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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance nvs20

Formatsⓘ	ams gms mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	230.92216520 p1 ( gdx sol ) (infeas: 2e-16)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	230.92216000 (ANTIGONE) 230.92216500 (BARON) 230.92216520 (COUENNE) 230.92216520 (LINDO) 230.92216090 (SCIP) 46.00000000 (SHOT)
Referencesⓘ	Gupta, Omprakash K and Ravindran, A, Branch and Bound Experiments in Convex Nonlinear Integer Programming, Management Science, 13:12, 1985, 1533-1546. Tawarmalani, M and Sahinidis, N V, Exact Algorithms for Global Optimization of Mixed-Integer Nonlinear Programs. In Pardalos, Panos M and Romeijn, H Edwin, Eds, Handbook of Global Optimization - Volume 2: Heuristic Approaches, Kluwer Academic Publishers, 65-85. Tawarmalani, M and Sahinidis, N V, Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications, Kluwer, 2002.
Sourceⓘ	BARON book instance gupta/gupta20
Added to libraryⓘ	25 Jul 2002
Problem typeⓘ	MINLP
#Variablesⓘ	16
#Binary Variablesⓘ	0
#Integer Variablesⓘ	5
#Nonlinear Variablesⓘ	16
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	5
Objective Senseⓘ	min
Objective typeⓘ	polynomial
Objective curvatureⓘ	nonconcave
#Nonzeros in Objectiveⓘ	16
#Nonlinear Nonzeros in Objectiveⓘ	16
#Constraintsⓘ	8
#Linear Constraintsⓘ	8
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	linear
#Nonzeros in Jacobianⓘ	53
#Nonlinear Nonzeros in Jacobianⓘ	0
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	76
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	16
#Blocks in Hessian of Lagrangianⓘ	1
Minimal blocksize in Hessian of Lagrangianⓘ	16
Maximal blocksize in Hessian of Lagrangianⓘ	16
Average blocksize in Hessian of Lagrangianⓘ	16.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	1.0000e-01
Maximal coefficientⓘ	1.8200e+00
Infeasibility of initial pointⓘ	1.39
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          9        1        8        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         17       12        0        5        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         70       54       16        0
*
*  Solve m using MINLP minimizing objvar;


Variables  i1,i2,i3,i4,i5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,objvar;

Positive Variables  x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;

Integer Variables  i1,i2,i3,i4,i5;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9;


e1..    0.22*i1 + 0.2*i2 + 0.19*i3 + 0.25*i4 + 0.15*i5 + 0.11*x6 + 0.12*x7
      + 0.13*x8 + x9 =G= 2.5;

e2..  - 1.46*i1 - 1.3*i3 + 1.82*i4 - 1.15*i5 + 0.8*x7 + x10 =G= 1.1;

e3..    1.29*i1 - 0.89*i2 - 1.16*i5 - 0.96*x6 - 0.49*x8 + x11 =G= -3.1;

e4..  - 1.1*i1 - 1.06*i2 + 0.95*i3 - 0.54*i4 - 1.78*x6 - 0.41*x7 + x12 =G= -3.5
     ;

e5..  - 1.43*i4 + 1.51*i5 + 0.59*x6 - 0.33*x7 - 0.43*x8 + x13 =G= 1.3;

e6..  - 1.72*i2 - 0.33*i3 + 1.62*i5 + 1.24*x6 + 0.21*x7 - 0.26*x8 + x14 =G= 2.1
     ;

e7..    1.12*i1 + 0.31*i4 + 1.12*x7 - 0.36*x9 + x15 =G= 2.3;

e8..    0.45*i2 + 0.26*i3 - 1.1*i4 + 0.58*i5 - 1.03*x7 + 0.1*x8 + x16 =G= -1.5;

e9.. -(sqr(1 + sqr(i1) + i1) + (1 + sqr(i1) + i1)*(1 + sqr(i4) + i4) + (1 + 
     sqr(i1) + i1)*(1 + sqr(x7) + x7) + (1 + sqr(i1) + i1)*(1 + sqr(x8) + x8)
      + (1 + sqr(i1) + i1)*(1 + sqr(x16) + x16) + sqr(1 + sqr(i2) + i2) + (1 + 
     sqr(i2) + i2)*(1 + sqr(i3) + i3) + (1 + sqr(i2) + i2)*(1 + sqr(x7) + x7)
      + (1 + sqr(i2) + i2)*(1 + sqr(x10) + x10) + sqr(1 + sqr(i3) + i3) + (1 + 
     sqr(i3) + i3)*(1 + sqr(x7) + x7) + (1 + sqr(i3) + i3)*(1 + sqr(x9) + x9)
      + (1 + sqr(i3) + i3)*(1 + sqr(x10) + x10) + (1 + sqr(i3) + i3)*(1 + sqr(
     x14) + x14) + sqr(1 + sqr(i4) + i4) + (1 + sqr(i4) + i4)*(1 + sqr(x7) + x7
     ) + (1 + sqr(i4) + i4)*(1 + sqr(x11) + x11) + (1 + sqr(i4) + i4)*(1 + sqr(
     x15) + x15) + sqr(1 + sqr(i5) + i5) + (1 + sqr(i5) + i5)*(1 + sqr(x6) + x6
     ) + (1 + sqr(i5) + i5)*(1 + sqr(x10) + x10) + (1 + sqr(i5) + i5)*(1 + sqr(
     x12) + x12) + (1 + sqr(i5) + i5)*(1 + sqr(x16) + x16) + sqr(1 + sqr(x6) + 
     x6) + (1 + sqr(x6) + x6)*(1 + sqr(x8) + x8) + (1 + sqr(x6) + x6)*(1 + sqr(
     x15) + x15) + sqr(1 + sqr(x7) + x7) + (1 + sqr(x7) + x7)*(1 + sqr(x11) + 
     x11) + (1 + sqr(x7) + x7)*(1 + sqr(x13) + x13) + sqr(1 + sqr(x8) + x8) + (
     1 + sqr(x8) + x8)*(1 + sqr(x10) + x10) + (1 + sqr(x8) + x8)*(1 + sqr(x15)
      + x15) + sqr(1 + sqr(x9) + x9) + (1 + sqr(x9) + x9)*(1 + sqr(x12) + x12)
      + (1 + sqr(x9) + x9)*(1 + sqr(x16) + x16) + sqr(1 + sqr(x10) + x10) + (1
      + sqr(x10) + x10)*(1 + sqr(x14) + x14) + sqr(1 + sqr(x11) + x11) + (1 + 
     sqr(x11) + x11)*(1 + sqr(x13) + x13) + sqr(1 + sqr(x12) + x12) + (1 + sqr(
     x12) + x12)*(1 + sqr(x14) + x14) + sqr(1 + sqr(x13) + x13) + (1 + sqr(x13)
      + x13)*(1 + sqr(x14) + x14) + sqr(1 + sqr(x14) + x14) + sqr(1 + sqr(x15)
      + x15) + sqr(1 + sqr(x16) + x16)) + objvar =E= 0;

* set non-default bounds
i1.up = 200;
i2.up = 200;
i3.up = 200;
i4.up = 200;
i5.up = 200;
x6.up = 200;
x7.up = 200;
x8.up = 200;
x9.up = 200;
x10.up = 200;
x11.up = 200;
x12.up = 200;
x13.up = 200;
x14.up = 200;
x15.up = 200;
x16.up = 200;

* set non-default levels
i1.l = 1;
i2.l = 1;
i3.l = 1;
i4.l = 1;
i5.l = 1;
x6.l = 1;
x7.l = 1;
x8.l = 1;
x9.l = 1;
x10.l = 1;
x11.l = 1;
x12.l = 1;
x13.l = 1;
x14.l = 1;
x15.l = 1;
x16.l = 1;

Model m / all /;

m.limrow=0; m.limcol=0;
m.tolproj=0.0;

$if NOT '%gams.u1%' == '' $include '%gams.u1%'

$if not set MINLP $set MINLP MINLP
Solve m using %MINLP% minimizing objvar;