrt(x9)) - x10 =E= 0;
e10.. 0.73427818977281*sqr(0.652741639941018 - x3) + 9.84239329440621*sqr(
0.0802775036072991 - x4) - x11 =E= 0;
e11.. 0.0409492741385585*(1 + 2.23606797749979*sqrt(x11) + 1.66666666666667*x11
)*exp(-2.23606797749979*sqrt(x11)) - x12 =E= 0;
e12.. 0.73427818977281*sqr(0.273052837124171 - x3) + 9.84239329440621*sqr(
0.232245875826583 - x4) - x13 =E= 0;
e13.. 0.0409492741385585*(1 + 2.23606797749979*sqrt(x13) + 1.66666666666667*x13
)*exp(-2.23606797749979*sqrt(x13)) - x14 =E= 0;
e14.. 0.73427818977281*sqr(0.195512487913805 - x3) + 9.84239329440621*sqr(
0.82234538166963 - x4) - x15 =E= 0;
e15.. 0.0409492741385585*(1 + 2.23606797749979*sqrt(x15) + 1.66666666666667*x15
)*exp(-2.23606797749979*sqrt(x15)) - x16 =E= 0;
e16.. 0.73427818977281*sqr(0.790016403526876 - x3) + 9.84239329440621*sqr(
0.663073561881453 - x4) - x17 =E= 0;
e17.. 0.0409492741385585*(1 + 2.23606797749979*sqrt(x17) + 1.66666666666667*x17
)*exp(-2.23606797749979*sqrt(x17)) - x18 =E= 0;
e18.. 0.73427818977281*sqr(0.471577255892049 - x3) + 9.84239329440621*sqr(
0.385779181808663 - x4) - x19 =E= 0;
e19.. 0.0409492741385585*(1 + 2.23606797749979*sqrt(x19) + 1.66666666666667*x19
)*exp(-2.23606797749979*sqrt(x19)) - x20 =E= 0;
e20.. 0.73427818977281*sqr(0.932437642614655 - x3) + 9.84239329440621*sqr(
0.426569457455376 - x4) - x21 =E= 0;
e21.. 0.0409492741385585*(1 + 2.23606797749979*sqrt(x21) + 1.66666666666667*x21
)*exp(-2.23606797749979*sqrt(x21)) - x22 =E= 0;
e22.. 0.73427818977281*sqr(0.509888721470545 - x3) + 9.84239329440621*sqr(
0.630133547648043 - x4) - x23 =E= 0;
e23.. 0.0409492741385585*(1 + 2.23606797749979*sqrt(x23) + 1.66666666666667*x23
)*exp(-2.23606797749979*sqrt(x23)) - x24 =E= 0;
e24.. 0.73427818977281*sqr(0.0136476827399359 - x3) + 9.84239329440621*sqr(
0.470789817400026 - x4) - x25 =E= 0;
e25.. 0.0409492741385585*(1 + 2.23606797749979*sqrt(x25) + 1.66666666666667*x25
)*exp(-2.23606797749979*sqrt(x25)) - x26 =E= 0;
e26.. 0.73427818977281*sqr(0.0575971713888859 - x3) + 9.84239329440621*sqr(
0.118569216327591 - x4) - x27 =E= 0;
e27.. 0.0409492741385585*(1 + 2.23606797749979*sqrt(x27) + 1.66666666666667*x27
)*exp(-2.23606797749979*sqrt(x27)) - x28 =E= 0;
e28.. 0.73427818977281*sqr(0.563083352644902 - x3) + 9.84239329440621*sqr(
0.338196135850122 - x4) - x29 =E= 0;
e29.. 0.0409492741385585*(1 + 2.23606797749979*sqrt(x29) + 1.66666666666667*x29
)*exp(-2.23606797749979*sqrt(x29)) - x30 =E= 0;
e30.. 0.73427818977281*sqr(0.839284400175223 - x3) + 9.84239329440621*sqr(
0.259643892294303 - x4) - x31 =E= 0;
e31.. 0.0409492741385585*(1 + 2.23606797749979*sqrt(x31) + 1.66666666666667*x31
)*exp(-2.23606797749979*sqrt(x31)) - x32 =E= 0;
e32.. 0.73427818977281*sqr(0.974011769354471 - x3) + 9.84239329440621*sqr(
0.0267828631907671 - x4) - x33 =E= 0;
e33.. 0.0409492741385585*(1 + 2.23606797749979*sqrt(x33) + 1.66666666666667*x33
)*exp(-2.23606797749979*sqrt(x33)) - x34 =E= 0;
e34.. 0.73427818977281*sqr(0.11286497483506 - x3) + 9.84239329440621*sqr(
0.923555128783197 - x4) - x35 =E= 0;
e35.. 0.0409492741385585*(1 + 2.23606797749979*sqrt(x35) + 1.66666666666667*x35
)*exp(-2.23606797749979*sqrt(x35)) - x36 =E= 0;
e36.. 0.73427818977281*sqr(0.435562145986338 - x3) + 9.84239329440621*sqr(
0.865720321769559 - x4) - x37 =E= 0;
e37.. 0.0409492741385585*(1 + 2.23606797749979*sqrt(x37) + 1.66666666666667*x37
)*exp(-2.23606797749979*sqrt(x37)) - x38 =E= 0;
e38.. 0.73427818977281*sqr(0.63794971820171 - x3) + 9.84239329440621*sqr(
0.967908882200314 - x4) - x39 =E= 0;
e39.. 0.0409492741385585*(1 + 2.23606797749979*sqrt(x39) + 1.66666666666667*x39
)*exp(-2.23606797749979*sqrt(x39)) - x40 =E= 0;
e40.. 0.73427818977281*sqr(0.301539979219768 - x3) + 9.84239329440621*sqr(
0.541814542258204 - x4) - x41 =E= 0;
e41.. 0.0409492741385585*(1 + 2.23606797749979*sqrt(x41) + 1.66666666666667*x41
)*exp(-2.23606797749979*sqrt(x41)) - x42 =E= 0;
e42.. 0.73427818977281*sqr(0.883470054705633 - x3) + 9.84239329440621*sqr(
0.592628523460776 - x4) - x43 =E= 0;
e43.. 0.0409492741385585*(1 + 2.23606797749979*sqrt(x43) + 1.66666666666667*x43
)*exp(-2.23606797749979*sqrt(x43)) - x44 =E= 0;
e44.. - 0.19366130954505*x6 + 1.99578133111533*x8 + 0.478356086779243*x10
- 0.712549108992264*x12 - 0.0793956809008794*x14 - 0.29220029830489*x16
+ 0.298999166148701*x18 + 1.46252699178592*x20 - 0.179500313739889*x22
+ 0.610664044060392*x24 - 0.324066056909861*x26 - 0.239036711794172*x28
- 1.50560493680608*x30 - 0.196933949886066*x32 - 0.244695512372529*x34
- 0.389841242602821*x36 + 1.8088978316128*x38 - 0.189154302869901*x40
- 2.11349851812763*x42 - 0.0772484060654371*x44 - x45 =E= 0;
e45.. 1.60096340792774*x45 - x46 =E= -0.50206779640133;
* 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.lo = -10000000; x45.up = 10000000;
x46.lo = -10000000; x46.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