MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance st_e31
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | -2.00000000 (ANTIGONE) -2.00000812 (BARON) -2.00000000 (COUENNE) -2.00000050 (GUROBI) -2.00000000 (LINDO) -2.00000000 (SCIP) -3.00000000 (SHOT) |
| 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. Marin, R, Points of location on a fixture, 1998. Personal Communication. |
| Sourceⓘ | BARON book instance misc/e31 |
| Added to libraryⓘ | 01 Sep 2002 |
| Problem typeⓘ | MBQCP |
| #Variablesⓘ | 112 |
| #Binary Variablesⓘ | 24 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 7 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 1 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 135 |
| #Linear Constraintsⓘ | 130 |
| #Quadratic Constraintsⓘ | 5 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 312 |
| #Nonlinear Nonzeros in Jacobianⓘ | 14 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 14 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 2 |
| #Blocks in Hessian of Lagrangianⓘ | 2 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 3 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 4 |
| Average blocksize in Hessian of Lagrangianⓘ | 3.5 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 4.4720e-01 |
| Maximal coefficientⓘ | 3.5000e+00 |
| Infeasibility of initial pointⓘ | 1 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 136 82 28 26 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 113 89 24 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 314 300 14 0
*
* Solve m using MINLP minimizing objvar;
Variables b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17,b18,b19
,b20,b21,b22,b23,b24,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,x103
,x104,x105,x106,x107,x108,x109,x110,x111,x112,objvar;
Negative Variables x62,x64,x66,x68,x70,x72,x74,x76,x78,x80,x82,x84;
Positive Variables x35,x36,x37,x63,x65,x67,x69,x71,x73,x75,x77,x79,x81,x83
,x85,x86,x87,x88,x89,x90,x91,x92,x93,x94,x95,x96,x97,x102,x103,x104
,x105,x109,x110,x111,x112;
Binary Variables b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17
,b18,b19,b20,b21,b22,b23,b24;
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,e53
,e54,e55,e56,e57,e58,e59,e60,e61,e62,e63,e64,e65,e66,e67,e68,e69,e70
,e71,e72,e73,e74,e75,e76,e77,e78,e79,e80,e81,e82,e83,e84,e85,e86,e87
,e88,e89,e90,e91,e92,e93,e94,e95,e96,e97,e98,e99,e100,e101,e102,e103
,e104,e105,e106,e107,e108,e109,e110,e111,e112,e113,e114,e115,e116
,e117,e118,e119,e120,e121,e122,e123,e124,e125,e126,e127,e128,e129
,e130,e131,e132,e133,e134,e135,e136;
e1.. -x36*x31 - x25 + x27 =E= 0;
e2.. -x36*x32 - x26 + x28 =E= 0;
e3.. (-x37*x31) - x35*x33 - x25 + x29 =E= 0;
e4.. (-x37*x32) - x35*x34 - x26 + x30 =E= 0;
e5.. sqr(x31) + sqr(x32) =E= 1;
e6.. x32 + x33 =E= 0;
e7.. - x31 + x34 =E= 0;
e8.. - x36 + x112 =L= 0;
e9.. - x35 + x112 =L= 0;
e10.. - x25 - x50 =E= 0;
e11.. - x25 + x39 =E= 1;
e12.. - x25 + 0.8944*x40 - 0.4472*x52 =E= 1;
e13.. - x25 - 0.8944*x41 - 0.4772*x53 =E= 1;
e14.. - x27 - x54 =E= 0;
e15.. - x27 + x43 =E= 1;
e16.. - x27 + 0.8944*x44 - 0.4472*x56 =E= 1;
e17.. - x27 - 0.8944*x45 - 0.4772*x57 =E= 1;
e18.. - x29 - x58 =E= 0;
e19.. - x29 + x47 =E= 1;
e20.. - x29 + 0.8944*x48 - 0.4472*x60 =E= 1;
e21.. - x29 - 0.8944*x49 - 0.4772*x61 =E= 1;
e22.. - x26 + x38 =E= 1;
e23.. - x26 + x51 =E= 0;
e24.. - x26 + 0.4472*x40 + 0.8944*x52 =E= 0;
e25.. - x26 + 0.4772*x41 - 0.8944*x53 =E= 0;
e26.. - x28 + x42 =E= 1;
e27.. - x28 + x55 =E= 0;
e28.. - x28 + 0.4472*x44 + 0.8944*x56 =E= 0;
e29.. - x28 + 0.4772*x45 - 0.8944*x57 =E= 0;
e30.. - x30 + x46 =E= 1;
e31.. - x30 + x59 =E= 0;
e32.. - x30 + 0.4472*x48 + 0.8944*x60 =E= 0;
e33.. - x30 + 0.4772*x49 - 0.8944*x61 =E= 0;
e34.. - 3.5*b1 - x62 =L= 0;
e35.. - 3.5*b3 - x64 =L= 0;
e36.. - 3.5*b5 - x66 =L= 0;
e37.. - 3.5*b7 - x68 =L= 0;
e38.. - 3.5*b9 - x70 =L= 0;
e39.. - 3.5*b11 - x72 =L= 0;
e40.. - 3.5*b13 - x74 =L= 0;
e41.. - 3.5*b15 - x76 =L= 0;
e42.. - 3.5*b17 - x78 =L= 0;
e43.. - 3.5*b19 - x80 =L= 0;
e44.. - 3.5*b21 - x82 =L= 0;
e45.. - 3.5*b23 - x84 =L= 0;
e46.. - x63 =L= 0;
e47.. - x65 =L= 0;
e48.. - x67 =L= 0;
e49.. - x69 =L= 0;
e50.. - x71 =L= 0;
e51.. - x73 =L= 0;
e52.. - x75 =L= 0;
e53.. - x77 =L= 0;
e54.. - x79 =L= 0;
e55.. - x81 =L= 0;
e56.. - x83 =L= 0;
e57.. - x85 =L= 0;
e58.. - x62 =G= 0;
e59.. - x64 =G= 0;
e60.. - x66 =G= 0;
e61.. - x68 =G= 0;
e62.. - x70 =G= 0;
e63.. - x72 =G= 0;
e64.. - x74 =G= 0;
e65.. - x76 =G= 0;
e66.. - x78 =G= 0;
e67.. - x80 =G= 0;
e68.. - x82 =G= 0;
e69.. - x84 =G= 0;
e70.. 3.5*b2 - x63 =G= 0;
e71.. 3.5*b4 - x65 =G= 0;
e72.. 3.5*b6 - x67 =G= 0;
e73.. 3.5*b8 - x69 =G= 0;
e74.. 3.5*b10 - x71 =G= 0;
e75.. 3.5*b12 - x73 =G= 0;
e76.. 3.5*b14 - x75 =G= 0;
e77.. 3.5*b16 - x77 =G= 0;
e78.. 3.5*b18 - x79 =G= 0;
e79.. 3.5*b20 - x81 =G= 0;
e80.. 3.5*b22 - x83 =G= 0;
e81.. 3.5*b24 - x85 =G= 0;
e82.. b1 + b2 =E= 1;
e83.. b3 + b4 =E= 1;
e84.. b5 + b6 =E= 1;
e85.. b7 + b8 =E= 1;
e86.. b9 + b10 =E= 1;
e87.. b11 + b12 =E= 1;
e88.. b13 + b14 =E= 1;
e89.. b15 + b16 =E= 1;
e90.. b17 + b18 =E= 1;
e91.. b19 + b20 =E= 1;
e92.. b21 + b22 =E= 1;
e93.. b23 + b24 =E= 1;
e94.. x50 - x62 - x63 =E= 0;
e95.. x51 - x64 - x65 =E= 0;
e96.. x52 - x66 - x67 =E= 0;
e97.. x53 - x68 - x69 =E= 0;
e98.. x54 - x70 - x71 =E= 0;
e99.. x55 - x72 - x73 =E= 0;
e100.. x56 - x74 - x75 =E= 0;
e101.. x57 - x76 - x77 =E= 0;
e102.. x58 - x78 - x79 =E= 0;
e103.. x59 - x80 - x81 =E= 0;
e104.. x60 - x82 - x83 =E= 0;
e105.. x61 - x84 - x85 =E= 0;
e106.. - x63 + x86 =E= 0;
e107.. - x65 + x87 =E= 0;
e108.. - x67 + x88 =E= 0;
e109.. - x69 + x89 =E= 0;
e110.. - x71 + x90 =E= 0;
e111.. - x73 + x91 =E= 0;
e112.. - x75 + x92 =E= 0;
e113.. - x77 + x93 =E= 0;
e114.. - x79 + x94 =E= 0;
e115.. - x81 + x95 =E= 0;
e116.. - x83 + x96 =E= 0;
e117.. - x85 + x97 =E= 0;
e118.. - x50 - x54 - x58 + x98 =E= 0;
e119.. - x51 - x55 - x59 + x99 =E= 0;
e120.. - x52 - x56 - x60 + x100 =E= 0;
e121.. - x53 - x57 - x61 + x101 =E= 0;
e122.. - x86 - x90 - x94 + x102 =E= 0;
e123.. - x87 - x91 - x95 + x103 =E= 0;
e124.. - x88 - x92 - x96 + x104 =E= 0;
e125.. - x89 - x93 - x97 + x105 =E= 0;
e126.. x102 =G= 0;
e127.. x103 =G= 0;
e128.. x104 =G= 0;
e129.. x105 =G= 0;
e130.. - x50 - x51 - x52 - x53 + x106 =E= 0;
e131.. - x54 - x55 - x56 - x57 + x107 =E= 0;
e132.. - x58 - x59 - x60 - x61 + x108 =E= 0;
e133.. - x86 - x87 - x88 - x89 + x109 =E= 0;
e134.. - x90 - x91 - x92 - x93 + x110 =E= 0;
e135.. - x94 - x95 - x96 - x97 + x111 =E= 0;
e136.. x112 + objvar =E= 0;
* set non-default bounds
x25.lo = -1; x25.up = 1;
x26.lo = -1; x26.up = 1;
x27.lo = -1; x27.up = 1;
x28.lo = -1; x28.up = 1;
x29.lo = -1; x29.up = 1;
x30.lo = -1; x30.up = 1;
x31.lo = -1; x31.up = 1;
x32.lo = -1; x32.up = 1;
x33.lo = -1; x33.up = 1;
x34.lo = -1; x34.up = 1;
x35.up = 3;
x36.up = 3;
x37.up = 3;
x38.lo = -3; x38.up = 3;
x39.lo = -3; x39.up = 3;
x40.lo = -3; x40.up = 3;
x41.lo = -3; x41.up = 3;
x42.lo = -3; x42.up = 3;
x43.lo = -3; x43.up = 3;
x44.lo = -3; x44.up = 3;
x45.up = 3;
x46.lo = -3; x46.up = 3;
x47.lo = -3; x47.up = 3;
x48.lo = -3; x48.up = 3;
x49.lo = -3; x49.up = 3;
x50.lo = -3; x50.up = 3;
x51.lo = -3; x51.up = 3;
x52.lo = -3; x52.up = 3;
x53.lo = -3; x53.up = 3;
x54.lo = -3; x54.up = 3;
x55.lo = -3; x55.up = 3;
x56.lo = -3; x56.up = 3;
x57.up = 3;
x58.lo = -3; x58.up = 3;
x59.lo = -3; x59.up = 3;
x60.lo = -3; x60.up = 3;
x61.lo = -3; x61.up = 3;
x62.lo = -3;
x63.up = 3;
x64.lo = -3;
x65.up = 3;
x66.lo = -3;
x67.up = 3;
x68.lo = -3;
x69.up = 3;
x70.lo = -3;
x71.up = 3;
x72.lo = -3;
x73.up = 3;
x74.lo = -3;
x75.up = 3;
x76.lo = -3;
x77.up = 3;
x78.lo = -3;
x79.up = 3;
x80.lo = -3;
x81.up = 3;
x82.lo = -3;
x83.up = 3;
x84.lo = -3;
x85.up = 3;
x86.up = 3;
x87.up = 3;
x88.up = 3;
x89.up = 3;
x90.up = 3;
x91.up = 3;
x92.up = 3;
x93.up = 3;
x94.up = 3;
x95.up = 3;
x96.up = 3;
x97.up = 3;
x98.lo = -6; x98.up = 6;
x99.lo = -6; x99.up = 6;
x100.lo = -6;
x101.lo = -6;
x102.up = 6;
x103.up = 6;
x106.lo = -6; x106.up = 6;
x107.lo = -6; x107.up = 6;
x108.lo = -6; x108.up = 6;
x109.up = 6;
x110.up = 6;
x111.up = 6;
x112.up = 3;
Model m / all /;
m.limrow=0; m.limcol=0;
m.tolproj=0.0;
$if NOT '%gams.u1%' == '' $include '%gams.u1%'
$if not set MINLP $set MINLP MINLP
Solve m using %MINLP% minimizing objvar;
Last updated: 2024-04-02 Git hash: 1dd5fb9b