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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance: st_qpk3

Formats ams gms lp mod nl osil pip
Primal Bounds (infeas ≤ 1e-08)
0.00000000 p1 ( gdx sol )
(infeas: 0)
-32.08742900 p2 ( gdx sol )
(infeas: 0)
-36.00000000 p3 ( gdx sol )
(infeas: 0)
Other points (infeas > 1e-08)  
Dual Bounds
-36.00000004 (ANTIGONE)
-36.00000004 (BARON)
-36.00000000 (COUENNE)
-36.00000000 (LINDO)
-36.00000000 (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.
Shectman, J P, Finite Algorithms for Global Optimization of Concave Programs and General Quadratic Programs, PhD thesis, Department of Mechanical and Industrial Engineering, University of Illinois, Urbana Champagne, 1999.
Source BARON book instance iqp/qpk3
Added to library 03 Sep 2002
Problem type QP
#Variables 11
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 11
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type quadratic
Objective curvature concave
#Nonzeros in Objective 11
#Nonlinear Nonzeros in Objective 11
#Constraints 22
#Linear Constraints 22
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature linear
#Nonzeros in Jacobian 242
#Nonlinear Nonzeros in Jacobian 0
#Nonzeros in (Upper-Left) Hessian of Lagrangian 31
#Nonzeros in Diagonal of Hessian of Lagrangian 11
#Blocks in Hessian of Lagrangian 1
Minimal blocksize in Hessian of Lagrangian 11
Maximal blocksize in Hessian of Lagrangian 11
Average blocksize in Hessian of Lagrangian 11.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Infeasibility of initial point 0
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
*         12       12        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        254      243       11        0
*
*  Solve m using NLP minimizing objvar;


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

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

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..  - x1 - 2*x2 - 3*x3 - 4*x4 - 5*x5 - 6*x6 - 7*x7 - 8*x8 - 9*x9 - 10*x10
      - 11*x11 =L= 0;

e2..  - 2*x1 - 3*x2 - 4*x3 - 5*x4 - 6*x5 - 7*x6 - 8*x7 - 9*x8 - 10*x9 - 11*x10
      - x11 =L= 0;

e3..  - 3*x1 - 4*x2 - 5*x3 - 6*x4 - 7*x5 - 8*x6 - 9*x7 - 10*x8 - 11*x9 - x10
      - 2*x11 =L= 0;

e4..  - 4*x1 - 5*x2 - 6*x3 - 7*x4 - 8*x5 - 9*x6 - 10*x7 - 11*x8 - x9 - 2*x10
      - 3*x11 =L= 0;

e5..  - 5*x1 - 6*x2 - 7*x3 - 8*x4 - 9*x5 - 10*x6 - 11*x7 - x8 - 2*x9 - 3*x10
      - 4*x11 =L= 0;

e6..  - 6*x1 - 7*x2 - 8*x3 - 9*x4 - 10*x5 - 11*x6 - x7 - 2*x8 - 3*x9 - 4*x10
      - 5*x11 =L= 0;

e7..  - 7*x1 - 8*x2 - 9*x3 - 10*x4 - 11*x5 - x6 - 2*x7 - 3*x8 - 4*x9 - 5*x10
      - 6*x11 =L= 0;

e8..  - 8*x1 - 9*x2 - 10*x3 - 11*x4 - x5 - 2*x6 - 3*x7 - 4*x8 - 5*x9 - 6*x10
      - 7*x11 =L= 0;

e9..  - 9*x1 - 10*x2 - 11*x3 - x4 - 2*x5 - 3*x6 - 4*x7 - 5*x8 - 6*x9 - 7*x10
      - 8*x11 =L= 0;

e10..  - 10*x1 - 11*x2 - x3 - 2*x4 - 3*x5 - 4*x6 - 5*x7 - 6*x8 - 7*x9 - 8*x10
       - 9*x11 =L= 0;

e11..  - 11*x1 - x2 - 2*x3 - 3*x4 - 4*x5 - 5*x6 - 6*x7 - 7*x8 - 8*x9 - 9*x10
       - 10*x11 =L= 0;

e12..    x1 + 2*x2 + 3*x3 + 4*x4 + 5*x5 + 6*x6 + 7*x7 + 8*x8 + 9*x9 + 10*x10
       + 11*x11 =L= 66;

e13..    2*x1 + 3*x2 + 4*x3 + 5*x4 + 6*x5 + 7*x6 + 8*x7 + 9*x8 + 10*x9 + 11*x10
       + x11 =L= 66;

e14..    3*x1 + 4*x2 + 5*x3 + 6*x4 + 7*x5 + 8*x6 + 9*x7 + 10*x8 + 11*x9 + x10
       + 2*x11 =L= 66;

e15..    4*x1 + 5*x2 + 6*x3 + 7*x4 + 8*x5 + 9*x6 + 10*x7 + 11*x8 + x9 + 2*x10
       + 3*x11 =L= 66;

e16..    5*x1 + 6*x2 + 7*x3 + 8*x4 + 9*x5 + 10*x6 + 11*x7 + x8 + 2*x9 + 3*x10
       + 4*x11 =L= 66;

e17..    6*x1 + 7*x2 + 8*x3 + 9*x4 + 10*x5 + 11*x6 + x7 + 2*x8 + 3*x9 + 4*x10
       + 5*x11 =L= 66;

e18..    7*x1 + 8*x2 + 9*x3 + 10*x4 + 11*x5 + x6 + 2*x7 + 3*x8 + 4*x9 + 5*x10
       + 6*x11 =L= 66;

e19..    8*x1 + 9*x2 + 10*x3 + 11*x4 + x5 + 2*x6 + 3*x7 + 4*x8 + 5*x9 + 6*x10
       + 7*x11 =L= 66;

e20..    9*x1 + 10*x2 + 11*x3 + x4 + 2*x5 + 3*x6 + 4*x7 + 5*x8 + 6*x9 + 7*x10
       + 8*x11 =L= 66;

e21..    10*x1 + 11*x2 + x3 + 2*x4 + 3*x5 + 4*x6 + 5*x7 + 6*x8 + 7*x9 + 8*x10
       + 9*x11 =L= 66;

e22..    11*x1 + x2 + 2*x3 + 3*x4 + 4*x5 + 5*x6 + 6*x7 + 7*x8 + 8*x9 + 9*x10
       + 10*x11 =L= 66;

e23.. -(0.5*x1*x2 - x1*x1 + 0.5*x2*x1 - x2*x2 + 0.5*x2*x3 + 0.5*x3*x2 - x3*x3
       + 0.5*x3*x4 + 0.5*x4*x3 - x4*x4 + 0.5*x4*x5 + 0.5*x5*x4 - x5*x5 + 0.5*x5
      *x6 + 0.5*x6*x5 - x6*x6 + 0.5*x6*x7 + 0.5*x7*x6 - x7*x7 + 0.5*x7*x8 + 0.5
      *x8*x7 - x8*x8 + 0.5*x8*x9 + 0.5*x9*x8 - x9*x9 + 0.5*x9*x10 + 0.5*x10*x9
       - x10*x10 + 0.5*x10*x11 + 0.5*x11*x10 - x11*x11) + objvar =E= 0;

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: 2019-06-04 Git hash: 78444eaa
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