MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance prolog

Formats ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)
1.06218530 p1 ( gdx sol )
(infeas: 9e-13)
-0.00000000 p2 ( gdx sol )
(infeas: 3e-10)
Other points (infeas > 1e-08)  
Dual Bounds
-0.00000000 (ANTIGONE)
0.00000000 (BARON)
-0.00000000 (COUENNE)
0.00000000 (GUROBI)
0.00000000 (LINDO)
0.00000000 (SCIP)
References Norton, R D and Scandizzo, P L, Market Equilibrium Computations in Activity Analysis Models, Operations Research, 29:2, 1981, 243-262.
Source GAMS Model Library model prolog
Application Market Equilibrium
Added to library 31 Jul 2001
Problem type QCQP
#Variables 20
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 6
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type quadratic
Objective curvature indefinite
#Nonzeros in Objective 8
#Nonlinear Nonzeros in Objective 6
#Constraints 22
#Linear Constraints 20
#Quadratic Constraints 2
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 120
#Nonlinear Nonzeros in Jacobian 8
#Nonzeros in (Upper-Left) Hessian of Lagrangian 8
#Nonzeros in Diagonal of Hessian of Lagrangian 0
#Blocks in Hessian of Lagrangian 2
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 4.8000e-02
Maximal coefficient 5.0000e+03
Infeasibility of initial point 782
Sparsity Jacobian Sparsity of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangian Sparsity of Hessian of Lagrangian

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         23        1        0       22        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         21       21        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        129      115       14        0
*
*  Solve m using NLP minimizing objvar;


Variables  objvar,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18
          ,x19,x20,x21;

Positive Variables  x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,x20
          ,x21;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18,e19
          ,e20,e21,e22,e23;


e1..    x5 + x6 - 0.94*x11 - 0.94*x12 - 0.94*x13 + 0.244*x17 + 0.244*x18
      + 0.244*x19 =L= 0;

e2..    0.064*x11 + 0.064*x12 + 0.064*x13 - 0.58*x14 - 0.58*x15 - 0.58*x16
      + 0.172*x17 + 0.172*x18 + 0.172*x19 =L= 0;

e3..    x7 + x8 + 0.048*x11 + 0.048*x12 + 0.048*x13 + 0.247*x14 + 0.247*x15
      + 0.247*x16 - 0.916*x17 - 0.916*x18 - 0.916*x19 =L= 0;

e4..    x11 + 1.2*x12 + 0.8*x13 + 2*x14 + 1.8*x15 + 2.4*x16 + 3*x17 + 2.7*x18
      + 3.2*x19 =L= 3712;

e5..    2*x11 + 1.8*x12 + 2.2*x13 + 3*x14 + 3.5*x15 + 2.3*x16 + 3*x17 + 3.2*x18
      + 2.7*x19 =L= 5000;

e6..    356.474947137148*x2 + 53.7083537310174*x4 + x5 - 0.564264890180399*x20
      =L= 352;

e7..    339.983422262764*x2 + 43.5418249774113*x4 + x6 - 0.405939876920766*x21
      =L= 430;

e8..    106.946746119538*x2 + 145.018955433089*x4 + x7 - 0.507117039797071*x20
      =L= 222;

e9..    173.929713444361*x2 + 203.031384299627*x4 + x8 - 0.578889145413521*x21
      =L= 292;

e10.. x5*x2 + x7*x4 - x20 =L= 0;

e11.. x6*x2 + x8*x4 - x21 =L= 0;

e12..  - 3340.8*x9 - 500*x10 + x20 =L= 0;

e13..  - 371.2*x9 - 4500*x10 + x21 =L= 0;

e14..    0.94*x2 - 0.064*x3 - 0.048*x4 - x9 - 2*x10 =L= 0;

e15..    0.94*x2 - 0.064*x3 - 0.048*x4 - 1.2*x9 - 1.8*x10 =L= 0;

e16..    0.94*x2 - 0.064*x3 - 0.048*x4 - 0.8*x9 - 2.2*x10 =L= 0;

e17..    0.58*x3 - 0.247*x4 - 2*x9 - 3*x10 =L= 0;

e18..    0.58*x3 - 0.247*x4 - 1.8*x9 - 3.5*x10 =L= 0;

e19..    0.58*x3 - 0.247*x4 - 2.4*x9 - 2.3*x10 =L= 0;

e20..  - 0.244*x2 - 0.172*x3 + 0.916*x4 - 3*x9 - 3*x10 =L= 0;

e21..  - 0.244*x2 - 0.172*x3 + 0.916*x4 - 2.7*x9 - 3.2*x10 =L= 0;

e22..  - 0.244*x2 - 0.172*x3 + 0.916*x4 - 3.2*x9 - 2.7*x10 =L= 0;

e23.. -(x5*x2 + x6*x2 + x7*x4 + x8*x4) - objvar + 3712*x9 + 5000*x10 =E= 0;

* set non-default bounds
x2.lo = 0.2;
x3.lo = 0.2;
x4.lo = 0.2;

* set non-default levels
x2.l = 0.5942;
x3.l = 1.6167;
x4.l = 1.31077;
x5.l = 352;
x6.l = 430;
x7.l = 222;
x8.l = 292;
x9.l = 0.130670360422406;
x10.l = 0.130670360422406;
x20.l = 500.14934;
x21.l = 638.25084;

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;


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