MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance haverly

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-400.00000000 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-600.00000000 (ANTIGONE) -400.00000040 (BARON) -400.00000000 (COUENNE) -400.00000000 (GUROBI) -400.00000000 (LINDO) -400.00000190 (SCIP)
Referencesⓘ	Haverly, C A, Studies of the Behavior of Recursion for the Pooling Problem, ACM SIGMAP Bull, 25, 1978, 19-28. Adhya, N, Tawarmalani, M, and Sahinidis, N V, A Lagrangian Approach to the Pooling Problem, Industrial and Engineering Chemistry Research, 38:5, 1999, 1956-1972.
Sourceⓘ	GAMS Model Library model haverly
Applicationⓘ	Pooling Problem
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	QCP
#Variablesⓘ	12
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	3
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	linear
Objective curvatureⓘ	linear
#Nonzeros in Objectiveⓘ	2
#Nonlinear Nonzeros in Objectiveⓘ	0
#Constraintsⓘ	9
#Linear Constraintsⓘ	6
#Quadratic Constraintsⓘ	3
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	31
#Nonlinear Nonzeros in Jacobianⓘ	7
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	4
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	0
#Blocks in Hessian of Lagrangianⓘ	1
Minimal blocksize in Hessian of Lagrangianⓘ	3
Maximal blocksize in Hessian of Lagrangianⓘ	3
Average blocksize in Hessian of Lagrangianⓘ	3.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	5.0000e-01
Maximal coefficientⓘ	1.6000e+01
Infeasibility of initial pointⓘ	2
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         10        8        0        2        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
*         34       27        7        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,x9,x10,x11,x12;

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


e1..    x1 - 6*x3 - 16*x4 - 10*x5 =E= 0;

e2..    x2 - 9*x6 - 15*x7 =E= 0;

e3..    x6 - x8 - x10 =E= 0;

e4..    x7 - x9 - x11 =E= 0;

e5..    x3 + x4 - x10 - x11 =E= 0;

e6..    x5 - x8 - x9 =E= 0;

e7.. x12*(x10 + x11) - 3*x3 - x4 =E= 0;

e8.. x12*x10 - 2.5*x10 - 0.5*x8 =L= 0;

e9.. x12*x11 - 1.5*x11 + 0.5*x9 =L= 0;

e10..    x1 - x2 - objvar =E= 0;

* set non-default bounds
x6.up = 100;
x7.up = 200;

* set non-default levels
x8.l = 1;
x9.l = 1;
x10.l = 1;
x11.l = 1;
x12.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 NLP $set NLP NLP
Solve m using %NLP% minimizing objvar;