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Instance: chain50

Formats ams gms mod nl osil
Primal Bounds
5.07226149 p1 ( gdx sol )
(infeas: 2e-16)
Dual Bounds
0.17451499 (ANTIGONE)
-45.23482993 (BARON)
-49.77370804 (COUENNE)
-64.28415089 (LINDO)
-97.64949747 (SCIP)
References Cesari, L, Optimization - Theory and Applications, Springer Verlag, 1983.
Dolan, E D and More, J J, Benchmarking Optimization Software with COPS, Tech. Rep. ANL/MCS-246, Mathematics and Computer Science Division, 2000.
Source GAMS Model Library model chain, Constrained Optimization Problem Set (COPS)
Application Hanging Chain
Added to library 31 Jul 2001
Problem type NLP
#Variables 102
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 102
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type nonlinear
Objective curvature indefinite
#Nonzeros in Objective 102
#Nonlinear Nonzeros in Objective 102
#Constraints 51
#Linear Constraints 50
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 1
Operands in Gen. Nonlin. Functions mul sqrt sqr
Constraints curvature indefinite
#Nonzeros in Jacobian 251
#Nonlinear Nonzeros in Jacobian 51
#Nonzeros in (Upper-Left) Hessian of Lagrangian 153
#Nonzeros in Diagonal of Hessian of Lagrangian 51
#Blocks in Hessian of Lagrangian 51
Minimal blocksize in Hessian of Lagrangian 2
Maximal blocksize in Hessian of Lagrangian 2
Average blocksize in Hessian of Lagrangian 2.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Infeasibility of initial point 1.193
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
*         52       52        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        103      103        0        0        0        0        0        0
*  FX      2
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        354      201      153        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,x31,x32,x33,x34,x35,x36
          ,x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51,x52,x53
          ,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65,x66,x67,x68,x69,x70
          ,x71,x72,x73,x74,x75,x76,x77,x78,x79,x80,x81,x82,x83,x84,x85,x86,x87
          ,x88,x89,x90,x91,x92,x93,x94,x95,x96,x97,x98,x99,x100,x101,x102
          ,objvar;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18,e19
          ,e20,e21,e22,e23,e24,e25,e26,e27,e28,e29,e30,e31,e32,e33,e34,e35,e36
          ,e37,e38,e39,e40,e41,e42,e43,e44,e45,e46,e47,e48,e49,e50,e51,e52;


e1.. -0.01*(sqrt(1 + sqr(x52))*x1 + sqrt(1 + sqr(x53))*x2 + sqrt(1 + sqr(x53))*
     x2 + sqrt(1 + sqr(x54))*x3 + sqrt(1 + sqr(x54))*x3 + sqrt(1 + sqr(x55))*x4
      + sqrt(1 + sqr(x55))*x4 + sqrt(1 + sqr(x56))*x5 + sqrt(1 + sqr(x56))*x5
      + sqrt(1 + sqr(x57))*x6 + sqrt(1 + sqr(x57))*x6 + sqrt(1 + sqr(x58))*x7
      + sqrt(1 + sqr(x58))*x7 + sqrt(1 + sqr(x59))*x8 + sqrt(1 + sqr(x59))*x8
      + sqrt(1 + sqr(x60))*x9 + sqrt(1 + sqr(x60))*x9 + sqrt(1 + sqr(x61))*x10
      + sqrt(1 + sqr(x61))*x10 + sqrt(1 + sqr(x62))*x11 + sqrt(1 + sqr(x62))*
     x11 + sqrt(1 + sqr(x63))*x12 + sqrt(1 + sqr(x63))*x12 + sqrt(1 + sqr(x64))
     *x13 + sqrt(1 + sqr(x64))*x13 + sqrt(1 + sqr(x65))*x14 + sqrt(1 + sqr(x65)
     )*x14 + sqrt(1 + sqr(x66))*x15 + sqrt(1 + sqr(x66))*x15 + sqrt(1 + sqr(x67
     ))*x16 + sqrt(1 + sqr(x67))*x16 + sqrt(1 + sqr(x68))*x17 + sqrt(1 + sqr(
     x68))*x17 + sqrt(1 + sqr(x69))*x18 + sqrt(1 + sqr(x69))*x18 + sqrt(1 + 
     sqr(x70))*x19 + sqrt(1 + sqr(x70))*x19 + sqrt(1 + sqr(x71))*x20 + sqrt(1
      + sqr(x71))*x20 + sqrt(1 + sqr(x72))*x21 + sqrt(1 + sqr(x72))*x21 + sqrt(
     1 + sqr(x73))*x22 + sqrt(1 + sqr(x73))*x22 + sqrt(1 + sqr(x74))*x23 + 
     sqrt(1 + sqr(x74))*x23 + sqrt(1 + sqr(x75))*x24 + sqrt(1 + sqr(x75))*x24
      + sqrt(1 + sqr(x76))*x25 + sqrt(1 + sqr(x76))*x25 + sqrt(1 + sqr(x77))*
     x26 + sqrt(1 + sqr(x77))*x26 + sqrt(1 + sqr(x78))*x27 + sqrt(1 + sqr(x78))
     *x27 + sqrt(1 + sqr(x79))*x28 + sqrt(1 + sqr(x79))*x28 + sqrt(1 + sqr(x80)
     )*x29 + sqrt(1 + sqr(x80))*x29 + sqrt(1 + sqr(x81))*x30 + sqrt(1 + sqr(x81
     ))*x30 + sqrt(1 + sqr(x82))*x31 + sqrt(1 + sqr(x82))*x31 + sqrt(1 + sqr(
     x83))*x32 + sqrt(1 + sqr(x83))*x32 + sqrt(1 + sqr(x84))*x33 + sqrt(1 + 
     sqr(x84))*x33 + sqrt(1 + sqr(x85))*x34 + sqrt(1 + sqr(x85))*x34 + sqrt(1
      + sqr(x86))*x35 + sqrt(1 + sqr(x86))*x35 + sqrt(1 + sqr(x87))*x36 + sqrt(
     1 + sqr(x87))*x36 + sqrt(1 + sqr(x88))*x37 + sqrt(1 + sqr(x88))*x37 + 
     sqrt(1 + sqr(x89))*x38 + sqrt(1 + sqr(x89))*x38 + sqrt(1 + sqr(x90))*x39
      + sqrt(1 + sqr(x90))*x39 + sqrt(1 + sqr(x91))*x40 + sqrt(1 + sqr(x91))*
     x40 + sqrt(1 + sqr(x92))*x41 + sqrt(1 + sqr(x92))*x41 + sqrt(1 + sqr(x93))
     *x42 + sqrt(1 + sqr(x93))*x42 + sqrt(1 + sqr(x94))*x43 + sqrt(1 + sqr(x94)
     )*x43 + sqrt(1 + sqr(x95))*x44 + sqrt(1 + sqr(x95))*x44 + sqrt(1 + sqr(x96
     ))*x45 + sqrt(1 + sqr(x96))*x45 + sqrt(1 + sqr(x97))*x46 + sqrt(1 + sqr(
     x97))*x46 + sqrt(1 + sqr(x98))*x47 + sqrt(1 + sqr(x98))*x47 + sqrt(1 + 
     sqr(x99))*x48 + sqrt(1 + sqr(x99))*x48 + sqrt(1 + sqr(x100))*x49 + sqrt(1
      + sqr(x100))*x49 + sqrt(1 + sqr(x101))*x50 + sqrt(1 + sqr(x101))*x50 + 
     sqrt(1 + sqr(x102))*x51) + objvar =E= 0;

e2..  - x1 + x2 - 0.01*x52 - 0.01*x53 =E= 0;

e3..  - x2 + x3 - 0.01*x53 - 0.01*x54 =E= 0;

e4..  - x3 + x4 - 0.01*x54 - 0.01*x55 =E= 0;

e5..  - x4 + x5 - 0.01*x55 - 0.01*x56 =E= 0;

e6..  - x5 + x6 - 0.01*x56 - 0.01*x57 =E= 0;

e7..  - x6 + x7 - 0.01*x57 - 0.01*x58 =E= 0;

e8..  - x7 + x8 - 0.01*x58 - 0.01*x59 =E= 0;

e9..  - x8 + x9 - 0.01*x59 - 0.01*x60 =E= 0;

e10..  - x9 + x10 - 0.01*x60 - 0.01*x61 =E= 0;

e11..  - x10 + x11 - 0.01*x61 - 0.01*x62 =E= 0;

e12..  - x11 + x12 - 0.01*x62 - 0.01*x63 =E= 0;

e13..  - x12 + x13 - 0.01*x63 - 0.01*x64 =E= 0;

e14..  - x13 + x14 - 0.01*x64 - 0.01*x65 =E= 0;

e15..  - x14 + x15 - 0.01*x65 - 0.01*x66 =E= 0;

e16..  - x15 + x16 - 0.01*x66 - 0.01*x67 =E= 0;

e17..  - x16 + x17 - 0.01*x67 - 0.01*x68 =E= 0;

e18..  - x17 + x18 - 0.01*x68 - 0.01*x69 =E= 0;

e19..  - x18 + x19 - 0.01*x69 - 0.01*x70 =E= 0;

e20..  - x19 + x20 - 0.01*x70 - 0.01*x71 =E= 0;

e21..  - x20 + x21 - 0.01*x71 - 0.01*x72 =E= 0;

e22..  - x21 + x22 - 0.01*x72 - 0.01*x73 =E= 0;

e23..  - x22 + x23 - 0.01*x73 - 0.01*x74 =E= 0;

e24..  - x23 + x24 - 0.01*x74 - 0.01*x75 =E= 0;

e25..  - x24 + x25 - 0.01*x75 - 0.01*x76 =E= 0;

e26..  - x25 + x26 - 0.01*x76 - 0.01*x77 =E= 0;

e27..  - x26 + x27 - 0.01*x77 - 0.01*x78 =E= 0;

e28..  - x27 + x28 - 0.01*x78 - 0.01*x79 =E= 0;

e29..  - x28 + x29 - 0.01*x79 - 0.01*x80 =E= 0;

e30..  - x29 + x30 - 0.01*x80 - 0.01*x81 =E= 0;

e31..  - x30 + x31 - 0.01*x81 - 0.01*x82 =E= 0;

e32..  - x31 + x32 - 0.01*x82 - 0.01*x83 =E= 0;

e33..  - x32 + x33 - 0.01*x83 - 0.01*x84 =E= 0;

e34..  - x33 + x34 - 0.01*x84 - 0.01*x85 =E= 0;

e35..  - x34 + x35 - 0.01*x85 - 0.01*x86 =E= 0;

e36..  - x35 + x36 - 0.01*x86 - 0.01*x87 =E= 0;

e37..  - x36 + x37 - 0.01*x87 - 0.01*x88 =E= 0;

e38..  - x37 + x38 - 0.01*x88 - 0.01*x89 =E= 0;

e39..  - x38 + x39 - 0.01*x89 - 0.01*x90 =E= 0;

e40..  - x39 + x40 - 0.01*x90 - 0.01*x91 =E= 0;

e41..  - x40 + x41 - 0.01*x91 - 0.01*x92 =E= 0;

e42..  - x41 + x42 - 0.01*x92 - 0.01*x93 =E= 0;

e43..  - x42 + x43 - 0.01*x93 - 0.01*x94 =E= 0;

e44..  - x43 + x44 - 0.01*x94 - 0.01*x95 =E= 0;

e45..  - x44 + x45 - 0.01*x95 - 0.01*x96 =E= 0;

e46..  - x45 + x46 - 0.01*x96 - 0.01*x97 =E= 0;

e47..  - x46 + x47 - 0.01*x97 - 0.01*x98 =E= 0;

e48..  - x47 + x48 - 0.01*x98 - 0.01*x99 =E= 0;

e49..  - x48 + x49 - 0.01*x99 - 0.01*x100 =E= 0;

e50..  - x49 + x50 - 0.01*x100 - 0.01*x101 =E= 0;

e51..  - x50 + x51 - 0.01*x101 - 0.01*x102 =E= 0;

e52.. 0.01*(sqrt(1 + sqr(x52)) + sqrt(1 + sqr(x53)) + sqrt(1 + sqr(x53)) + 
      sqrt(1 + sqr(x54)) + sqrt(1 + sqr(x54)) + sqrt(1 + sqr(x55)) + sqrt(1 + 
      sqr(x55)) + sqrt(1 + sqr(x56)) + sqrt(1 + sqr(x56)) + sqrt(1 + sqr(x57))
       + sqrt(1 + sqr(x57)) + sqrt(1 + sqr(x58)) + sqrt(1 + sqr(x58)) + sqrt(1
       + sqr(x59)) + sqrt(1 + sqr(x59)) + sqrt(1 + sqr(x60)) + sqrt(1 + sqr(x60
      )) + sqrt(1 + sqr(x61)) + sqrt(1 + sqr(x61)) + sqrt(1 + sqr(x62)) + sqrt(
      1 + sqr(x62)) + sqrt(1 + sqr(x63)) + sqrt(1 + sqr(x63)) + sqrt(1 + sqr(
      x64)) + sqrt(1 + sqr(x64)) + sqrt(1 + sqr(x65)) + sqrt(1 + sqr(x65)) + 
      sqrt(1 + sqr(x66)) + sqrt(1 + sqr(x66)) + sqrt(1 + sqr(x67)) + sqrt(1 + 
      sqr(x67)) + sqrt(1 + sqr(x68)) + sqrt(1 + sqr(x68)) + sqrt(1 + sqr(x69))
       + sqrt(1 + sqr(x69)) + sqrt(1 + sqr(x70)) + sqrt(1 + sqr(x70)) + sqrt(1
       + sqr(x71)) + sqrt(1 + sqr(x71)) + sqrt(1 + sqr(x72)) + sqrt(1 + sqr(x72
      )) + sqrt(1 + sqr(x73)) + sqrt(1 + sqr(x73)) + sqrt(1 + sqr(x74)) + sqrt(
      1 + sqr(x74)) + sqrt(1 + sqr(x75)) + sqrt(1 + sqr(x75)) + sqrt(1 + sqr(
      x76)) + sqrt(1 + sqr(x76)) + sqrt(1 + sqr(x77)) + sqrt(1 + sqr(x77)) + 
      sqrt(1 + sqr(x78)) + sqrt(1 + sqr(x78)) + sqrt(1 + sqr(x79)) + sqrt(1 + 
      sqr(x79)) + sqrt(1 + sqr(x80)) + sqrt(1 + sqr(x80)) + sqrt(1 + sqr(x81))
       + sqrt(1 + sqr(x81)) + sqrt(1 + sqr(x82)) + sqrt(1 + sqr(x82)) + sqrt(1
       + sqr(x83)) + sqrt(1 + sqr(x83)) + sqrt(1 + sqr(x84)) + sqrt(1 + sqr(x84
      )) + sqrt(1 + sqr(x85)) + sqrt(1 + sqr(x85)) + sqrt(1 + sqr(x86)) + sqrt(
      1 + sqr(x86)) + sqrt(1 + sqr(x87)) + sqrt(1 + sqr(x87)) + sqrt(1 + sqr(
      x88)) + sqrt(1 + sqr(x88)) + sqrt(1 + sqr(x89)) + sqrt(1 + sqr(x89)) + 
      sqrt(1 + sqr(x90)) + sqrt(1 + sqr(x90)) + sqrt(1 + sqr(x91)) + sqrt(1 + 
      sqr(x91)) + sqrt(1 + sqr(x92)) + sqrt(1 + sqr(x92)) + sqrt(1 + sqr(x93))
       + sqrt(1 + sqr(x93)) + sqrt(1 + sqr(x94)) + sqrt(1 + sqr(x94)) + sqrt(1
       + sqr(x95)) + sqrt(1 + sqr(x95)) + sqrt(1 + sqr(x96)) + sqrt(1 + sqr(x96
      )) + sqrt(1 + sqr(x97)) + sqrt(1 + sqr(x97)) + sqrt(1 + sqr(x98)) + sqrt(
      1 + sqr(x98)) + sqrt(1 + sqr(x99)) + sqrt(1 + sqr(x99)) + sqrt(1 + sqr(
      x100)) + sqrt(1 + sqr(x100)) + sqrt(1 + sqr(x101)) + sqrt(1 + sqr(x101))
       + sqrt(1 + sqr(x102))) =E= 4;

* set non-default bounds
x1.fx = 1;
x51.fx = 3;

* set non-default levels
x2.l = 0.9616;
x3.l = 0.9264;
x4.l = 0.8944;
x5.l = 0.8656;
x6.l = 0.84;
x7.l = 0.8176;
x8.l = 0.7984;
x9.l = 0.7824;
x10.l = 0.7696;
x11.l = 0.76;
x12.l = 0.7536;
x13.l = 0.7504;
x14.l = 0.7504;
x15.l = 0.7536;
x16.l = 0.76;
x17.l = 0.7696;
x18.l = 0.7824;
x19.l = 0.7984;
x20.l = 0.8176;
x21.l = 0.84;
x22.l = 0.8656;
x23.l = 0.8944;
x24.l = 0.9264;
x25.l = 0.9616;
x26.l = 1;
x27.l = 1.0416;
x28.l = 1.0864;
x29.l = 1.1344;
x30.l = 1.1856;
x31.l = 1.24;
x32.l = 1.2976;
x33.l = 1.3584;
x34.l = 1.4224;
x35.l = 1.4896;
x36.l = 1.56;
x37.l = 1.6336;
x38.l = 1.7104;
x39.l = 1.7904;
x40.l = 1.8736;
x41.l = 1.96;
x42.l = 2.0496;
x43.l = 2.1424;
x44.l = 2.2384;
x45.l = 2.3376;
x46.l = 2.44;
x47.l = 2.5456;
x48.l = 2.6544;
x49.l = 2.7664;
x50.l = 2.8816;
x52.l = -2;
x53.l = -1.84;
x54.l = -1.68;
x55.l = -1.52;
x56.l = -1.36;
x57.l = -1.2;
x58.l = -1.04;
x59.l = -0.88;
x60.l = -0.72;
x61.l = -0.56;
x62.l = -0.4;
x63.l = -0.24;
x64.l = -0.0800000000000001;
x65.l = 0.0800000000000001;
x66.l = 0.24;
x67.l = 0.4;
x68.l = 0.56;
x69.l = 0.72;
x70.l = 0.88;
x71.l = 1.04;
x72.l = 1.2;
x73.l = 1.36;
x74.l = 1.52;
x75.l = 1.68;
x76.l = 1.84;
x77.l = 2;
x78.l = 2.16;
x79.l = 2.32;
x80.l = 2.48;
x81.l = 2.64;
x82.l = 2.8;
x83.l = 2.96;
x84.l = 3.12;
x85.l = 3.28;
x86.l = 3.44;
x87.l = 3.6;
x88.l = 3.76;
x89.l = 3.92;
x90.l = 4.08;
x91.l = 4.24;
x92.l = 4.4;
x93.l = 4.56;
x94.l = 4.72;
x95.l = 4.88;
x96.l = 5.04;
x97.l = 5.2;
x98.l = 5.36;
x99.l = 5.52;
x100.l = 5.68;
x101.l = 5.84;
x102.l = 6;

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: 2018-05-28 Git hash: ac4a64c1
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