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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)
0.37242854 p1 ( gdx sol )
(infeas: 2e-15)
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 of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangian Sparsity of 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: 2022-05-24 Git hash: 1198c186
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