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Instance kriging_peaks-full010

Gaussian process regression for the peaks functions using 10 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)
0.29112078 p1 ( gdx sol )
(infeas: 8e-17)
Other points (infeas > 1e-08)  
Dual Bounds
0.29112078 (ANTIGONE)
0.29108221 (BARON)
0.29112068 (LINDO)
0.29111461 (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 26
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 12
#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 24
#Linear Constraints 4
#Quadratic Constraints 10
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 10
Operands in Gen. Nonlin. Functions exp mul sqrt
Constraints curvature indefinite
#Nonzeros in Jacobian 67
#Nonlinear Nonzeros in Jacobian 30
#Nonzeros in (Upper-Left) Hessian of Lagrangian 12
#Nonzeros in Diagonal of Hessian of Lagrangian 12
#Blocks in Hessian of Lagrangian 12
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 6.4807e-02
Maximal coefficient 6.4256e+01
Infeasibility of initial point 54.01
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
*         25       25        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         27       27        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         69       39       30        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,objvar;

Positive Variables  x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,x20
          ,x21,x22,x23,x24;

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;


e1..  - x26 + objvar =E= 0;

e2..    0.166666666666667*x1 - x3 =E= -0.5;

e3..    0.166666666666667*x2 - x4 =E= -0.5;

e4.. 64.2558879895505*sqr(0.694030125231034 - x3) + 0.451453304154821*sqr(
     0.095158202540104 - x4) - x5 =E= 0;

e5.. 0.256658143048259*(1 + 2.23606797749979*sqrt(x5) + 1.66666666666667*x5)*
     exp(-2.23606797749979*sqrt(x5)) - x6 =E= 0;

e6.. 64.2558879895505*sqr(0.768324435572052 - x3) + 0.451453304154821*sqr(
     0.279169765904797 - x4) - x7 =E= 0;

e7.. 0.256658143048259*(1 + 2.23606797749979*sqrt(x7) + 1.66666666666667*x7)*
     exp(-2.23606797749979*sqrt(x7)) - x8 =E= 0;

e8.. 64.2558879895505*sqr(0.449417796221557 - x3) + 0.451453304154821*sqr(
     0.690399166851636 - x4) - x9 =E= 0;

e9.. 0.256658143048259*(1 + 2.23606797749979*sqrt(x9) + 1.66666666666667*x9)*
     exp(-2.23606797749979*sqrt(x9)) - x10 =E= 0;

e10.. 64.2558879895505*sqr(0.835653234585859 - x3) + 0.451453304154821*sqr(
      0.819274707641782 - x4) - x11 =E= 0;

e11.. 0.256658143048259*(1 + 2.23606797749979*sqrt(x11) + 1.66666666666667*x11)
      *exp(-2.23606797749979*sqrt(x11)) - x12 =E= 0;

e12.. 64.2558879895505*sqr(0.916115262788179 - x3) + 0.451453304154821*sqr(
      0.417060019884486 - x4) - x13 =E= 0;

e13.. 0.256658143048259*(1 + 2.23606797749979*sqrt(x13) + 1.66666666666667*x13)
      *exp(-2.23606797749979*sqrt(x13)) - x14 =E= 0;

e14.. 64.2558879895505*sqr(0.175655940777394 - x3) + 0.451453304154821*sqr(
      0.577517381141589 - x4) - x15 =E= 0;

e15.. 0.256658143048259*(1 + 2.23606797749979*sqrt(x15) + 1.66666666666667*x15)
      *exp(-2.23606797749979*sqrt(x15)) - x16 =E= 0;

e16.. 64.2558879895505*sqr(0.210585980433571 - x3) + 0.451453304154821*sqr(
      0.162363431410791 - x4) - x17 =E= 0;

e17.. 0.256658143048259*(1 + 2.23606797749979*sqrt(x17) + 1.66666666666667*x17)
      *exp(-2.23606797749979*sqrt(x17)) - x18 =E= 0;

e18.. 64.2558879895505*sqr(0.379111099961924 - x3) + 0.451453304154821*sqr(
      0.374896738086211 - x4) - x19 =E= 0;

e19.. 0.256658143048259*(1 + 2.23606797749979*sqrt(x19) + 1.66666666666667*x19)
      *exp(-2.23606797749979*sqrt(x19)) - x20 =E= 0;

e20.. 64.2558879895505*sqr(0.58269047049772 - x3) + 0.451453304154821*sqr(
      0.958984274331446 - x4) - x21 =E= 0;

e21.. 0.256658143048259*(1 + 2.23606797749979*sqrt(x21) + 1.66666666666667*x21)
      *exp(-2.23606797749979*sqrt(x21)) - x22 =E= 0;

e22.. 64.2558879895505*sqr(0.064807191405694 - x3) + 0.451453304154821*sqr(
      0.720400711043696 - x4) - x23 =E= 0;

e23.. 0.256658143048259*(1 + 2.23606797749979*sqrt(x23) + 1.66666666666667*x23)
      *exp(-2.23606797749979*sqrt(x23)) - x24 =E= 0;

e24..  - 0.554050919391022*x6 - 0.182361458467212*x8 + 1.70198363249747*x10
       - 0.15810145595015*x12 - 0.149505342468411*x14 - 0.88102258631443*x16
       - 0.215467740313008*x18 + 0.85857179829172*x20 - 0.171283188932011*x22
       - 0.218571179976833*x24 - x25 =E= 0;

e25..    1.86360571672641*x25 - x26 =E= -0.727377686265491;

* 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.lo = -10000000; x25.up = 10000000;
x26.lo = -10000000; x26.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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