MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance p_ball_10b_5p_2d_h
Select 5-points in 2-dimensional balls, such that the l1-distance between all points is minimized. Only one point can be assigned to each ball, and in total there are 10 balls with radius one. This is a convex-hull formulation.
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 18.71835427 (ALPHAECP) 18.71857797 (ANTIGONE) 18.71857003 (BARON) 18.71857797 (BONMIN) 18.71856412 (COUENNE) 18.71857799 (LINDO) 18.71857507 (SCIP) 0.00000000 (SHOT) |
| Referencesⓘ | Kronqvist, Jan and Misener, Ruth, A disjunctive cut strengthening technique for convex MINLP, Tech. Rep., 2020. |
| Sourceⓘ | p_ball_10b_5p_2d_H.gms with the epsilon in the perspective formulation changed to 1e-4, contributed by Jan Kronqvist and Ruth Misener |
| Applicationⓘ | Geometry |
| Added to libraryⓘ | 26 Aug 2020 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 180 |
| #Binary Variablesⓘ | 50 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 150 |
| #Nonlinear Binary Variablesⓘ | 50 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 20 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 219 |
| #Linear Constraintsⓘ | 169 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 50 |
| Operands in Gen. Nonlin. Functionsⓘ | div mul sqr |
| Constraints curvatureⓘ | convex |
| #Nonzeros in Jacobianⓘ | 688 |
| #Nonlinear Nonzeros in Jacobianⓘ | 150 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 350 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 150 |
| #Blocks in Hessian of Lagrangianⓘ | 50 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 3 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 3 |
| Average blocksize in Hessian of Lagrangianⓘ | 3.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e-04 |
| Maximal coefficientⓘ | 1.0000e+01 |
| Infeasibility of initial pointⓘ | 1 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 220 16 0 204 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 181 131 50 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 709 559 150 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,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34,b35,b36
,b37,b38,b39,b40,b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,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,x113,x114,x115,x116
,x117,x118,x119,x120,x121,x122,x123,x124,x125,x126,x127,x128,x129
,x130,x131,x132,x133,x134,x135,x136,x137,x138,x139,x140,x141,x142
,x143,x144,x145,x146,x147,x148,x149,x150,x151,x152,x153,x154,x155
,x156,x157,x158,x159,x160,x161,x162,x163,x164,x165,x166,x167,x168
,x169,x170,x171,x172,x173,x174,x175,x176,x177,x178,x179,x180,objvar;
Positive Variables 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,x113,x114,x115,x116,x117,x118,x119,x120,x121,x122,x123,x124
,x125,x126,x127,x128,x129,x130,x131,x132,x133,x134,x135,x136,x137
,x138,x139,x140,x141,x142,x143,x144,x145,x146,x147,x148,x149,x150
,x151,x152,x153,x154,x155,x156,x157,x158,x159,x160,x161,x162,x163
,x164,x165,x166,x167,x168,x169,x170,x171,x172,x173,x174,x175,x176
,x177,x178,x179,x180;
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,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34
,b35,b36,b37,b38,b39,b40,b41,b42,b43,b44,b45,b46,b47,b48,b49,b50;
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,e137,e138,e139,e140,e141,e142
,e143,e144,e145,e146,e147,e148,e149,e150,e151,e152,e153,e154,e155
,e156,e157,e158,e159,e160,e161,e162,e163,e164,e165,e166,e167,e168
,e169,e170,e171,e172,e173,e174,e175,e176,e177,e178,e179,e180,e181
,e182,e183,e184,e185,e186,e187,e188,e189,e190,e191,e192,e193,e194
,e195,e196,e197,e198,e199,e200,e201,e202,e203,e204,e205,e206,e207
,e208,e209,e210,e211,e212,e213,e214,e215,e216,e217,e218,e219,e220;
e1.. x51 - x52 - x53 =L= 0;
e2.. - x51 + x52 - x53 =L= 0;
e3.. x54 - x55 - x56 =L= 0;
e4.. - x54 + x55 - x56 =L= 0;
e5.. x51 - x57 - x58 =L= 0;
e6.. - x51 + x57 - x58 =L= 0;
e7.. x54 - x59 - x60 =L= 0;
e8.. - x54 + x59 - x60 =L= 0;
e9.. x51 - x61 - x62 =L= 0;
e10.. - x51 + x61 - x62 =L= 0;
e11.. x54 - x63 - x64 =L= 0;
e12.. - x54 + x63 - x64 =L= 0;
e13.. x51 - x65 - x66 =L= 0;
e14.. - x51 + x65 - x66 =L= 0;
e15.. x54 - x67 - x68 =L= 0;
e16.. - x54 + x67 - x68 =L= 0;
e17.. x52 - x57 - x69 =L= 0;
e18.. - x52 + x57 - x69 =L= 0;
e19.. x55 - x59 - x70 =L= 0;
e20.. - x55 + x59 - x70 =L= 0;
e21.. x52 - x61 - x71 =L= 0;
e22.. - x52 + x61 - x71 =L= 0;
e23.. x55 - x63 - x72 =L= 0;
e24.. - x55 + x63 - x72 =L= 0;
e25.. x52 - x65 - x73 =L= 0;
e26.. - x52 + x65 - x73 =L= 0;
e27.. x55 - x67 - x74 =L= 0;
e28.. - x55 + x67 - x74 =L= 0;
e29.. x57 - x61 - x75 =L= 0;
e30.. - x57 + x61 - x75 =L= 0;
e31.. x59 - x63 - x76 =L= 0;
e32.. - x59 + x63 - x76 =L= 0;
e33.. x57 - x65 - x77 =L= 0;
e34.. - x57 + x65 - x77 =L= 0;
e35.. x59 - x67 - x78 =L= 0;
e36.. - x59 + x67 - x78 =L= 0;
e37.. x61 - x65 - x79 =L= 0;
e38.. - x61 + x65 - x79 =L= 0;
e39.. x63 - x67 - x80 =L= 0;
e40.. - x63 + x67 - x80 =L= 0;
e41.. (-1 + sqr(0.648386267690458 - x81/(0.0001 + 0.9999*b1)) + sqr(
5.34198386756466 - x82/(0.0001 + 0.9999*b1)))*(0.0001 + 0.9999*b1) +
0.00279571963934506*b1 =L= 0.00279571963934506;
e42.. (-1 + sqr(0.38028139143083 - x83/(0.0001 + 0.9999*b2)) + sqr(
4.79200736168083 - x84/(0.0001 + 0.9999*b2)))*(0.0001 + 0.9999*b2) +
0.00221079484910719*b2 =L= 0.00221079484910719;
e43.. (-1 + sqr(4.59553989190787 - x85/(0.0001 + 0.9999*b3)) + sqr(
2.92927044373959 - x86/(0.0001 + 0.9999*b3)))*(0.0001 + 0.9999*b3) +
0.00286996122306829*b3 =L= 0.00286996122306829;
e44.. (-1 + sqr(7.79089239319392 - x87/(0.0001 + 0.9999*b4)) + sqr(
3.09688601355012 - x88/(0.0001 + 0.9999*b4)))*(0.0001 + 0.9999*b4) +
0.00692887072632492*b4 =L= 0.00692887072632492;
e45.. (-1 + sqr(2.20597420581599 - x89/(0.0001 + 0.9999*b5)) + sqr(
0.880296019425143 - x90/(0.0001 + 0.9999*b5)))*(0.0001 + 0.9999*b5) +
0.000464124327854123*b5 =L= 0.000464124327854123;
e46.. (-1 + sqr(4.31093077060147 - x91/(0.0001 + 0.9999*b6)) + sqr(
5.42555328385657 - x92/(0.0001 + 0.9999*b6)))*(0.0001 + 0.9999*b6) +
0.00470207525448854*b6 =L= 0.00470207525448854;
e47.. (-1 + sqr(8.68776252232421 - x93/(0.0001 + 0.9999*b7)) + sqr(
7.42106012944621 - x94/(0.0001 + 0.9999*b7)))*(0.0001 + 0.9999*b7) +
0.0129549351089157*b7 =L= 0.0129549351089157;
e48.. (-1 + sqr(3.86794113528858 - x95/(0.0001 + 0.9999*b8)) + sqr(
9.34863265837716 - x96/(0.0001 + 0.9999*b8)))*(0.0001 + 0.9999*b8) +
0.0101357901207334*b8 =L= 0.0101357901207334;
e49.. (-1 + sqr(8.94294324678777 - x97/(0.0001 + 0.9999*b9)) + sqr(
0.712193380632226 - x98/(0.0001 + 0.9999*b9)))*(0.0001 + 0.9999*b9) +
0.00794834533266834*b9 =L= 0.00794834533266834;
e50.. (-1 + sqr(1.56734614217404 - x99/(0.0001 + 0.9999*b10)) + sqr(
5.6469805099144 - x100/(0.0001 + 0.9999*b10)))*(0.0001 + 0.9999*b10) +
0.00333449628087409*b10 =L= 0.00333449628087409;
e51.. b1 + b2 + b3 + b4 + b5 + b6 + b7 + b8 + b9 + b10 =E= 1;
e52.. (-1 + sqr(0.648386267690458 - x101/(0.0001 + 0.9999*b11)) + sqr(
5.34198386756466 - x102/(0.0001 + 0.9999*b11)))*(0.0001 + 0.9999*b11) +
0.00279571963934506*b11 =L= 0.00279571963934506;
e53.. (-1 + sqr(0.38028139143083 - x103/(0.0001 + 0.9999*b12)) + sqr(
4.79200736168083 - x104/(0.0001 + 0.9999*b12)))*(0.0001 + 0.9999*b12) +
0.00221079484910719*b12 =L= 0.00221079484910719;
e54.. (-1 + sqr(4.59553989190787 - x105/(0.0001 + 0.9999*b13)) + sqr(
2.92927044373959 - x106/(0.0001 + 0.9999*b13)))*(0.0001 + 0.9999*b13) +
0.00286996122306829*b13 =L= 0.00286996122306829;
e55.. (-1 + sqr(7.79089239319392 - x107/(0.0001 + 0.9999*b14)) + sqr(
3.09688601355012 - x108/(0.0001 + 0.9999*b14)))*(0.0001 + 0.9999*b14) +
0.00692887072632492*b14 =L= 0.00692887072632492;
e56.. (-1 + sqr(2.20597420581599 - x109/(0.0001 + 0.9999*b15)) + sqr(
0.880296019425143 - x110/(0.0001 + 0.9999*b15)))*(0.0001 + 0.9999*b15) +
0.000464124327854123*b15 =L= 0.000464124327854123;
e57.. (-1 + sqr(4.31093077060147 - x111/(0.0001 + 0.9999*b16)) + sqr(
5.42555328385657 - x112/(0.0001 + 0.9999*b16)))*(0.0001 + 0.9999*b16) +
0.00470207525448854*b16 =L= 0.00470207525448854;
e58.. (-1 + sqr(8.68776252232421 - x113/(0.0001 + 0.9999*b17)) + sqr(
7.42106012944621 - x114/(0.0001 + 0.9999*b17)))*(0.0001 + 0.9999*b17) +
0.0129549351089157*b17 =L= 0.0129549351089157;
e59.. (-1 + sqr(3.86794113528858 - x115/(0.0001 + 0.9999*b18)) + sqr(
9.34863265837716 - x116/(0.0001 + 0.9999*b18)))*(0.0001 + 0.9999*b18) +
0.0101357901207334*b18 =L= 0.0101357901207334;
e60.. (-1 + sqr(8.94294324678777 - x117/(0.0001 + 0.9999*b19)) + sqr(
0.712193380632226 - x118/(0.0001 + 0.9999*b19)))*(0.0001 + 0.9999*b19) +
0.00794834533266834*b19 =L= 0.00794834533266834;
e61.. (-1 + sqr(1.56734614217404 - x119/(0.0001 + 0.9999*b20)) + sqr(
5.6469805099144 - x120/(0.0001 + 0.9999*b20)))*(0.0001 + 0.9999*b20) +
0.00333449628087409*b20 =L= 0.00333449628087409;
e62.. b11 + b12 + b13 + b14 + b15 + b16 + b17 + b18 + b19 + b20 =E= 1;
e63.. (-1 + sqr(0.648386267690458 - x121/(0.0001 + 0.9999*b21)) + sqr(
5.34198386756466 - x122/(0.0001 + 0.9999*b21)))*(0.0001 + 0.9999*b21) +
0.00279571963934506*b21 =L= 0.00279571963934506;
e64.. (-1 + sqr(0.38028139143083 - x123/(0.0001 + 0.9999*b22)) + sqr(
4.79200736168083 - x124/(0.0001 + 0.9999*b22)))*(0.0001 + 0.9999*b22) +
0.00221079484910719*b22 =L= 0.00221079484910719;
e65.. (-1 + sqr(4.59553989190787 - x125/(0.0001 + 0.9999*b23)) + sqr(
2.92927044373959 - x126/(0.0001 + 0.9999*b23)))*(0.0001 + 0.9999*b23) +
0.00286996122306829*b23 =L= 0.00286996122306829;
e66.. (-1 + sqr(7.79089239319392 - x127/(0.0001 + 0.9999*b24)) + sqr(
3.09688601355012 - x128/(0.0001 + 0.9999*b24)))*(0.0001 + 0.9999*b24) +
0.00692887072632492*b24 =L= 0.00692887072632492;
e67.. (-1 + sqr(2.20597420581599 - x129/(0.0001 + 0.9999*b25)) + sqr(
0.880296019425143 - x130/(0.0001 + 0.9999*b25)))*(0.0001 + 0.9999*b25) +
0.000464124327854123*b25 =L= 0.000464124327854123;
e68.. (-1 + sqr(4.31093077060147 - x131/(0.0001 + 0.9999*b26)) + sqr(
5.42555328385657 - x132/(0.0001 + 0.9999*b26)))*(0.0001 + 0.9999*b26) +
0.00470207525448854*b26 =L= 0.00470207525448854;
e69.. (-1 + sqr(8.68776252232421 - x133/(0.0001 + 0.9999*b27)) + sqr(
7.42106012944621 - x134/(0.0001 + 0.9999*b27)))*(0.0001 + 0.9999*b27) +
0.0129549351089157*b27 =L= 0.0129549351089157;
e70.. (-1 + sqr(3.86794113528858 - x135/(0.0001 + 0.9999*b28)) + sqr(
9.34863265837716 - x136/(0.0001 + 0.9999*b28)))*(0.0001 + 0.9999*b28) +
0.0101357901207334*b28 =L= 0.0101357901207334;
e71.. (-1 + sqr(8.94294324678777 - x137/(0.0001 + 0.9999*b29)) + sqr(
0.712193380632226 - x138/(0.0001 + 0.9999*b29)))*(0.0001 + 0.9999*b29) +
0.00794834533266834*b29 =L= 0.00794834533266834;
e72.. (-1 + sqr(1.56734614217404 - x139/(0.0001 + 0.9999*b30)) + sqr(
5.6469805099144 - x140/(0.0001 + 0.9999*b30)))*(0.0001 + 0.9999*b30) +
0.00333449628087409*b30 =L= 0.00333449628087409;
e73.. b21 + b22 + b23 + b24 + b25 + b26 + b27 + b28 + b29 + b30 =E= 1;
e74.. (-1 + sqr(0.648386267690458 - x141/(0.0001 + 0.9999*b31)) + sqr(
5.34198386756466 - x142/(0.0001 + 0.9999*b31)))*(0.0001 + 0.9999*b31) +
0.00279571963934506*b31 =L= 0.00279571963934506;
e75.. (-1 + sqr(0.38028139143083 - x143/(0.0001 + 0.9999*b32)) + sqr(
4.79200736168083 - x144/(0.0001 + 0.9999*b32)))*(0.0001 + 0.9999*b32) +
0.00221079484910719*b32 =L= 0.00221079484910719;
e76.. (-1 + sqr(4.59553989190787 - x145/(0.0001 + 0.9999*b33)) + sqr(
2.92927044373959 - x146/(0.0001 + 0.9999*b33)))*(0.0001 + 0.9999*b33) +
0.00286996122306829*b33 =L= 0.00286996122306829;
e77.. (-1 + sqr(7.79089239319392 - x147/(0.0001 + 0.9999*b34)) + sqr(
3.09688601355012 - x148/(0.0001 + 0.9999*b34)))*(0.0001 + 0.9999*b34) +
0.00692887072632492*b34 =L= 0.00692887072632492;
e78.. (-1 + sqr(2.20597420581599 - x149/(0.0001 + 0.9999*b35)) + sqr(
0.880296019425143 - x150/(0.0001 + 0.9999*b35)))*(0.0001 + 0.9999*b35) +
0.000464124327854123*b35 =L= 0.000464124327854123;
e79.. (-1 + sqr(4.31093077060147 - x151/(0.0001 + 0.9999*b36)) + sqr(
5.42555328385657 - x152/(0.0001 + 0.9999*b36)))*(0.0001 + 0.9999*b36) +
0.00470207525448854*b36 =L= 0.00470207525448854;
e80.. (-1 + sqr(8.68776252232421 - x153/(0.0001 + 0.9999*b37)) + sqr(
7.42106012944621 - x154/(0.0001 + 0.9999*b37)))*(0.0001 + 0.9999*b37) +
0.0129549351089157*b37 =L= 0.0129549351089157;
e81.. (-1 + sqr(3.86794113528858 - x155/(0.0001 + 0.9999*b38)) + sqr(
9.34863265837716 - x156/(0.0001 + 0.9999*b38)))*(0.0001 + 0.9999*b38) +
0.0101357901207334*b38 =L= 0.0101357901207334;
e82.. (-1 + sqr(8.94294324678777 - x157/(0.0001 + 0.9999*b39)) + sqr(
0.712193380632226 - x158/(0.0001 + 0.9999*b39)))*(0.0001 + 0.9999*b39) +
0.00794834533266834*b39 =L= 0.00794834533266834;
e83.. (-1 + sqr(1.56734614217404 - x159/(0.0001 + 0.9999*b40)) + sqr(
5.6469805099144 - x160/(0.0001 + 0.9999*b40)))*(0.0001 + 0.9999*b40) +
0.00333449628087409*b40 =L= 0.00333449628087409;
e84.. b31 + b32 + b33 + b34 + b35 + b36 + b37 + b38 + b39 + b40 =E= 1;
e85.. (-1 + sqr(0.648386267690458 - x161/(0.0001 + 0.9999*b41)) + sqr(
5.34198386756466 - x162/(0.0001 + 0.9999*b41)))*(0.0001 + 0.9999*b41) +
0.00279571963934506*b41 =L= 0.00279571963934506;
e86.. (-1 + sqr(0.38028139143083 - x163/(0.0001 + 0.9999*b42)) + sqr(
4.79200736168083 - x164/(0.0001 + 0.9999*b42)))*(0.0001 + 0.9999*b42) +
0.00221079484910719*b42 =L= 0.00221079484910719;
e87.. (-1 + sqr(4.59553989190787 - x165/(0.0001 + 0.9999*b43)) + sqr(
2.92927044373959 - x166/(0.0001 + 0.9999*b43)))*(0.0001 + 0.9999*b43) +
0.00286996122306829*b43 =L= 0.00286996122306829;
e88.. (-1 + sqr(7.79089239319392 - x167/(0.0001 + 0.9999*b44)) + sqr(
3.09688601355012 - x168/(0.0001 + 0.9999*b44)))*(0.0001 + 0.9999*b44) +
0.00692887072632492*b44 =L= 0.00692887072632492;
e89.. (-1 + sqr(2.20597420581599 - x169/(0.0001 + 0.9999*b45)) + sqr(
0.880296019425143 - x170/(0.0001 + 0.9999*b45)))*(0.0001 + 0.9999*b45) +
0.000464124327854123*b45 =L= 0.000464124327854123;
e90.. (-1 + sqr(4.31093077060147 - x171/(0.0001 + 0.9999*b46)) + sqr(
5.42555328385657 - x172/(0.0001 + 0.9999*b46)))*(0.0001 + 0.9999*b46) +
0.00470207525448854*b46 =L= 0.00470207525448854;
e91.. (-1 + sqr(8.68776252232421 - x173/(0.0001 + 0.9999*b47)) + sqr(
7.42106012944621 - x174/(0.0001 + 0.9999*b47)))*(0.0001 + 0.9999*b47) +
0.0129549351089157*b47 =L= 0.0129549351089157;
e92.. (-1 + sqr(3.86794113528858 - x175/(0.0001 + 0.9999*b48)) + sqr(
9.34863265837716 - x176/(0.0001 + 0.9999*b48)))*(0.0001 + 0.9999*b48) +
0.0101357901207334*b48 =L= 0.0101357901207334;
e93.. (-1 + sqr(8.94294324678777 - x177/(0.0001 + 0.9999*b49)) + sqr(
0.712193380632226 - x178/(0.0001 + 0.9999*b49)))*(0.0001 + 0.9999*b49) +
0.00794834533266834*b49 =L= 0.00794834533266834;
e94.. (-1 + sqr(1.56734614217404 - x179/(0.0001 + 0.9999*b50)) + sqr(
5.6469805099144 - x180/(0.0001 + 0.9999*b50)))*(0.0001 + 0.9999*b50) +
0.00333449628087409*b50 =L= 0.00333449628087409;
e95.. b41 + b42 + b43 + b44 + b45 + b46 + b47 + b48 + b49 + b50 =E= 1;
e96.. b1 + b11 + b21 + b31 + b41 =L= 1;
e97.. b2 + b12 + b22 + b32 + b42 =L= 1;
e98.. b3 + b13 + b23 + b33 + b43 =L= 1;
e99.. b4 + b14 + b24 + b34 + b44 =L= 1;
e100.. b5 + b15 + b25 + b35 + b45 =L= 1;
e101.. b6 + b16 + b26 + b36 + b46 =L= 1;
e102.. b7 + b17 + b27 + b37 + b47 =L= 1;
e103.. b8 + b18 + b28 + b38 + b48 =L= 1;
e104.. b9 + b19 + b29 + b39 + b49 =L= 1;
e105.. b10 + b20 + b30 + b40 + b50 =L= 1;
e106.. - x51 + x81 + x83 + x85 + x87 + x89 + x91 + x93 + x95 + x97 + x99 =E= 0
;
e107.. - x54 + x82 + x84 + x86 + x88 + x90 + x92 + x94 + x96 + x98 + x100
=E= 0;
e108.. - x52 + x101 + x103 + x105 + x107 + x109 + x111 + x113 + x115 + x117
+ x119 =E= 0;
e109.. - x55 + x102 + x104 + x106 + x108 + x110 + x112 + x114 + x116 + x118
+ x120 =E= 0;
e110.. - x57 + x121 + x123 + x125 + x127 + x129 + x131 + x133 + x135 + x137
+ x139 =E= 0;
e111.. - x59 + x122 + x124 + x126 + x128 + x130 + x132 + x134 + x136 + x138
+ x140 =E= 0;
e112.. - x61 + x141 + x143 + x145 + x147 + x149 + x151 + x153 + x155 + x157
+ x159 =E= 0;
e113.. - x63 + x142 + x144 + x146 + x148 + x150 + x152 + x154 + x156 + x158
+ x160 =E= 0;
e114.. - x65 + x161 + x163 + x165 + x167 + x169 + x171 + x173 + x175 + x177
+ x179 =E= 0;
e115.. - x67 + x162 + x164 + x166 + x168 + x170 + x172 + x174 + x176 + x178
+ x180 =E= 0;
e116.. - 10*b1 + x81 =L= 0;
e117.. - 10*b2 + x83 =L= 0;
e118.. - 10*b3 + x85 =L= 0;
e119.. - 10*b4 + x87 =L= 0;
e120.. - 10*b5 + x89 =L= 0;
e121.. - 10*b6 + x91 =L= 0;
e122.. - 10*b7 + x93 =L= 0;
e123.. - 10*b8 + x95 =L= 0;
e124.. - 10*b9 + x97 =L= 0;
e125.. - 10*b10 + x99 =L= 0;
e126.. - 10*b1 + x82 =L= 0;
e127.. - 10*b2 + x84 =L= 0;
e128.. - 10*b3 + x86 =L= 0;
e129.. - 10*b4 + x88 =L= 0;
e130.. - 10*b5 + x90 =L= 0;
e131.. - 10*b6 + x92 =L= 0;
e132.. - 10*b7 + x94 =L= 0;
e133.. - 10*b8 + x96 =L= 0;
e134.. - 10*b9 + x98 =L= 0;
e135.. - 10*b10 + x100 =L= 0;
e136.. - 10*b11 + x101 =L= 0;
e137.. - 10*b12 + x103 =L= 0;
e138.. - 10*b13 + x105 =L= 0;
e139.. - 10*b14 + x107 =L= 0;
e140.. - 10*b15 + x109 =L= 0;
e141.. - 10*b16 + x111 =L= 0;
e142.. - 10*b17 + x113 =L= 0;
e143.. - 10*b18 + x115 =L= 0;
e144.. - 10*b19 + x117 =L= 0;
e145.. - 10*b20 + x119 =L= 0;
e146.. - 10*b11 + x102 =L= 0;
e147.. - 10*b12 + x104 =L= 0;
e148.. - 10*b13 + x106 =L= 0;
e149.. - 10*b14 + x108 =L= 0;
e150.. - 10*b15 + x110 =L= 0;
e151.. - 10*b16 + x112 =L= 0;
e152.. - 10*b17 + x114 =L= 0;
e153.. - 10*b18 + x116 =L= 0;
e154.. - 10*b19 + x118 =L= 0;
e155.. - 10*b20 + x120 =L= 0;
e156.. - 10*b21 + x121 =L= 0;
e157.. - 10*b22 + x123 =L= 0;
e158.. - 10*b23 + x125 =L= 0;
e159.. - 10*b24 + x127 =L= 0;
e160.. - 10*b25 + x129 =L= 0;
e161.. - 10*b26 + x131 =L= 0;
e162.. - 10*b27 + x133 =L= 0;
e163.. - 10*b28 + x135 =L= 0;
e164.. - 10*b29 + x137 =L= 0;
e165.. - 10*b30 + x139 =L= 0;
e166.. - 10*b21 + x122 =L= 0;
e167.. - 10*b22 + x124 =L= 0;
e168.. - 10*b23 + x126 =L= 0;
e169.. - 10*b24 + x128 =L= 0;
e170.. - 10*b25 + x130 =L= 0;
e171.. - 10*b26 + x132 =L= 0;
e172.. - 10*b27 + x134 =L= 0;
e173.. - 10*b28 + x136 =L= 0;
e174.. - 10*b29 + x138 =L= 0;
e175.. - 10*b30 + x140 =L= 0;
e176.. - 10*b31 + x141 =L= 0;
e177.. - 10*b32 + x143 =L= 0;
e178.. - 10*b33 + x145 =L= 0;
e179.. - 10*b34 + x147 =L= 0;
e180.. - 10*b35 + x149 =L= 0;
e181.. - 10*b36 + x151 =L= 0;
e182.. - 10*b37 + x153 =L= 0;
e183.. - 10*b38 + x155 =L= 0;
e184.. - 10*b39 + x157 =L= 0;
e185.. - 10*b40 + x159 =L= 0;
e186.. - 10*b31 + x142 =L= 0;
e187.. - 10*b32 + x144 =L= 0;
e188.. - 10*b33 + x146 =L= 0;
e189.. - 10*b34 + x148 =L= 0;
e190.. - 10*b35 + x150 =L= 0;
e191.. - 10*b36 + x152 =L= 0;
e192.. - 10*b37 + x154 =L= 0;
e193.. - 10*b38 + x156 =L= 0;
e194.. - 10*b39 + x158 =L= 0;
e195.. - 10*b40 + x160 =L= 0;
e196.. - 10*b41 + x161 =L= 0;
e197.. - 10*b42 + x163 =L= 0;
e198.. - 10*b43 + x165 =L= 0;
e199.. - 10*b44 + x167 =L= 0;
e200.. - 10*b45 + x169 =L= 0;
e201.. - 10*b46 + x171 =L= 0;
e202.. - 10*b47 + x173 =L= 0;
e203.. - 10*b48 + x175 =L= 0;
e204.. - 10*b49 + x177 =L= 0;
e205.. - 10*b50 + x179 =L= 0;
e206.. - 10*b41 + x162 =L= 0;
e207.. - 10*b42 + x164 =L= 0;
e208.. - 10*b43 + x166 =L= 0;
e209.. - 10*b44 + x168 =L= 0;
e210.. - 10*b45 + x170 =L= 0;
e211.. - 10*b46 + x172 =L= 0;
e212.. - 10*b47 + x174 =L= 0;
e213.. - 10*b48 + x176 =L= 0;
e214.. - 10*b49 + x178 =L= 0;
e215.. - 10*b50 + x180 =L= 0;
e216.. x51 - x52 =L= 0;
e217.. x52 - x57 =L= 0;
e218.. x57 - x61 =L= 0;
e219.. x61 - x65 =L= 0;
e220.. - x53 - x56 - x58 - x60 - x62 - x64 - x66 - x68 - x69 - x70 - x71 - x72
- x73 - x74 - x75 - x76 - x77 - x78 - x79 - x80 + objvar =E= 0;
* set non-default bounds
x51.up = 10;
x52.up = 10;
x53.up = 10;
x54.up = 10;
x55.up = 10;
x56.up = 10;
x57.up = 10;
x58.up = 10;
x59.up = 10;
x60.up = 10;
x61.up = 10;
x62.up = 10;
x63.up = 10;
x64.up = 10;
x65.up = 10;
x66.up = 10;
x67.up = 10;
x68.up = 10;
x69.up = 10;
x70.up = 10;
x71.up = 10;
x72.up = 10;
x73.up = 10;
x74.up = 10;
x75.up = 10;
x76.up = 10;
x77.up = 10;
x78.up = 10;
x79.up = 10;
x80.up = 10;
x81.up = 10;
x82.up = 10;
x83.up = 10;
x84.up = 10;
x85.up = 10;
x86.up = 10;
x87.up = 10;
x88.up = 10;
x89.up = 10;
x90.up = 10;
x91.up = 10;
x92.up = 10;
x93.up = 10;
x94.up = 10;
x95.up = 10;
x96.up = 10;
x97.up = 10;
x98.up = 10;
x99.up = 10;
x100.up = 10;
x101.up = 10;
x102.up = 10;
x103.up = 10;
x104.up = 10;
x105.up = 10;
x106.up = 10;
x107.up = 10;
x108.up = 10;
x109.up = 10;
x110.up = 10;
x111.up = 10;
x112.up = 10;
x113.up = 10;
x114.up = 10;
x115.up = 10;
x116.up = 10;
x117.up = 10;
x118.up = 10;
x119.up = 10;
x120.up = 10;
x121.up = 10;
x122.up = 10;
x123.up = 10;
x124.up = 10;
x125.up = 10;
x126.up = 10;
x127.up = 10;
x128.up = 10;
x129.up = 10;
x130.up = 10;
x131.up = 10;
x132.up = 10;
x133.up = 10;
x134.up = 10;
x135.up = 10;
x136.up = 10;
x137.up = 10;
x138.up = 10;
x139.up = 10;
x140.up = 10;
x141.up = 10;
x142.up = 10;
x143.up = 10;
x144.up = 10;
x145.up = 10;
x146.up = 10;
x147.up = 10;
x148.up = 10;
x149.up = 10;
x150.up = 10;
x151.up = 10;
x152.up = 10;
x153.up = 10;
x154.up = 10;
x155.up = 10;
x156.up = 10;
x157.up = 10;
x158.up = 10;
x159.up = 10;
x160.up = 10;
x161.up = 10;
x162.up = 10;
x163.up = 10;
x164.up = 10;
x165.up = 10;
x166.up = 10;
x167.up = 10;
x168.up = 10;
x169.up = 10;
x170.up = 10;
x171.up = 10;
x172.up = 10;
x173.up = 10;
x174.up = 10;
x175.up = 10;
x176.up = 10;
x177.up = 10;
x178.up = 10;
x179.up = 10;
x180.up = 10;
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: 2025-08-07 Git hash: e62cedfc