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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance sep1

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-510.08098440 p1 ( gdx sol ) (infeas: 5e-13)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-510.08098600 (ANTIGONE) -510.08098440 (BARON) -510.08098440 (COUENNE) -510.08099500 (GUROBI) -510.08098440 (LINDO) -510.08098440 (SCIP) -723.50000000 (SHOT)
Referencesⓘ	Kocis, Gary R and Grossmann, I E, A Modeling and Decomposition Strategy for the MINLP Optimization of Process Flowsheets, Computers and Chemical Engineering, 13:7, 1989, 797-819.
Sourceⓘ	MINOPT Model Library model kocis87-2.dat
Added to libraryⓘ	01 May 2001
Problem typeⓘ	MBQCP
#Variablesⓘ	29
#Binary Variablesⓘ	2
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	5
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	linear
Objective curvatureⓘ	linear
#Nonzeros in Objectiveⓘ	10
#Nonlinear Nonzeros in Objectiveⓘ	0
#Constraintsⓘ	31
#Linear Constraintsⓘ	25
#Quadratic Constraintsⓘ	6
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	88
#Nonlinear Nonzeros in Jacobianⓘ	12
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	12
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	0
#Blocks in Hessian of Lagrangianⓘ	1
Minimal blocksize in Hessian of Lagrangianⓘ	5
Maximal blocksize in Hessian of Lagrangianⓘ	5
Average blocksize in Hessian of Lagrangianⓘ	5.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	2.5000e-02
Maximal coefficientⓘ	5.0000e+01
Infeasibility of initial pointⓘ	16.9
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         32       23        5        4        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         30       28        2        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         99       87       12        0
*
*  Solve m using MINLP 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,b28,b29,objvar;

Positive 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;

Binary Variables  b28,b29;

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;


e1..  - 0.55*x5 - 0.5*x6 + x7 =E= 0;

e2..  - 0.45*x5 - 0.5*x6 + x8 =E= 0;

e3.. -x25*x7 + x9 =E= 0;

e4.. -x25*x8 + x10 =E= 0;

e5.. -x26*x7 + x11 =E= 0;

e6.. -x26*x8 + x12 =E= 0;

e7.. -x27*x7 + x13 =E= 0;

e8.. -x27*x8 + x14 =E= 0;

e9..  - x7 + x9 + x11 + x13 + x15 =E= 0;

e10..  - x8 + x10 + x12 + x14 + x16 =E= 0;

e11..  - 0.85*x9 + x17 =E= 0;

e12..  - 0.2*x10 + x18 =E= 0;

e13..  - 0.15*x9 + x19 =E= 0;

e14..  - 0.8*x10 + x20 =E= 0;

e15..  - 0.975*x11 + x21 =E= 0;

e16..  - 0.05*x12 + x22 =E= 0;

e17..  - 0.025*x11 + x23 =E= 0;

e18..  - 0.95*x12 + x24 =E= 0;

e19..    x1 - x13 - x17 - x21 =E= 0;

e20..    x2 - x14 - x18 - x22 =E= 0;

e21..    x3 - x15 - x19 - x23 =E= 0;

e22..    x4 - x16 - x20 - x24 =E= 0;

e23..    x9 + x10 - 2.5*b29 =G= 0;

e24..    x9 + x10 - 25*b29 =L= 0;

e25..    x11 + x12 - 2.5*b28 =G= 0;

e26..    x11 + x12 - 25*b28 =L= 0;

e27..    x1 - 4*x2 =G= 0;

e28..  - 3*x3 + x4 =G= 0;

e29..    x1 + x2 =L= 15;

e30..    x3 + x4 =L= 18;

e31..    b28 + b29 =G= 1;

e32..    35*x1 + 30*x4 - 10*x5 - 8*x6 - x9 - x10 - 4*x11 - 4*x12 - 50*b28
       - 2*b29 + objvar =E= 0;

* set non-default bounds
x1.up = 50;
x2.up = 50;
x3.up = 50;
x4.up = 50;
x5.up = 25;
x6.up = 25;
x7.up = 50;
x8.up = 50;
x9.up = 50;
x10.up = 50;
x11.up = 50;
x12.up = 50;
x13.up = 50;
x14.up = 50;
x15.up = 50;
x16.up = 50;
x17.up = 50;
x18.up = 50;
x19.up = 50;
x20.up = 50;
x21.up = 50;
x22.up = 50;
x23.up = 50;
x24.up = 50;
x25.up = 1;
x26.up = 1;
x27.up = 1;

* set non-default levels
x1.l = 10;
x2.l = 2.5;
x3.l = 4;
x4.l = 14;
x5.l = 8;
x6.l = 25;
x25.l = 0.1;
x26.l = 0.1;
x27.l = 0.1;
b28.l = 0.5;
b29.l = 0.5;

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;