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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance polygon25
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | -5.79971418 (COUENNE) -1.56605883 (GUROBI) -6.12466502 (LINDO) -4.71115118 (SCIP) |
| Referencesⓘ | Graham, R L, The Largest Small Hexagon, Journal of Combinatorial Theory, Series A, 18:2, 1975, 165-170. 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 polygon, Constrained Optimization Problem Set (COPS) |
| Applicationⓘ | Geometry |
| Added to libraryⓘ | 31 Jul 2001 |
| Problem typeⓘ | NLP |
| #Variablesⓘ | 50 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 50 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | nonlinear |
| Objective curvatureⓘ | indefinite |
| #Nonzeros in Objectiveⓘ | 50 |
| #Nonlinear Nonzeros in Objectiveⓘ | 50 |
| #Constraintsⓘ | 324 |
| #Linear Constraintsⓘ | 24 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 300 |
| Operands in Gen. Nonlin. Functionsⓘ | cos mul sin sqr |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 1248 |
| #Nonlinear Nonzeros in Jacobianⓘ | 1200 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 2500 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 50 |
| #Blocks in Hessian of Lagrangianⓘ | 1 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 50 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 50 |
| Average blocksize in Hessian of Lagrangianⓘ | 50.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 5.0000e-01 |
| Maximal coefficientⓘ | 2.0000e+00 |
| Infeasibility of initial pointⓘ | 0.1973 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 325 1 0 324 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 51 51 0 0 0 0 0 0
* FX 2
*
* Nonzero counts
* Total const NL DLL
* 1299 49 1250 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,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,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35
,x36,x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49;
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
,e221,e222,e223,e224,e225,e226,e227,e228,e229,e230,e231,e232,e233
,e234,e235,e236,e237,e238,e239,e240,e241,e242,e243,e244,e245,e246
,e247,e248,e249,e250,e251,e252,e253,e254,e255,e256,e257,e258,e259
,e260,e261,e262,e263,e264,e265,e266,e267,e268,e269,e270,e271,e272
,e273,e274,e275,e276,e277,e278,e279,e280,e281,e282,e283,e284,e285
,e286,e287,e288,e289,e290,e291,e292,e293,e294,e295,e296,e297,e298
,e299,e300,e301,e302,e303,e304,e305,e306,e307,e308,e309,e310,e311
,e312,e313,e314,e315,e316,e317,e318,e319,e320,e321,e322,e323,e324
,e325;
e1.. -0.5*(x2*x1*sin(x27 - x26) + x3*x2*sin(x28 - x27) + x4*x3*sin(x29 - x28)
+ x5*x4*sin(x30 - x29) + x6*x5*sin(x31 - x30) + x7*x6*sin(x32 - x31) + x8
*x7*sin(x33 - x32) + x9*x8*sin(x34 - x33) + x10*x9*sin(x35 - x34) + x11*
x10*sin(x36 - x35) + x12*x11*sin(x37 - x36) + x13*x12*sin(x38 - x37) + x14
*x13*sin(x39 - x38) + x15*x14*sin(x40 - x39) + x16*x15*sin(x41 - x40) +
x17*x16*sin(x42 - x41) + x18*x17*sin(x43 - x42) + x19*x18*sin(x44 - x43)
+ x20*x19*sin(x45 - x44) + x21*x20*sin(x46 - x45) + x22*x21*sin(x47 - x46
) + x23*x22*sin(x48 - x47) + x24*x23*sin(x49 - x48) + x25*x24*sin(x50 -
x49)) - objvar =E= 0;
e2.. sqr(x1) + sqr(x2) - 2*x1*x2*cos(x27 - x26) =L= 1;
e3.. sqr(x1) + sqr(x3) - 2*x1*x3*cos(x28 - x26) =L= 1;
e4.. sqr(x1) + sqr(x4) - 2*x1*x4*cos(x29 - x26) =L= 1;
e5.. sqr(x1) + sqr(x5) - 2*x1*x5*cos(x30 - x26) =L= 1;
e6.. sqr(x1) + sqr(x6) - 2*x1*x6*cos(x31 - x26) =L= 1;
e7.. sqr(x1) + sqr(x7) - 2*x1*x7*cos(x32 - x26) =L= 1;
e8.. sqr(x1) + sqr(x8) - 2*x1*x8*cos(x33 - x26) =L= 1;
e9.. sqr(x1) + sqr(x9) - 2*x1*x9*cos(x34 - x26) =L= 1;
e10.. sqr(x1) + sqr(x10) - 2*x1*x10*cos(x35 - x26) =L= 1;
e11.. sqr(x1) + sqr(x11) - 2*x1*x11*cos(x36 - x26) =L= 1;
e12.. sqr(x1) + sqr(x12) - 2*x1*x12*cos(x37 - x26) =L= 1;
e13.. sqr(x1) + sqr(x13) - 2*x1*x13*cos(x38 - x26) =L= 1;
e14.. sqr(x1) + sqr(x14) - 2*x1*x14*cos(x39 - x26) =L= 1;
e15.. sqr(x1) + sqr(x15) - 2*x1*x15*cos(x40 - x26) =L= 1;
e16.. sqr(x1) + sqr(x16) - 2*x1*x16*cos(x41 - x26) =L= 1;
e17.. sqr(x1) + sqr(x17) - 2*x1*x17*cos(x42 - x26) =L= 1;
e18.. sqr(x1) + sqr(x18) - 2*x1*x18*cos(x43 - x26) =L= 1;
e19.. sqr(x1) + sqr(x19) - 2*x1*x19*cos(x44 - x26) =L= 1;
e20.. sqr(x1) + sqr(x20) - 2*x1*x20*cos(x45 - x26) =L= 1;
e21.. sqr(x1) + sqr(x21) - 2*x1*x21*cos(x46 - x26) =L= 1;
e22.. sqr(x1) + sqr(x22) - 2*x1*x22*cos(x47 - x26) =L= 1;
e23.. sqr(x1) + sqr(x23) - 2*x1*x23*cos(x48 - x26) =L= 1;
e24.. sqr(x1) + sqr(x24) - 2*x1*x24*cos(x49 - x26) =L= 1;
e25.. sqr(x1) + sqr(x25) - 2*x1*x25*cos(x50 - x26) =L= 1;
e26.. sqr(x2) + sqr(x3) - 2*x2*x3*cos(x28 - x27) =L= 1;
e27.. sqr(x2) + sqr(x4) - 2*x2*x4*cos(x29 - x27) =L= 1;
e28.. sqr(x2) + sqr(x5) - 2*x2*x5*cos(x30 - x27) =L= 1;
e29.. sqr(x2) + sqr(x6) - 2*x2*x6*cos(x31 - x27) =L= 1;
e30.. sqr(x2) + sqr(x7) - 2*x2*x7*cos(x32 - x27) =L= 1;
e31.. sqr(x2) + sqr(x8) - 2*x2*x8*cos(x33 - x27) =L= 1;
e32.. sqr(x2) + sqr(x9) - 2*x2*x9*cos(x34 - x27) =L= 1;
e33.. sqr(x2) + sqr(x10) - 2*x2*x10*cos(x35 - x27) =L= 1;
e34.. sqr(x2) + sqr(x11) - 2*x2*x11*cos(x36 - x27) =L= 1;
e35.. sqr(x2) + sqr(x12) - 2*x2*x12*cos(x37 - x27) =L= 1;
e36.. sqr(x2) + sqr(x13) - 2*x2*x13*cos(x38 - x27) =L= 1;
e37.. sqr(x2) + sqr(x14) - 2*x2*x14*cos(x39 - x27) =L= 1;
e38.. sqr(x2) + sqr(x15) - 2*x2*x15*cos(x40 - x27) =L= 1;
e39.. sqr(x2) + sqr(x16) - 2*x2*x16*cos(x41 - x27) =L= 1;
e40.. sqr(x2) + sqr(x17) - 2*x2*x17*cos(x42 - x27) =L= 1;
e41.. sqr(x2) + sqr(x18) - 2*x2*x18*cos(x43 - x27) =L= 1;
e42.. sqr(x2) + sqr(x19) - 2*x2*x19*cos(x44 - x27) =L= 1;
e43.. sqr(x2) + sqr(x20) - 2*x2*x20*cos(x45 - x27) =L= 1;
e44.. sqr(x2) + sqr(x21) - 2*x2*x21*cos(x46 - x27) =L= 1;
e45.. sqr(x2) + sqr(x22) - 2*x2*x22*cos(x47 - x27) =L= 1;
e46.. sqr(x2) + sqr(x23) - 2*x2*x23*cos(x48 - x27) =L= 1;
e47.. sqr(x2) + sqr(x24) - 2*x2*x24*cos(x49 - x27) =L= 1;
e48.. sqr(x2) + sqr(x25) - 2*x2*x25*cos(x50 - x27) =L= 1;
e49.. sqr(x3) + sqr(x4) - 2*x3*x4*cos(x29 - x28) =L= 1;
e50.. sqr(x3) + sqr(x5) - 2*x3*x5*cos(x30 - x28) =L= 1;
e51.. sqr(x3) + sqr(x6) - 2*x3*x6*cos(x31 - x28) =L= 1;
e52.. sqr(x3) + sqr(x7) - 2*x3*x7*cos(x32 - x28) =L= 1;
e53.. sqr(x3) + sqr(x8) - 2*x3*x8*cos(x33 - x28) =L= 1;
e54.. sqr(x3) + sqr(x9) - 2*x3*x9*cos(x34 - x28) =L= 1;
e55.. sqr(x3) + sqr(x10) - 2*x3*x10*cos(x35 - x28) =L= 1;
e56.. sqr(x3) + sqr(x11) - 2*x3*x11*cos(x36 - x28) =L= 1;
e57.. sqr(x3) + sqr(x12) - 2*x3*x12*cos(x37 - x28) =L= 1;
e58.. sqr(x3) + sqr(x13) - 2*x3*x13*cos(x38 - x28) =L= 1;
e59.. sqr(x3) + sqr(x14) - 2*x3*x14*cos(x39 - x28) =L= 1;
e60.. sqr(x3) + sqr(x15) - 2*x3*x15*cos(x40 - x28) =L= 1;
e61.. sqr(x3) + sqr(x16) - 2*x3*x16*cos(x41 - x28) =L= 1;
e62.. sqr(x3) + sqr(x17) - 2*x3*x17*cos(x42 - x28) =L= 1;
e63.. sqr(x3) + sqr(x18) - 2*x3*x18*cos(x43 - x28) =L= 1;
e64.. sqr(x3) + sqr(x19) - 2*x3*x19*cos(x44 - x28) =L= 1;
e65.. sqr(x3) + sqr(x20) - 2*x3*x20*cos(x45 - x28) =L= 1;
e66.. sqr(x3) + sqr(x21) - 2*x3*x21*cos(x46 - x28) =L= 1;
e67.. sqr(x3) + sqr(x22) - 2*x3*x22*cos(x47 - x28) =L= 1;
e68.. sqr(x3) + sqr(x23) - 2*x3*x23*cos(x48 - x28) =L= 1;
e69.. sqr(x3) + sqr(x24) - 2*x3*x24*cos(x49 - x28) =L= 1;
e70.. sqr(x3) + sqr(x25) - 2*x3*x25*cos(x50 - x28) =L= 1;
e71.. sqr(x4) + sqr(x5) - 2*x4*x5*cos(x30 - x29) =L= 1;
e72.. sqr(x4) + sqr(x6) - 2*x4*x6*cos(x31 - x29) =L= 1;
e73.. sqr(x4) + sqr(x7) - 2*x4*x7*cos(x32 - x29) =L= 1;
e74.. sqr(x4) + sqr(x8) - 2*x4*x8*cos(x33 - x29) =L= 1;
e75.. sqr(x4) + sqr(x9) - 2*x4*x9*cos(x34 - x29) =L= 1;
e76.. sqr(x4) + sqr(x10) - 2*x4*x10*cos(x35 - x29) =L= 1;
e77.. sqr(x4) + sqr(x11) - 2*x4*x11*cos(x36 - x29) =L= 1;
e78.. sqr(x4) + sqr(x12) - 2*x4*x12*cos(x37 - x29) =L= 1;
e79.. sqr(x4) + sqr(x13) - 2*x4*x13*cos(x38 - x29) =L= 1;
e80.. sqr(x4) + sqr(x14) - 2*x4*x14*cos(x39 - x29) =L= 1;
e81.. sqr(x4) + sqr(x15) - 2*x4*x15*cos(x40 - x29) =L= 1;
e82.. sqr(x4) + sqr(x16) - 2*x4*x16*cos(x41 - x29) =L= 1;
e83.. sqr(x4) + sqr(x17) - 2*x4*x17*cos(x42 - x29) =L= 1;
e84.. sqr(x4) + sqr(x18) - 2*x4*x18*cos(x43 - x29) =L= 1;
e85.. sqr(x4) + sqr(x19) - 2*x4*x19*cos(x44 - x29) =L= 1;
e86.. sqr(x4) + sqr(x20) - 2*x4*x20*cos(x45 - x29) =L= 1;
e87.. sqr(x4) + sqr(x21) - 2*x4*x21*cos(x46 - x29) =L= 1;
e88.. sqr(x4) + sqr(x22) - 2*x4*x22*cos(x47 - x29) =L= 1;
e89.. sqr(x4) + sqr(x23) - 2*x4*x23*cos(x48 - x29) =L= 1;
e90.. sqr(x4) + sqr(x24) - 2*x4*x24*cos(x49 - x29) =L= 1;
e91.. sqr(x4) + sqr(x25) - 2*x4*x25*cos(x50 - x29) =L= 1;
e92.. sqr(x5) + sqr(x6) - 2*x5*x6*cos(x31 - x30) =L= 1;
e93.. sqr(x5) + sqr(x7) - 2*x5*x7*cos(x32 - x30) =L= 1;
e94.. sqr(x5) + sqr(x8) - 2*x5*x8*cos(x33 - x30) =L= 1;
e95.. sqr(x5) + sqr(x9) - 2*x5*x9*cos(x34 - x30) =L= 1;
e96.. sqr(x5) + sqr(x10) - 2*x5*x10*cos(x35 - x30) =L= 1;
e97.. sqr(x5) + sqr(x11) - 2*x5*x11*cos(x36 - x30) =L= 1;
e98.. sqr(x5) + sqr(x12) - 2*x5*x12*cos(x37 - x30) =L= 1;
e99.. sqr(x5) + sqr(x13) - 2*x5*x13*cos(x38 - x30) =L= 1;
e100.. sqr(x5) + sqr(x14) - 2*x5*x14*cos(x39 - x30) =L= 1;
e101.. sqr(x5) + sqr(x15) - 2*x5*x15*cos(x40 - x30) =L= 1;
e102.. sqr(x5) + sqr(x16) - 2*x5*x16*cos(x41 - x30) =L= 1;
e103.. sqr(x5) + sqr(x17) - 2*x5*x17*cos(x42 - x30) =L= 1;
e104.. sqr(x5) + sqr(x18) - 2*x5*x18*cos(x43 - x30) =L= 1;
e105.. sqr(x5) + sqr(x19) - 2*x5*x19*cos(x44 - x30) =L= 1;
e106.. sqr(x5) + sqr(x20) - 2*x5*x20*cos(x45 - x30) =L= 1;
e107.. sqr(x5) + sqr(x21) - 2*x5*x21*cos(x46 - x30) =L= 1;
e108.. sqr(x5) + sqr(x22) - 2*x5*x22*cos(x47 - x30) =L= 1;
e109.. sqr(x5) + sqr(x23) - 2*x5*x23*cos(x48 - x30) =L= 1;
e110.. sqr(x5) + sqr(x24) - 2*x5*x24*cos(x49 - x30) =L= 1;
e111.. sqr(x5) + sqr(x25) - 2*x5*x25*cos(x50 - x30) =L= 1;
e112.. sqr(x6) + sqr(x7) - 2*x6*x7*cos(x32 - x31) =L= 1;
e113.. sqr(x6) + sqr(x8) - 2*x6*x8*cos(x33 - x31) =L= 1;
e114.. sqr(x6) + sqr(x9) - 2*x6*x9*cos(x34 - x31) =L= 1;
e115.. sqr(x6) + sqr(x10) - 2*x6*x10*cos(x35 - x31) =L= 1;
e116.. sqr(x6) + sqr(x11) - 2*x6*x11*cos(x36 - x31) =L= 1;
e117.. sqr(x6) + sqr(x12) - 2*x6*x12*cos(x37 - x31) =L= 1;
e118.. sqr(x6) + sqr(x13) - 2*x6*x13*cos(x38 - x31) =L= 1;
e119.. sqr(x6) + sqr(x14) - 2*x6*x14*cos(x39 - x31) =L= 1;
e120.. sqr(x6) + sqr(x15) - 2*x6*x15*cos(x40 - x31) =L= 1;
e121.. sqr(x6) + sqr(x16) - 2*x6*x16*cos(x41 - x31) =L= 1;
e122.. sqr(x6) + sqr(x17) - 2*x6*x17*cos(x42 - x31) =L= 1;
e123.. sqr(x6) + sqr(x18) - 2*x6*x18*cos(x43 - x31) =L= 1;
e124.. sqr(x6) + sqr(x19) - 2*x6*x19*cos(x44 - x31) =L= 1;
e125.. sqr(x6) + sqr(x20) - 2*x6*x20*cos(x45 - x31) =L= 1;
e126.. sqr(x6) + sqr(x21) - 2*x6*x21*cos(x46 - x31) =L= 1;
e127.. sqr(x6) + sqr(x22) - 2*x6*x22*cos(x47 - x31) =L= 1;
e128.. sqr(x6) + sqr(x23) - 2*x6*x23*cos(x48 - x31) =L= 1;
e129.. sqr(x6) + sqr(x24) - 2*x6*x24*cos(x49 - x31) =L= 1;
e130.. sqr(x6) + sqr(x25) - 2*x6*x25*cos(x50 - x31) =L= 1;
e131.. sqr(x7) + sqr(x8) - 2*x7*x8*cos(x33 - x32) =L= 1;
e132.. sqr(x7) + sqr(x9) - 2*x7*x9*cos(x34 - x32) =L= 1;
e133.. sqr(x7) + sqr(x10) - 2*x7*x10*cos(x35 - x32) =L= 1;
e134.. sqr(x7) + sqr(x11) - 2*x7*x11*cos(x36 - x32) =L= 1;
e135.. sqr(x7) + sqr(x12) - 2*x7*x12*cos(x37 - x32) =L= 1;
e136.. sqr(x7) + sqr(x13) - 2*x7*x13*cos(x38 - x32) =L= 1;
e137.. sqr(x7) + sqr(x14) - 2*x7*x14*cos(x39 - x32) =L= 1;
e138.. sqr(x7) + sqr(x15) - 2*x7*x15*cos(x40 - x32) =L= 1;
e139.. sqr(x7) + sqr(x16) - 2*x7*x16*cos(x41 - x32) =L= 1;
e140.. sqr(x7) + sqr(x17) - 2*x7*x17*cos(x42 - x32) =L= 1;
e141.. sqr(x7) + sqr(x18) - 2*x7*x18*cos(x43 - x32) =L= 1;
e142.. sqr(x7) + sqr(x19) - 2*x7*x19*cos(x44 - x32) =L= 1;
e143.. sqr(x7) + sqr(x20) - 2*x7*x20*cos(x45 - x32) =L= 1;
e144.. sqr(x7) + sqr(x21) - 2*x7*x21*cos(x46 - x32) =L= 1;
e145.. sqr(x7) + sqr(x22) - 2*x7*x22*cos(x47 - x32) =L= 1;
e146.. sqr(x7) + sqr(x23) - 2*x7*x23*cos(x48 - x32) =L= 1;
e147.. sqr(x7) + sqr(x24) - 2*x7*x24*cos(x49 - x32) =L= 1;
e148.. sqr(x7) + sqr(x25) - 2*x7*x25*cos(x50 - x32) =L= 1;
e149.. sqr(x8) + sqr(x9) - 2*x8*x9*cos(x34 - x33) =L= 1;
e150.. sqr(x8) + sqr(x10) - 2*x8*x10*cos(x35 - x33) =L= 1;
e151.. sqr(x8) + sqr(x11) - 2*x8*x11*cos(x36 - x33) =L= 1;
e152.. sqr(x8) + sqr(x12) - 2*x8*x12*cos(x37 - x33) =L= 1;
e153.. sqr(x8) + sqr(x13) - 2*x8*x13*cos(x38 - x33) =L= 1;
e154.. sqr(x8) + sqr(x14) - 2*x8*x14*cos(x39 - x33) =L= 1;
e155.. sqr(x8) + sqr(x15) - 2*x8*x15*cos(x40 - x33) =L= 1;
e156.. sqr(x8) + sqr(x16) - 2*x8*x16*cos(x41 - x33) =L= 1;
e157.. sqr(x8) + sqr(x17) - 2*x8*x17*cos(x42 - x33) =L= 1;
e158.. sqr(x8) + sqr(x18) - 2*x8*x18*cos(x43 - x33) =L= 1;
e159.. sqr(x8) + sqr(x19) - 2*x8*x19*cos(x44 - x33) =L= 1;
e160.. sqr(x8) + sqr(x20) - 2*x8*x20*cos(x45 - x33) =L= 1;
e161.. sqr(x8) + sqr(x21) - 2*x8*x21*cos(x46 - x33) =L= 1;
e162.. sqr(x8) + sqr(x22) - 2*x8*x22*cos(x47 - x33) =L= 1;
e163.. sqr(x8) + sqr(x23) - 2*x8*x23*cos(x48 - x33) =L= 1;
e164.. sqr(x8) + sqr(x24) - 2*x8*x24*cos(x49 - x33) =L= 1;
e165.. sqr(x8) + sqr(x25) - 2*x8*x25*cos(x50 - x33) =L= 1;
e166.. sqr(x9) + sqr(x10) - 2*x9*x10*cos(x35 - x34) =L= 1;
e167.. sqr(x9) + sqr(x11) - 2*x9*x11*cos(x36 - x34) =L= 1;
e168.. sqr(x9) + sqr(x12) - 2*x9*x12*cos(x37 - x34) =L= 1;
e169.. sqr(x9) + sqr(x13) - 2*x9*x13*cos(x38 - x34) =L= 1;
e170.. sqr(x9) + sqr(x14) - 2*x9*x14*cos(x39 - x34) =L= 1;
e171.. sqr(x9) + sqr(x15) - 2*x9*x15*cos(x40 - x34) =L= 1;
e172.. sqr(x9) + sqr(x16) - 2*x9*x16*cos(x41 - x34) =L= 1;
e173.. sqr(x9) + sqr(x17) - 2*x9*x17*cos(x42 - x34) =L= 1;
e174.. sqr(x9) + sqr(x18) - 2*x9*x18*cos(x43 - x34) =L= 1;
e175.. sqr(x9) + sqr(x19) - 2*x9*x19*cos(x44 - x34) =L= 1;
e176.. sqr(x9) + sqr(x20) - 2*x9*x20*cos(x45 - x34) =L= 1;
e177.. sqr(x9) + sqr(x21) - 2*x9*x21*cos(x46 - x34) =L= 1;
e178.. sqr(x9) + sqr(x22) - 2*x9*x22*cos(x47 - x34) =L= 1;
e179.. sqr(x9) + sqr(x23) - 2*x9*x23*cos(x48 - x34) =L= 1;
e180.. sqr(x9) + sqr(x24) - 2*x9*x24*cos(x49 - x34) =L= 1;
e181.. sqr(x9) + sqr(x25) - 2*x9*x25*cos(x50 - x34) =L= 1;
e182.. sqr(x10) + sqr(x11) - 2*x10*x11*cos(x36 - x35) =L= 1;
e183.. sqr(x10) + sqr(x12) - 2*x10*x12*cos(x37 - x35) =L= 1;
e184.. sqr(x10) + sqr(x13) - 2*x10*x13*cos(x38 - x35) =L= 1;
e185.. sqr(x10) + sqr(x14) - 2*x10*x14*cos(x39 - x35) =L= 1;
e186.. sqr(x10) + sqr(x15) - 2*x10*x15*cos(x40 - x35) =L= 1;
e187.. sqr(x10) + sqr(x16) - 2*x10*x16*cos(x41 - x35) =L= 1;
e188.. sqr(x10) + sqr(x17) - 2*x10*x17*cos(x42 - x35) =L= 1;
e189.. sqr(x10) + sqr(x18) - 2*x10*x18*cos(x43 - x35) =L= 1;
e190.. sqr(x10) + sqr(x19) - 2*x10*x19*cos(x44 - x35) =L= 1;
e191.. sqr(x10) + sqr(x20) - 2*x10*x20*cos(x45 - x35) =L= 1;
e192.. sqr(x10) + sqr(x21) - 2*x10*x21*cos(x46 - x35) =L= 1;
e193.. sqr(x10) + sqr(x22) - 2*x10*x22*cos(x47 - x35) =L= 1;
e194.. sqr(x10) + sqr(x23) - 2*x10*x23*cos(x48 - x35) =L= 1;
e195.. sqr(x10) + sqr(x24) - 2*x10*x24*cos(x49 - x35) =L= 1;
e196.. sqr(x10) + sqr(x25) - 2*x10*x25*cos(x50 - x35) =L= 1;
e197.. sqr(x11) + sqr(x12) - 2*x11*x12*cos(x37 - x36) =L= 1;
e198.. sqr(x11) + sqr(x13) - 2*x11*x13*cos(x38 - x36) =L= 1;
e199.. sqr(x11) + sqr(x14) - 2*x11*x14*cos(x39 - x36) =L= 1;
e200.. sqr(x11) + sqr(x15) - 2*x11*x15*cos(x40 - x36) =L= 1;
e201.. sqr(x11) + sqr(x16) - 2*x11*x16*cos(x41 - x36) =L= 1;
e202.. sqr(x11) + sqr(x17) - 2*x11*x17*cos(x42 - x36) =L= 1;
e203.. sqr(x11) + sqr(x18) - 2*x11*x18*cos(x43 - x36) =L= 1;
e204.. sqr(x11) + sqr(x19) - 2*x11*x19*cos(x44 - x36) =L= 1;
e205.. sqr(x11) + sqr(x20) - 2*x11*x20*cos(x45 - x36) =L= 1;
e206.. sqr(x11) + sqr(x21) - 2*x11*x21*cos(x46 - x36) =L= 1;
e207.. sqr(x11) + sqr(x22) - 2*x11*x22*cos(x47 - x36) =L= 1;
e208.. sqr(x11) + sqr(x23) - 2*x11*x23*cos(x48 - x36) =L= 1;
e209.. sqr(x11) + sqr(x24) - 2*x11*x24*cos(x49 - x36) =L= 1;
e210.. sqr(x11) + sqr(x25) - 2*x11*x25*cos(x50 - x36) =L= 1;
e211.. sqr(x12) + sqr(x13) - 2*x12*x13*cos(x38 - x37) =L= 1;
e212.. sqr(x12) + sqr(x14) - 2*x12*x14*cos(x39 - x37) =L= 1;
e213.. sqr(x12) + sqr(x15) - 2*x12*x15*cos(x40 - x37) =L= 1;
e214.. sqr(x12) + sqr(x16) - 2*x12*x16*cos(x41 - x37) =L= 1;
e215.. sqr(x12) + sqr(x17) - 2*x12*x17*cos(x42 - x37) =L= 1;
e216.. sqr(x12) + sqr(x18) - 2*x12*x18*cos(x43 - x37) =L= 1;
e217.. sqr(x12) + sqr(x19) - 2*x12*x19*cos(x44 - x37) =L= 1;
e218.. sqr(x12) + sqr(x20) - 2*x12*x20*cos(x45 - x37) =L= 1;
e219.. sqr(x12) + sqr(x21) - 2*x12*x21*cos(x46 - x37) =L= 1;
e220.. sqr(x12) + sqr(x22) - 2*x12*x22*cos(x47 - x37) =L= 1;
e221.. sqr(x12) + sqr(x23) - 2*x12*x23*cos(x48 - x37) =L= 1;
e222.. sqr(x12) + sqr(x24) - 2*x12*x24*cos(x49 - x37) =L= 1;
e223.. sqr(x12) + sqr(x25) - 2*x12*x25*cos(x50 - x37) =L= 1;
e224.. sqr(x13) + sqr(x14) - 2*x13*x14*cos(x39 - x38) =L= 1;
e225.. sqr(x13) + sqr(x15) - 2*x13*x15*cos(x40 - x38) =L= 1;
e226.. sqr(x13) + sqr(x16) - 2*x13*x16*cos(x41 - x38) =L= 1;
e227.. sqr(x13) + sqr(x17) - 2*x13*x17*cos(x42 - x38) =L= 1;
e228.. sqr(x13) + sqr(x18) - 2*x13*x18*cos(x43 - x38) =L= 1;
e229.. sqr(x13) + sqr(x19) - 2*x13*x19*cos(x44 - x38) =L= 1;
e230.. sqr(x13) + sqr(x20) - 2*x13*x20*cos(x45 - x38) =L= 1;
e231.. sqr(x13) + sqr(x21) - 2*x13*x21*cos(x46 - x38) =L= 1;
e232.. sqr(x13) + sqr(x22) - 2*x13*x22*cos(x47 - x38) =L= 1;
e233.. sqr(x13) + sqr(x23) - 2*x13*x23*cos(x48 - x38) =L= 1;
e234.. sqr(x13) + sqr(x24) - 2*x13*x24*cos(x49 - x38) =L= 1;
e235.. sqr(x13) + sqr(x25) - 2*x13*x25*cos(x50 - x38) =L= 1;
e236.. sqr(x14) + sqr(x15) - 2*x14*x15*cos(x40 - x39) =L= 1;
e237.. sqr(x14) + sqr(x16) - 2*x14*x16*cos(x41 - x39) =L= 1;
e238.. sqr(x14) + sqr(x17) - 2*x14*x17*cos(x42 - x39) =L= 1;
e239.. sqr(x14) + sqr(x18) - 2*x14*x18*cos(x43 - x39) =L= 1;
e240.. sqr(x14) + sqr(x19) - 2*x14*x19*cos(x44 - x39) =L= 1;
e241.. sqr(x14) + sqr(x20) - 2*x14*x20*cos(x45 - x39) =L= 1;
e242.. sqr(x14) + sqr(x21) - 2*x14*x21*cos(x46 - x39) =L= 1;
e243.. sqr(x14) + sqr(x22) - 2*x14*x22*cos(x47 - x39) =L= 1;
e244.. sqr(x14) + sqr(x23) - 2*x14*x23*cos(x48 - x39) =L= 1;
e245.. sqr(x14) + sqr(x24) - 2*x14*x24*cos(x49 - x39) =L= 1;
e246.. sqr(x14) + sqr(x25) - 2*x14*x25*cos(x50 - x39) =L= 1;
e247.. sqr(x15) + sqr(x16) - 2*x15*x16*cos(x41 - x40) =L= 1;
e248.. sqr(x15) + sqr(x17) - 2*x15*x17*cos(x42 - x40) =L= 1;
e249.. sqr(x15) + sqr(x18) - 2*x15*x18*cos(x43 - x40) =L= 1;
e250.. sqr(x15) + sqr(x19) - 2*x15*x19*cos(x44 - x40) =L= 1;
e251.. sqr(x15) + sqr(x20) - 2*x15*x20*cos(x45 - x40) =L= 1;
e252.. sqr(x15) + sqr(x21) - 2*x15*x21*cos(x46 - x40) =L= 1;
e253.. sqr(x15) + sqr(x22) - 2*x15*x22*cos(x47 - x40) =L= 1;
e254.. sqr(x15) + sqr(x23) - 2*x15*x23*cos(x48 - x40) =L= 1;
e255.. sqr(x15) + sqr(x24) - 2*x15*x24*cos(x49 - x40) =L= 1;
e256.. sqr(x15) + sqr(x25) - 2*x15*x25*cos(x50 - x40) =L= 1;
e257.. sqr(x16) + sqr(x17) - 2*x16*x17*cos(x42 - x41) =L= 1;
e258.. sqr(x16) + sqr(x18) - 2*x16*x18*cos(x43 - x41) =L= 1;
e259.. sqr(x16) + sqr(x19) - 2*x16*x19*cos(x44 - x41) =L= 1;
e260.. sqr(x16) + sqr(x20) - 2*x16*x20*cos(x45 - x41) =L= 1;
e261.. sqr(x16) + sqr(x21) - 2*x16*x21*cos(x46 - x41) =L= 1;
e262.. sqr(x16) + sqr(x22) - 2*x16*x22*cos(x47 - x41) =L= 1;
e263.. sqr(x16) + sqr(x23) - 2*x16*x23*cos(x48 - x41) =L= 1;
e264.. sqr(x16) + sqr(x24) - 2*x16*x24*cos(x49 - x41) =L= 1;
e265.. sqr(x16) + sqr(x25) - 2*x16*x25*cos(x50 - x41) =L= 1;
e266.. sqr(x17) + sqr(x18) - 2*x17*x18*cos(x43 - x42) =L= 1;
e267.. sqr(x17) + sqr(x19) - 2*x17*x19*cos(x44 - x42) =L= 1;
e268.. sqr(x17) + sqr(x20) - 2*x17*x20*cos(x45 - x42) =L= 1;
e269.. sqr(x17) + sqr(x21) - 2*x17*x21*cos(x46 - x42) =L= 1;
e270.. sqr(x17) + sqr(x22) - 2*x17*x22*cos(x47 - x42) =L= 1;
e271.. sqr(x17) + sqr(x23) - 2*x17*x23*cos(x48 - x42) =L= 1;
e272.. sqr(x17) + sqr(x24) - 2*x17*x24*cos(x49 - x42) =L= 1;
e273.. sqr(x17) + sqr(x25) - 2*x17*x25*cos(x50 - x42) =L= 1;
e274.. sqr(x18) + sqr(x19) - 2*x18*x19*cos(x44 - x43) =L= 1;
e275.. sqr(x18) + sqr(x20) - 2*x18*x20*cos(x45 - x43) =L= 1;
e276.. sqr(x18) + sqr(x21) - 2*x18*x21*cos(x46 - x43) =L= 1;
e277.. sqr(x18) + sqr(x22) - 2*x18*x22*cos(x47 - x43) =L= 1;
e278.. sqr(x18) + sqr(x23) - 2*x18*x23*cos(x48 - x43) =L= 1;
e279.. sqr(x18) + sqr(x24) - 2*x18*x24*cos(x49 - x43) =L= 1;
e280.. sqr(x18) + sqr(x25) - 2*x18*x25*cos(x50 - x43) =L= 1;
e281.. sqr(x19) + sqr(x20) - 2*x19*x20*cos(x45 - x44) =L= 1;
e282.. sqr(x19) + sqr(x21) - 2*x19*x21*cos(x46 - x44) =L= 1;
e283.. sqr(x19) + sqr(x22) - 2*x19*x22*cos(x47 - x44) =L= 1;
e284.. sqr(x19) + sqr(x23) - 2*x19*x23*cos(x48 - x44) =L= 1;
e285.. sqr(x19) + sqr(x24) - 2*x19*x24*cos(x49 - x44) =L= 1;
e286.. sqr(x19) + sqr(x25) - 2*x19*x25*cos(x50 - x44) =L= 1;
e287.. sqr(x20) + sqr(x21) - 2*x20*x21*cos(x46 - x45) =L= 1;
e288.. sqr(x20) + sqr(x22) - 2*x20*x22*cos(x47 - x45) =L= 1;
e289.. sqr(x20) + sqr(x23) - 2*x20*x23*cos(x48 - x45) =L= 1;
e290.. sqr(x20) + sqr(x24) - 2*x20*x24*cos(x49 - x45) =L= 1;
e291.. sqr(x20) + sqr(x25) - 2*x20*x25*cos(x50 - x45) =L= 1;
e292.. sqr(x21) + sqr(x22) - 2*x21*x22*cos(x47 - x46) =L= 1;
e293.. sqr(x21) + sqr(x23) - 2*x21*x23*cos(x48 - x46) =L= 1;
e294.. sqr(x21) + sqr(x24) - 2*x21*x24*cos(x49 - x46) =L= 1;
e295.. sqr(x21) + sqr(x25) - 2*x21*x25*cos(x50 - x46) =L= 1;
e296.. sqr(x22) + sqr(x23) - 2*x22*x23*cos(x48 - x47) =L= 1;
e297.. sqr(x22) + sqr(x24) - 2*x22*x24*cos(x49 - x47) =L= 1;
e298.. sqr(x22) + sqr(x25) - 2*x22*x25*cos(x50 - x47) =L= 1;
e299.. sqr(x23) + sqr(x24) - 2*x23*x24*cos(x49 - x48) =L= 1;
e300.. sqr(x23) + sqr(x25) - 2*x23*x25*cos(x50 - x48) =L= 1;
e301.. sqr(x24) + sqr(x25) - 2*x24*x25*cos(x50 - x49) =L= 1;
e302.. x26 - x27 =L= 0;
e303.. x27 - x28 =L= 0;
e304.. x28 - x29 =L= 0;
e305.. x29 - x30 =L= 0;
e306.. x30 - x31 =L= 0;
e307.. x31 - x32 =L= 0;
e308.. x32 - x33 =L= 0;
e309.. x33 - x34 =L= 0;
e310.. x34 - x35 =L= 0;
e311.. x35 - x36 =L= 0;
e312.. x36 - x37 =L= 0;
e313.. x37 - x38 =L= 0;
e314.. x38 - x39 =L= 0;
e315.. x39 - x40 =L= 0;
e316.. x40 - x41 =L= 0;
e317.. x41 - x42 =L= 0;
e318.. x42 - x43 =L= 0;
e319.. x43 - x44 =L= 0;
e320.. x44 - x45 =L= 0;
e321.. x45 - x46 =L= 0;
e322.. x46 - x47 =L= 0;
e323.. x47 - x48 =L= 0;
e324.. x48 - x49 =L= 0;
e325.. x49 - x50 =L= 0;
* set non-default bounds
x1.up = 1;
x2.up = 1;
x3.up = 1;
x4.up = 1;
x5.up = 1;
x6.up = 1;
x7.up = 1;
x8.up = 1;
x9.up = 1;
x10.up = 1;
x11.up = 1;
x12.up = 1;
x13.up = 1;
x14.up = 1;
x15.up = 1;
x16.up = 1;
x17.up = 1;
x18.up = 1;
x19.up = 1;
x20.up = 1;
x21.up = 1;
x22.up = 1;
x23.up = 1;
x24.up = 1;
x25.fx = 0;
x26.up = 3.14159265358979;
x27.up = 3.14159265358979;
x28.up = 3.14159265358979;
x29.up = 3.14159265358979;
x30.up = 3.14159265358979;
x31.up = 3.14159265358979;
x32.up = 3.14159265358979;
x33.up = 3.14159265358979;
x34.up = 3.14159265358979;
x35.up = 3.14159265358979;
x36.up = 3.14159265358979;
x37.up = 3.14159265358979;
x38.up = 3.14159265358979;
x39.up = 3.14159265358979;
x40.up = 3.14159265358979;
x41.up = 3.14159265358979;
x42.up = 3.14159265358979;
x43.up = 3.14159265358979;
x44.up = 3.14159265358979;
x45.up = 3.14159265358979;
x46.up = 3.14159265358979;
x47.up = 3.14159265358979;
x48.up = 3.14159265358979;
x49.up = 3.14159265358979;
x50.fx = 3.14159265358979;
* set non-default levels
x1.l = 0.14792899408284;
x2.l = 0.284023668639053;
x3.l = 0.408284023668639;
x4.l = 0.520710059171598;
x5.l = 0.621301775147929;
x6.l = 0.710059171597633;
x7.l = 0.78698224852071;
x8.l = 0.85207100591716;
x9.l = 0.905325443786982;
x10.l = 0.946745562130177;
x11.l = 0.976331360946746;
x12.l = 0.994082840236686;
x13.l = 1;
x14.l = 0.994082840236686;
x15.l = 0.976331360946746;
x16.l = 0.946745562130177;
x17.l = 0.905325443786982;
x18.l = 0.85207100591716;
x19.l = 0.78698224852071;
x20.l = 0.710059171597633;
x21.l = 0.621301775147929;
x22.l = 0.520710059171598;
x23.l = 0.408284023668639;
x24.l = 0.284023668639053;
x26.l = 0.125663706143592;
x27.l = 0.251327412287183;
x28.l = 0.376991118430775;
x29.l = 0.502654824574367;
x30.l = 0.628318530717959;
x31.l = 0.75398223686155;
x32.l = 0.879645943005142;
x33.l = 1.00530964914873;
x34.l = 1.13097335529233;
x35.l = 1.25663706143592;
x36.l = 1.38230076757951;
x37.l = 1.5079644737231;
x38.l = 1.63362817986669;
x39.l = 1.75929188601028;
x40.l = 1.88495559215388;
x41.l = 2.01061929829747;
x42.l = 2.13628300444106;
x43.l = 2.26194671058465;
x44.l = 2.38761041672824;
x45.l = 2.51327412287183;
x46.l = 2.63893782901543;
x47.l = 2.76460153515902;
x48.l = 2.89026524130261;
x49.l = 3.0159289474462;
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