MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance chain50
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 0.17451499 (ANTIGONE) -45.23482993 (BARON) -49.77370804 (COUENNE) -37.10261783 (GUROBI) -32.76724002 (LINDO) -38.83725545 (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 sqr sqrt |
| 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 |
| Minimal coefficientⓘ | 1.0000e-02 |
| Maximal coefficientⓘ | 1.0000e+00 |
| Infeasibility of initial pointⓘ | 1.193 |
| Sparsity Jacobianⓘ |  |
| Sparsity 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: 2025-08-07 Git hash: e62cedfc