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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Removed Instance sambal

Formats ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)
3.96822036 p1 ( gdx sol )
(infeas: 3e-14)
Other points (infeas > 1e-08)  
Dual Bounds
3.96822036 (ANTIGONE)
3.96822036 (BARON)
3.96822036 (COUENNE)
3.96822036 (CPLEX)
3.96822036 (LINDO)
3.96822036 (SCIP)
References Zenios, Stavros A, Drud, Arne S, and Mulvey, J, Balancing some large Social Accounting Matrices with Nonlinear Programming, Tech. Rep., Department of Civil Engineering, Princeton University, 1986.
Source GAMS Model Library model sambal
Application Social Accounting Matrix Balancing
Added to library 31 Jul 2001
Removed from library 16 Feb 2022
Removed because Instance is continuous and convex.
Problem type QP
#Variables 17
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 13
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type quadratic
Objective curvature convex
#Nonzeros in Objective 13
#Nonlinear Nonzeros in Objective 13
#Constraints 10
#Linear Constraints 10
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature linear
#Nonzeros in Jacobian 34
#Nonlinear Nonzeros in Jacobian 0
#Nonzeros in (Upper-Left) Hessian of Lagrangian 13
#Nonzeros in Diagonal of Hessian of Lagrangian 13
#Blocks in Hessian of Lagrangian 13
Minimal blocksize in Hessian of Lagrangian 1
Maximal blocksize in Hessian of Lagrangian 1
Average blocksize in Hessian of Lagrangian 1.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 4.5455e-03
Maximal coefficient 2.2000e+02
Infeasibility of initial point 220
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
*         11       11        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         18       18        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         48       35       13        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,objvar;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11;


e1..  - x1 - x2 - x3 - x4 + x13 =E= 0;

e2..  - x5 + x14 =E= 0;

e3..  - x6 + x15 =E= 0;

e4..  - x7 - x8 - x9 + x16 =E= 0;

e5..  - x10 - x11 - x12 + x17 =E= 0;

e6..  - x5 - x6 + x13 =E= 0;

e7..  - x1 - x7 - x10 + x14 =E= 0;

e8..  - x2 - x8 - x11 + x15 =E= 0;

e9..  - x3 - x12 + x16 =E= 0;

e10..  - x4 - x9 + x17 =E= 0;

e11.. -(0.0666666666666667*sqr(15 - x1) + 0.333333333333333*sqr(3 - x2) + 
      0.00769230769230769*sqr(130 - x3) + 0.0125*sqr(80 - x4) + 
      0.0666666666666667*sqr(15 - x7) + 0.00769230769230769*sqr(130 - x8) + 
      0.05*sqr(20 - x9) + 0.04*sqr(25 - x10) + 0.025*sqr(40 - x11) + 
      0.0181818181818182*sqr(55 - x12) + 0.00454545454545455*sqr(220 - x13) + 
      0.00526315789473684*sqr(190 - x16) + 0.00952380952380952*sqr(105 - x17))
       + objvar =E= 0;

* set non-default levels
x1.l = 15;
x2.l = 3;
x3.l = 130;
x4.l = 80;
x7.l = 15;
x8.l = 130;
x9.l = 20;
x10.l = 25;
x11.l = 40;
x12.l = 55;
x13.l = 220;
x16.l = 190;
x17.l = 105;

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;


Last updated: 2022-05-24 Git hash: 1198c186
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