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Instance st_m2

Formats ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)
-856648.81870000 p1 ( gdx sol )
(infeas: 3e-13)
Other points (infeas > 1e-08)  
Dual Bounds
-856648.82540000 (ANTIGONE)
-856648.81950000 (BARON)
-856648.81910000 (COUENNE)
-856648.81870000 (CPLEX)
-856648.81870000 (GUROBI)
-856648.81870000 (LINDO)
-856648.84610000 (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 and Sahinidis, N V, A finite algorithm for global minimization of separable concave programs, Journal of Global Optimization, 12:1, 1998, 1-36.
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.
Added to library 03 Sep 2002
Problem type QP
#Variables 30
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 30
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type quadratic
Objective curvature concave
#Nonzeros in Objective 30
#Nonlinear Nonzeros in Objective 30
#Constraints 21
#Linear Constraints 21
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature linear
#Nonzeros in Jacobian 592
#Nonlinear Nonzeros in Jacobian 0
#Nonzeros in (Upper-Left) Hessian of Lagrangian 30
#Nonzeros in Diagonal of Hessian of Lagrangian 30
#Blocks in Hessian of Lagrangian 30
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 2.9148e-02
Maximal coefficient 1.1930e+05
Infeasibility of initial point 36.23
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
*         22        1        0       21        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         31       31        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        623      593       30        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,x18,x19
          ,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,objvar;

Positive Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17
          ,x18,x19,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30;

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


e1..  - 6*x1 + x2 - 9*x3 + 3*x5 + x6 + 4*x7 - 2*x8 + 8*x9 - 6*x10 - 4*x11
      - 6*x13 + 3*x14 + 6*x15 + 2*x16 + x17 + 9*x18 + 8*x19 - 10*x20 - 4*x21
      - 7*x22 - 8*x23 - x24 + 5*x25 - 7*x26 + 10*x27 - 3*x28 - 6*x29 - 7*x30
      =L= -5;

e2..  - 9*x1 - 8*x2 + 3*x3 - 5*x4 + 5*x5 + 6*x6 + 9*x7 - 7*x8 - x9 + 4*x10
      + x11 + 3*x12 + 10*x13 - 6*x14 - 7*x15 - 5*x16 - 4*x17 - x18 - 5*x19
      + 6*x21 - 4*x22 + 9*x23 - 5*x24 + 9*x25 + 5*x26 - x27 + 4*x28 + 6*x29
      + 6*x30 =L= 37;

e3..    4*x1 + 3*x2 + 8*x3 - 8*x4 + 5*x5 - 9*x6 - 5*x7 + x8 - 7*x9 + 8*x10
      + 4*x12 - 7*x13 - 6*x14 - 2*x15 - 4*x16 + 2*x17 + 9*x18 + 9*x19 - 8*x20
      - 3*x21 + 7*x22 - 6*x23 + 3*x24 - 5*x25 - 7*x26 - 3*x27 + 2*x28 + x29
      + 9*x30 =L= 12;

e4..    4*x1 - 2*x2 - 5*x3 + 9*x4 + 10*x5 + x6 - 6*x7 - 5*x8 + 9*x9 - 5*x10
      - 8*x11 - 6*x12 + 3*x13 - 8*x14 + 2*x15 + 4*x16 - 4*x18 - 5*x19 - 7*x20
      + 4*x21 + 4*x22 - 3*x23 - 8*x24 - 3*x25 - 9*x26 - x27 + 7*x28 + 3*x29
      - 7*x30 =L= -11;

e5..    9*x1 + 4*x2 - x3 - 9*x4 + 8*x5 - 4*x7 - 2*x9 + 7*x10 - 2*x11 + 8*x12
      + 2*x13 - 2*x14 - 6*x15 - 8*x16 - x17 - x18 + 7*x19 + 8*x20 - 4*x21
      + 2*x22 + 2*x23 - 6*x24 + 5*x25 + 3*x26 + 5*x27 + 5*x28 + 7*x29 + 2*x30
      =L= 59;

e6..  - 2*x1 + 8*x2 + 5*x3 - 5*x5 + 9*x6 + 8*x7 - x8 - 7*x9 - x10 + 2*x11
      + 7*x12 - 10*x13 + 9*x14 + 7*x15 + 5*x16 - 5*x17 + 4*x19 + 6*x20 - 10*x21
      + 4*x22 + 2*x23 - 8*x24 - 8*x26 - 6*x27 + 7*x28 - 5*x29 - 9*x30 =L= 26;

e7..    5*x2 - 2*x4 - 4*x5 + 5*x6 + 3*x7 + 9*x8 + 8*x9 + 8*x11 + 8*x12 - 10*x13
      + 9*x14 - 7*x15 + x16 - 3*x17 + 3*x18 - x19 + 5*x20 - 8*x21 - 3*x22
      - 7*x23 + x24 + 5*x25 + 9*x26 - 7*x27 + 4*x28 + 4*x29 - 3*x30 =L= 51;

e8..    7*x1 - 5*x2 - 5*x3 - 4*x4 - 3*x5 + x6 - 7*x7 - 7*x8 - 8*x9 + 2*x10
      - x11 + x12 + 5*x13 - 2*x14 + 10*x15 + x16 - 2*x17 - 2*x18 + 6*x19 - x20
      - 9*x22 + x23 - 10*x24 + 3*x25 - 3*x27 - 2*x28 - 5*x29 - 4*x30 =L= -24;

e9..  - 9*x1 - 9*x2 - 5*x3 + 8*x4 + 8*x6 + 4*x7 - 6*x8 - 7*x9 + 6*x10 + 5*x11
      - 7*x12 + 5*x13 - 5*x14 - 5*x15 + 2*x16 - x17 + 2*x18 - 10*x19 - 10*x20
      + 6*x21 + 10*x22 + 9*x23 - 6*x24 + 4*x25 + 2*x26 + 9*x27 + 9*x28 - 2*x29
      =L= 25;

e10..  - 9*x1 + 5*x2 - 3*x3 + x4 + 2*x5 + 2*x6 - 2*x7 - 4*x8 - 9*x9 + 5*x10
       + 7*x11 - x12 - 4*x13 + 4*x14 - 5*x15 - 3*x16 + 10*x18 - 7*x19 + 2*x20
       - 6*x21 + x22 - 3*x23 + 2*x24 + 5*x25 + 8*x26 + 9*x27 + 2*x28 - 8*x29
       + 7*x30 =L= 27;

e11..    x1 - 3*x2 - 7*x3 - x4 + 7*x5 + 7*x6 - 2*x7 + 3*x8 - 3*x9 - x10 + 4*x11
       + 10*x12 - 2*x13 - 4*x14 - 8*x15 + 4*x16 - 2*x17 - 7*x18 + 4*x19 - 9*x21
       - 10*x22 + 7*x23 - x24 - 9*x25 - 10*x26 - 5*x27 - 3*x28 - x29 + 7*x30
       =L= -15;

e12..    3*x1 + 3*x2 + 9*x4 - 2*x5 - 7*x6 - 7*x8 - 5*x9 + 9*x10 + 6*x11 - 6*x12
       + 4*x13 + 6*x14 - 6*x15 - 7*x16 - 4*x17 + 3*x18 + 4*x19 - 9*x20 - 9*x21
       + 7*x22 + 9*x23 - 8*x24 - 5*x25 + 2*x26 - 9*x27 + x28 - 5*x29 + 5*x30
       =L= 1;

e13..  - 10*x1 + 5*x2 + 8*x3 - 9*x4 + 7*x5 - 6*x6 - 7*x7 + 3*x8 - 7*x9 + 3*x10
       + 4*x11 - x12 + 4*x13 + 6*x14 + 3*x15 - 7*x16 - 8*x17 - 3*x18 - x19
       + x20 - 7*x21 - 9*x22 - 5*x23 + 4*x24 - 6*x25 + 4*x26 - 8*x27 - x28
       + 6*x29 - 3*x30 =L= -22;

e14..  - 2*x1 + 10*x2 + 8*x3 + 5*x4 - 5*x5 + 4*x6 + 2*x7 + 2*x8 + 6*x9 - x10
       + 5*x11 - 4*x12 - 6*x13 - 2*x14 + 4*x15 - 3*x17 + x18 + 2*x19 - 2*x20
       + 4*x21 - 2*x22 - 5*x23 - 2*x24 + x25 + x27 - 2*x28 + 6*x30 =L= 44;

e15..  - 9*x1 - 3*x2 - 9*x3 + 5*x4 - 2*x5 - 7*x6 + 7*x7 + 6*x8 - x9 + 6*x10
       - 10*x11 + 7*x13 - 4*x14 + 6*x15 + 7*x16 - 5*x17 + 5*x19 - 6*x20 - 4*x21
       - 2*x23 + 7*x24 + 3*x25 - 9*x26 - 7*x27 - 5*x28 - 10*x29 + 3*x30 =L= -9;

e16..  - 2*x1 - 5*x2 + 8*x3 + 7*x4 + x5 - 8*x6 + 2*x7 - 5*x8 - 3*x9 + 4*x10
       + 8*x11 + 8*x12 + 4*x13 - 6*x14 + 4*x15 + 6*x16 + 3*x17 + 7*x18 + 10*x19
       - 2*x20 - 9*x21 + 2*x22 + 6*x23 - 8*x24 + 2*x25 - x26 - 8*x28 - 5*x29
       - 9*x30 =L= 29;

e17..    4*x1 + 10*x2 - 7*x4 - x5 - 5*x6 + 9*x7 - x9 + 4*x10 - x12 + 7*x13
       - 10*x14 + 5*x15 + x16 + 4*x17 - 10*x18 + 4*x19 + 3*x20 + 5*x22 + 8*x23
       + 9*x24 - 3*x25 - 8*x27 - 2*x28 + 3*x29 - 9*x30 =L= 39;

e18..    2*x1 + 4*x2 - 10*x4 - 4*x5 - 10*x6 + x7 - 2*x8 + 6*x9 + 10*x10 - x11
       - x12 - 8*x13 - 6*x14 + 3*x15 + 5*x16 - 5*x18 - 4*x19 + 3*x20 - x21
       + 4*x22 - 5*x23 - 9*x24 - 6*x25 + 5*x26 + 7*x27 - x28 - x29 - 7*x30
       =L= -10;

e19..    9*x1 + 5*x2 - 4*x3 + 4*x4 - 6*x5 - 2*x6 - 7*x7 - 6*x8 + 9*x9 + 9*x10
       - 9*x11 + 6*x12 - 8*x13 + 10*x14 + 3*x15 - 4*x16 + 5*x17 + 3*x18 + 5*x19
       + 4*x20 + x22 + 5*x23 - 8*x24 - 5*x25 - 9*x26 - 3*x27 - 4*x28 - 6*x29
       + 5*x30 =L= 20;

e20..    5*x1 + 9*x2 + 2*x3 + 2*x4 + x5 + 7*x6 + 7*x7 + 5*x8 + 3*x9 + 7*x10
       + 4*x11 + 2*x12 + 2*x13 + 4*x14 + 5*x15 + 9*x16 + 10*x17 + 5*x18 + x19
       + 5*x20 + x21 + 8*x22 + 6*x23 + 8*x24 + 3*x25 + 2*x26 + 5*x27 + 4*x28
       + 4*x29 + 10*x30 =L= 1680;

e21..    0.20403741*x1 + 0.20403741*x2 - 0.1165928*x3 - 0.2040374*x4
       + 0.29148202*x5 + 0.08744461*x6 - 0.0291482*x7 + 0.26233382*x8
       + 0.11659281*x9 + 0.17488921*x10 + 0.0291482*x11 + 0.0291482*x12
       - 0.2040374*x13 + 0.26233382*x14 + 0.17488921*x15 - 0.2040374*x16
       - 0.2623338*x17 - 0.0874446*x18 - 0.2331856*x19 - 0.2331856*x20
       - 0.291482*x22 + 0.0291482*x23 + 0.20403741*x24 + 0.08744461*x26
       + 0.14574101*x27 + 0.11659281*x28 - 0.291482*x29 - 0.1748892*x30
       =L= -36.228832;

e22.. -(14571.3167*x1 - 3*sqr(x1) - sqr(x2) - 37250.204*x2 - 7*sqr(x3) + 
      1578.40997*x3 - 7*sqr(x4) - 23199.31*x4 - 9*sqr(x5) - 36532.101*x5 - 4*
      sqr(x6) + 14991.9969*x6 - 6*sqr(x7) - 46241.855*x7 - 8*sqr(x8) + 
      59634.0121*x8 - sqr(x9) + 11781.1616*x9 - sqr(x10) - 62617.461*x10 - 6*
      sqr(x11) + 23226.6837*x11 - 7*sqr(x12) - 16497.431*x12 - sqr(x13) + 
      350.55924*x13 - 4*sqr(x14) + 25674.7606*x14 - 2*sqr(x15) + 56334.3262*x15
       - 5*sqr(x16) - 2159.2486*x16 - 7*sqr(x17) + 30150.9571*x17 - 6*sqr(x18)
       - 13688.295*x18 - 9*sqr(x19) - 41755.296*x19 - 9*sqr(x20) + 34911.6548*
      x20 - 6*sqr(x21) + 104801.315*x21 - 2*sqr(x22) - 47888.471*x22 - 7*sqr(
      x23) - 10644.315*x23 - 5*sqr(x24) + 119299.448*x24 - 7*sqr(x25) + 
      27859.4823*x25 - 9*sqr(x26) + 89793.8375*x26 - 8*sqr(x27) + 108734.2*x27
       - 3*sqr(x28) - 31798.43*x28 - sqr(x29) + 15961.706*x29 - 8*sqr(x30) - 
      5450.7111*x30) + 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: 2022-08-11 Git hash: f176bd52
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