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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)
-1.58658792 p1 ( gdx sol )
(infeas: 4e-15)
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 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
*         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: 2022-08-11 Git hash: f176bd52
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