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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance st_e16

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	12292.46728000 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	12292.46623000 (ANTIGONE) 12292.46726000 (BARON) 12292.46680000 (COUENNE) 12292.46728000 (LINDO) 12292.46728000 (SCIP)
Referencesⓘ	Tawarmalani, M and Sahinidis, N V, Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications, Kluwer, 2002. Floudas, C A and Ciric, A R, Strategies for overcoming uncertainties in heat exchanger network synthesis, Computers and Chemical Engineering, 13:10, 1989, 1133-1152.
Sourceⓘ	BARON book instance misc/e16
Added to libraryⓘ	03 Sep 2002
Problem typeⓘ	NLP
#Variablesⓘ	12
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	8
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	nonlinear
Objective curvatureⓘ	nonconcave
#Nonzeros in Objectiveⓘ	4
#Nonlinear Nonzeros in Objectiveⓘ	4
#Constraintsⓘ	9
#Linear Constraintsⓘ	5
#Quadratic Constraintsⓘ	4
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ	div mul vcpower
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	30
#Nonlinear Nonzeros in Jacobianⓘ	14
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	20
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	4
#Blocks in Hessian of Lagrangianⓘ	2
Minimal blocksize in Hessian of Lagrangianⓘ	4
Maximal blocksize in Hessian of Lagrangianⓘ	4
Average blocksize in Hessian of Lagrangianⓘ	4.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	1.6667e-01
Maximal coefficientⓘ	5.0000e+03
Infeasibility of initial pointⓘ	1000
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         10       10        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         13       13        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         35       17       18        0
*
*  Solve m using NLP minimizing objvar;


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

Positive Variables  x1,x2,x3,x4,x5,x6,x7,x8;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10;


e1..    x1 + x2 =E= 10;

e2..    x1 - x3 + x6 =E= 0;

e3..    x2 - x4 + x5 =E= 0;

e4..  - x3 + x5 + x7 =E= 0;

e5..  - x4 + x6 + x8 =E= 0;

e6.. x12*x6 - x9*x3 + 100*x1 =E= 0;

e7.. x10*x5 - x11*x4 + 100*x2 =E= 0;

e8.. x3*(x10 - x9) =E= 800;

e9.. x4*(x12 - x11) =E= 1000;

e10.. -(1200*(800/(258.333333333333 + 2.5*(0.666666666666667*((320 - x10)*(300
       - x9))**0.5 - 0.166666666666667*x9 - 0.166666666666667*x10)))**0.6 + 
      1200*(5000/(106.666666666667 + 0.666666666666667*((340 - x12)*(300 - x11)
      )**0.5 - 0.166666666666667*x11 - 0.166666666666667*x12))**0.6) + objvar
       =E= 0;

* set non-default bounds
x1.up = 10;
x2.up = 10;
x3.up = 10;
x4.up = 10;
x5.up = 10;
x6.up = 10;
x7.up = 10;
x8.up = 10;
x9.lo = 100; x9.up = 290;
x10.lo = 100; x10.up = 310;
x11.lo = 100; x11.up = 290;
x12.lo = 100; x12.up = 330;

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;