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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 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;