MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance prob07

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	154990.22940000 p1 ( gdx sol ) (infeas: 2e-11)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	154990.22590000 (ANTIGONE) 154990.22910000 (BARON) 154990.22940000 (COUENNE) 154990.22930000 (LINDO) 154990.16600000 (SCIP)
Referencesⓘ	Reklaitis, G and Ragsdell, K, Engineering Optimization, John Wiley and Sons, New York, NY, 1983. Westerlund, Tapio and Lundqvist, Kurt, Alpha-ECP, Version 5.01 An Interactive MINLP-Solver Based on the Extended Cutting Plane Method, Tech. Rep. 01-178-A, Process Design Laboratory at Abo University, 2001.
Sourceⓘ	Example models from AlphaECP
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	NLP
#Variablesⓘ	15
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	14
#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ⓘ	36
#Linear Constraintsⓘ	12
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	24
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	110
#Nonlinear Nonzeros in Jacobianⓘ	63
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	45
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	11
#Blocks in Hessian of Lagrangianⓘ	4
Minimal blocksize in Hessian of Lagrangianⓘ	1
Maximal blocksize in Hessian of Lagrangianⓘ	11
Average blocksize in Hessian of Lagrangianⓘ	3.5
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	2.2000e-01
Maximal coefficientⓘ	4.0000e+05
Infeasibility of initial pointⓘ	2.161e-05
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         36        1        8       27        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         15       15        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        110       47       63        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,objvar;

Positive Variables  x1,x2,x3;

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;


e1..    x1 - 1.2*x4 =G= 0;

e2..    x1 - 1.5*x5 =G= 0;

e3..    x1 - 1.1*x6 =G= 0;

e4..    x2 - 1.4*x4 =G= 0;

e5..    x2 - 1.2*x6 =G= 0;

e6..    x3 - x4 =G= 0;

e7..    x3 - x5 =G= 0;

e8..    x3 - x6 =G= 0;

e9..    x8 - x9 =L= 0;

e10..    x10 - x11 =L= 0;

e11..    x8 - x11 =L= 0;

e12..  - x8 + x9 =E= 0;

e13.. 592*x1**0.65 + 582*x2**0.39 + 1200*x3**0.52 + 370*x7**0.22 + 250*x8**0.4
       + 210*x9**0.62 + 250*x10**0.4 + 200*x11**0.83 - objvar =L= 0;

e14.. 400000*x12/x4 + 300000*x13/x5 + 100000*x14/x6 =L= 8000;

e15.. 1.2*x4/x7 - x12 =L= 0;

e16.. 1.2*x4/x8 - x12 =L= 0;

e17.. 1.2*x4/x9 - x12 =L= 0;

e18.. 1.4*x4/x10 - x12 =L= 0;

e19.. 1.4*x4/x11 - x12 =L= 0;

e20.. 1.5*x5/x7 - x13 =L= 0;

e21.. 1.5*x5/x8 - x13 =L= 0;

e22.. 1.5*x5/x9 - x13 =L= 0;

e23.. 1.5*x5/x11 - x13 =L= 0;

e24.. 1.1*x6/x7 - x14 =L= 0;

e25.. 1.1*x6/x8 - x14 =L= 0;

e26.. 1.1*x6/x9 - x14 =L= 0;

e27.. 1.2*x6/x10 - x14 =L= 0;

e28.. 1.2*x6/x11 - x14 =L= 0;

e29.. 1.2*x4/x7 + 1.2*x4/x8 - x12 =L= -3;

e30.. 1.2*x4/x9 + 1.4*x4/x10 - x12 =L= -1;

e31.. 1.4*x4/x11 - x12 =L= -4;

e32.. 1.5*x5/x7 + 1.5*x5/x8 - x13 =L= -6;

e33.. 1.5*x5/x11 - x13 =L= -8;

e34.. 1.1*x6/x7 + 1.1*x6/x8 - x14 =L= -2;

e35.. 1.1*x6/x9 + 1.2*x6/x10 - x14 =L= -2;

e36.. 1.2*x6/x11 - x14 =L= -4;

* set non-default bounds
x4.lo = 100;
x5.lo = 100;
x6.lo = 100;
x7.lo = 300;
x8.lo = 300;
x9.lo = 300;
x10.lo = 300;
x11.lo = 300;
x12.lo = 5;
x13.lo = 5;
x14.lo = 5;

* set non-default levels
x1.l = 1100.53862181846;
x2.l = 1279.53722102267;
x3.l = 913.955157873337;
x4.l = 913.955157873337;
x5.l = 733.692414545642;
x6.l = 913.955157873337;
x7.l = 1399.16837300491;
x8.l = 365.579732331283;
x9.l = 365.579732331283;
x10.l = 459.625873931453;
x11.l = 459.625873931453;
x12.l = 6.78386433964926;
x13.l = 10.3944267123785;
x14.l = 7.13617632404846;
objvar.l = 155153.543657587;

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;