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Instance transswitch0014p
Optimal Transmission Switching problem modeled using trigonometric functions (polar coordinates)
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 0.00000000 (COUENNE) 7622.89441200 (GUROBI) 0.00000000 (LINDO) 0.00000000 (SCIP) 0.00000000 (SHOT) 0.00000001 (XPRESS) |
| Referencesⓘ | Hijazi, H L, Coffrin, C, and Van Hentenryck, P, Convex Quadratic Relaxations of Nonlinear Programs in Power Systems, Tech. Rep. 2013-09, Optimization Online, 2013. |
| Applicationⓘ | Electricity Networks |
| Added to libraryⓘ | 11 Mar 2014 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 138 |
| #Binary Variablesⓘ | 20 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 133 |
| #Nonlinear Binary Variablesⓘ | 20 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | quadratic |
| Objective curvatureⓘ | convex |
| #Nonzeros in Objectiveⓘ | 5 |
| #Nonlinear Nonzeros in Objectiveⓘ | 5 |
| #Constraintsⓘ | 277 |
| #Linear Constraintsⓘ | 157 |
| #Quadratic Constraintsⓘ | 40 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 80 |
| Operands in Gen. Nonlin. Functionsⓘ | cos mul sin sqr |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 859 |
| #Nonlinear Nonzeros in Jacobianⓘ | 480 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 461 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 113 |
| #Blocks in Hessian of Lagrangianⓘ | 86 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 1 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 48 |
| Average blocksize in Hessian of Lagrangianⓘ | 1.546512 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e+00 |
| Maximal coefficientⓘ | 4.0000e+03 |
| Infeasibility of initial pointⓘ | 0.942 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 278 110 64 104 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 139 119 20 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 865 380 485 0
*
* Solve m using MINLP 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,x103
,x104,x105,x106,x107,x108,b109,b110,b111,b112,b113,b114,b115,b116
,b117,b118,b119,b120,b121,b122,b123,b124,b125,b126,b127,b128,x129
,x130,x131,x132,x133,x134,x135,x136,x137,x138,objvar;
Binary Variables b109,b110,b111,b112,b113,b114,b115,b116,b117,b118,b119,b120
,b121,b122,b123,b124,b125,b126,b127,b128;
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;
e1.. 430.293*sqr(x129) + 2000*x129 + 2500*sqr(x130) + 2000*x130 + 100*sqr(x131)
+ 4000*x131 + 100*sqr(x132) + 4000*x132 + 100*sqr(x133) + 4000*x133
- objvar =E= 0;
e2.. -(1.1350191923074*sqr(x2) - 1.1350191923074*x2*x3*cos(x96 - x97) +
4.78186315175772*x2*x3*sin(x96 - x97))*b109 + x15 =E= 0;
e3.. -(1.1350191923074*sqr(x3) - 1.1350191923074*x3*x2*cos(x97 - x96) +
4.78186315175772*x3*x2*sin(x97 - x96))*b109 + x16 =E= 0;
e4.. -9.09008271975275*x7*x9*sin(x101 - x103)*b110 + x17 =E= 0;
e5.. -9.09008271975275*x9*x7*sin(x103 - x101)*b110 + x18 =E= 0;
e6.. -(1.8808847537004*sqr(x10) - 1.8808847537004*x10*x11*cos(x104 - x105) +
4.40294374946052*x10*x11*sin(x104 - x105))*b111 + x19 =E= 0;
e7.. -(1.8808847537004*sqr(x11) - 1.8808847537004*x11*x10*cos(x105 - x104) +
4.40294374946052*x11*x10*sin(x105 - x104))*b111 + x20 =E= 0;
e8.. -4.78194338179036*x4*x7*sin(x98 - x101)*b112 + x21 =E= 0;
e9.. -4.78194338179036*x7*x4*sin(x101 - x98)*b112 + x22 =E= 0;
e10.. -3.96793905245615*x5*x6*sin(x99 - x100)*b113 + x23 =E= 0;
e11.. -3.96793905245615*x6*x5*sin(x100 - x99)*b113 + x24 =E= 0;
e12.. -(1.42400548701993*sqr(x9) - 1.42400548701993*x9*x14*cos(x103 - x108) +
3.0290504569306*x9*x14*sin(x103 - x108))*b114 + x25 =E= 0;
e13.. -(1.42400548701993*sqr(x14) - 1.42400548701993*x14*x9*cos(x108 - x103) +
3.0290504569306*x14*x9*sin(x108 - x103))*b114 + x26 =E= 0;
e14.. -(6.84098066149567*sqr(x4) - 6.84098066149567*x4*x5*cos(x98 - x99) +
21.5785539816916*x4*x5*sin(x98 - x99))*b115 + x27 =E= 0;
e15.. -(6.84098066149567*sqr(x5) - 6.84098066149567*x5*x4*cos(x99 - x98) +
21.5785539816916*x5*x4*sin(x99 - x98))*b115 + x28 =E= 0;
e16.. -(3.09892740383799*sqr(x6) - 3.09892740383799*x6*x13*cos(x100 - x107) +
6.10275544819311*x6*x13*sin(x100 - x107))*b116 + x29 =E= 0;
e17.. -(3.09892740383799*sqr(x13) - 3.09892740383799*x13*x6*cos(x107 - x100) +
6.10275544819311*x13*x6*sin(x107 - x100))*b116 + x30 =E= 0;
e18.. -5.67697984672154*x7*x8*sin(x101 - x102)*b117 + x31 =E= 0;
e19.. -5.67697984672154*x8*x7*sin(x102 - x101)*b117 + x32 =E= 0;
e20.. -(1.13699415780633*sqr(x13) - 1.13699415780633*x13*x14*cos(x107 - x108)
+ 2.31496347510535*x13*x14*sin(x107 - x108))*b118 + x33 =E= 0;
e21.. -(1.13699415780633*sqr(x14) - 1.13699415780633*x14*x13*cos(x108 - x107)
+ 2.31496347510535*x14*x13*sin(x108 - x107))*b118 + x34 =E= 0;
e22.. -(1.52596744045097*sqr(x6) - 1.52596744045097*x6*x12*cos(x100 - x106) +
3.1759639650294*x6*x12*sin(x100 - x106))*b119 + x35 =E= 0;
e23.. -(1.52596744045097*sqr(x12) - 1.52596744045097*x12*x6*cos(x106 - x100) +
3.1759639650294*x12*x6*sin(x106 - x100))*b119 + x36 =E= 0;
e24.. -(1.95502856317726*sqr(x6) - 1.95502856317726*x6*x11*cos(x100 - x105) +
4.09407434424044*x6*x11*sin(x100 - x105))*b120 + x37 =E= 0;
e25.. -(1.95502856317726*sqr(x11) - 1.95502856317726*x11*x6*cos(x105 - x100) +
4.09407434424044*x11*x6*sin(x105 - x100))*b120 + x38 =E= 0;
e26.. -(2.48902458682192*sqr(x12) - 2.48902458682192*x12*x13*cos(x106 - x107)
+ 2.25197462617221*x12*x13*sin(x106 - x107))*b121 + x39 =E= 0;
e27.. -(2.48902458682192*sqr(x13) - 2.48902458682192*x13*x12*cos(x107 - x106)
+ 2.25197462617221*x13*x12*sin(x107 - x106))*b121 + x40 =E= 0;
e28.. -(1.02589745497019*sqr(x1) - 1.02589745497019*x1*x5*cos(x95 - x99) +
4.23498368233483*x1*x5*sin(x95 - x99))*b122 + x41 =E= 0;
e29.. -(1.02589745497019*sqr(x5) - 1.02589745497019*x5*x1*cos(x99 - x95) +
4.23498368233483*x5*x1*sin(x99 - x95))*b122 + x42 =E= 0;
e30.. -(3.90204955244743*sqr(x9) - 3.90204955244743*x9*x10*cos(x103 - x104) +
10.3653941270609*x9*x10*sin(x103 - x104))*b123 + x43 =E= 0;
e31.. -(3.90204955244743*sqr(x10) - 3.90204955244743*x10*x9*cos(x104 - x103) +
10.3653941270609*x10*x9*sin(x104 - x103))*b123 + x44 =E= 0;
e32.. -(4.99913160079803*sqr(x1) - 4.99913160079803*x1*x2*cos(x95 - x96) +
15.2630865231796*x1*x2*sin(x95 - x96))*b124 + x45 =E= 0;
e33.. -(4.99913160079803*sqr(x2) - 4.99913160079803*x2*x1*cos(x96 - x95) +
15.2630865231796*x2*x1*sin(x96 - x95))*b124 + x46 =E= 0;
e34.. -(1.7011396670944*sqr(x2) - 1.7011396670944*x2*x5*cos(x96 - x99) +
5.19392739796971*x2*x5*sin(x96 - x99))*b125 + x47 =E= 0;
e35.. -(1.7011396670944*sqr(x5) - 1.7011396670944*x5*x2*cos(x99 - x96) +
5.19392739796971*x5*x2*sin(x99 - x96))*b125 + x48 =E= 0;
e36.. -(1.98597570992556*sqr(x3) - 1.98597570992556*x3*x4*cos(x97 - x98) +
5.06881697759392*x3*x4*sin(x97 - x98))*b126 + x49 =E= 0;
e37.. -(1.98597570992556*sqr(x4) - 1.98597570992556*x4*x3*cos(x98 - x97) +
5.06881697759392*x4*x3*sin(x98 - x97))*b126 + x50 =E= 0;
e38.. -1.79797907152361*x4*x9*sin(x98 - x103)*b127 + x51 =E= 0;
e39.. -1.79797907152361*x9*x4*sin(x103 - x98)*b127 + x52 =E= 0;
e40.. -(1.68603315061494*sqr(x2) - 1.68603315061494*x2*x4*cos(x96 - x98) +
5.11583832587208*x2*x4*sin(x96 - x98))*b128 + x53 =E= 0;
e41.. -(1.68603315061494*sqr(x4) - 1.68603315061494*x4*x2*cos(x98 - x96) +
5.11583832587208*x4*x2*sin(x98 - x96))*b128 + x54 =E= 0;
e42.. -(4.75996315175772*sqr(x2) - 4.78186315175772*x2*x3*cos(x96 - x97) -
1.1350191923074*x2*x3*sin(x96 - x97))*b109 + x55 =E= 0;
e43.. -(4.75996315175772*sqr(x3) - 4.78186315175772*x3*x2*cos(x97 - x96) -
1.1350191923074*x3*x2*sin(x97 - x96))*b109 + x56 =E= 0;
e44.. -(9.09008271975275*sqr(x7) - 9.09008271975275*x7*x9*cos(x101 - x103))*
b110 + x57 =E= 0;
e45.. -(9.09008271975275*sqr(x9) - 9.09008271975275*x9*x7*cos(x103 - x101))*
b110 + x58 =E= 0;
e46.. -(4.40294374946052*sqr(x10) - 4.40294374946052*x10*x11*cos(x104 - x105)
- 1.8808847537004*x10*x11*sin(x104 - x105))*b111 + x59 =E= 0;
e47.. -(4.40294374946052*sqr(x11) - 4.40294374946052*x11*x10*cos(x105 - x104)
- 1.8808847537004*x11*x10*sin(x105 - x104))*b111 + x60 =E= 0;
e48.. -(4.78194338179036*sqr(x4) - 4.78194338179036*x4*x7*cos(x98 - x101))*b112
+ x61 =E= 0;
e49.. -(4.78194338179036*sqr(x7) - 4.78194338179036*x7*x4*cos(x101 - x98))*b112
+ x62 =E= 0;
e50.. -(3.96793905245615*sqr(x5) - 3.96793905245615*x5*x6*cos(x99 - x100))*b113
+ x63 =E= 0;
e51.. -(3.96793905245615*sqr(x6) - 3.96793905245615*x6*x5*cos(x100 - x99))*b113
+ x64 =E= 0;
e52.. -(3.0290504569306*sqr(x9) - 3.0290504569306*x9*x14*cos(x103 - x108) -
1.42400548701993*x9*x14*sin(x103 - x108))*b114 + x65 =E= 0;
e53.. -(3.0290504569306*sqr(x14) - 3.0290504569306*x14*x9*cos(x108 - x103) -
1.42400548701993*x14*x9*sin(x108 - x103))*b114 + x66 =E= 0;
e54.. -(21.5785539816916*sqr(x4) - 21.5785539816916*x4*x5*cos(x98 - x99) -
6.84098066149567*x4*x5*sin(x98 - x99))*b115 + x67 =E= 0;
e55.. -(21.5785539816916*sqr(x5) - 21.5785539816916*x5*x4*cos(x99 - x98) -
6.84098066149567*x5*x4*sin(x99 - x98))*b115 + x68 =E= 0;
e56.. -(6.10275544819311*sqr(x6) - 6.10275544819311*x6*x13*cos(x100 - x107) -
3.09892740383799*x6*x13*sin(x100 - x107))*b116 + x69 =E= 0;
e57.. -(6.10275544819311*sqr(x13) - 6.10275544819311*x13*x6*cos(x107 - x100) -
3.09892740383799*x13*x6*sin(x107 - x100))*b116 + x70 =E= 0;
e58.. -(5.67697984672154*sqr(x7) - 5.67697984672154*x7*x8*cos(x101 - x102))*
b117 + x71 =E= 0;
e59.. -(5.67697984672154*sqr(x8) - 5.67697984672154*x8*x7*cos(x102 - x101))*
b117 + x72 =E= 0;
e60.. -(2.31496347510535*sqr(x13) - 2.31496347510535*x13*x14*cos(x107 - x108)
- 1.13699415780633*x13*x14*sin(x107 - x108))*b118 + x73 =E= 0;
e61.. -(2.31496347510535*sqr(x14) - 2.31496347510535*x14*x13*cos(x108 - x107)
- 1.13699415780633*x14*x13*sin(x108 - x107))*b118 + x74 =E= 0;
e62.. -(3.1759639650294*sqr(x6) - 3.1759639650294*x6*x12*cos(x100 - x106) -
1.52596744045097*x6*x12*sin(x100 - x106))*b119 + x75 =E= 0;
e63.. -(3.1759639650294*sqr(x12) - 3.1759639650294*x12*x6*cos(x106 - x100) -
1.52596744045097*x12*x6*sin(x106 - x100))*b119 + x76 =E= 0;
e64.. -(4.09407434424044*sqr(x6) - 4.09407434424044*x6*x11*cos(x100 - x105) -
1.95502856317726*x6*x11*sin(x100 - x105))*b120 + x77 =E= 0;
e65.. -(4.09407434424044*sqr(x11) - 4.09407434424044*x11*x6*cos(x105 - x100) -
1.95502856317726*x11*x6*sin(x105 - x100))*b120 + x78 =E= 0;
e66.. -(2.25197462617221*sqr(x12) - 2.25197462617221*x12*x13*cos(x106 - x107)
- 2.48902458682192*x12*x13*sin(x106 - x107))*b121 + x79 =E= 0;
e67.. -(2.25197462617221*sqr(x13) - 2.25197462617221*x13*x12*cos(x107 - x106)
- 2.48902458682192*x13*x12*sin(x107 - x106))*b121 + x80 =E= 0;
e68.. -(4.21038368233483*sqr(x1) - 4.23498368233483*x1*x5*cos(x95 - x99) -
1.02589745497019*x1*x5*sin(x95 - x99))*b122 + x81 =E= 0;
e69.. -(4.21038368233483*sqr(x5) - 4.23498368233483*x5*x1*cos(x99 - x95) -
1.02589745497019*x5*x1*sin(x99 - x95))*b122 + x82 =E= 0;
e70.. -(10.3653941270609*sqr(x9) - 10.3653941270609*x9*x10*cos(x103 - x104) -
3.90204955244743*x9*x10*sin(x103 - x104))*b123 + x83 =E= 0;
e71.. -(10.3653941270609*sqr(x10) - 10.3653941270609*x10*x9*cos(x104 - x103) -
3.90204955244743*x10*x9*sin(x104 - x103))*b123 + x84 =E= 0;
e72.. -(15.2366865231796*sqr(x1) - 15.2630865231796*x1*x2*cos(x95 - x96) -
4.99913160079803*x1*x2*sin(x95 - x96))*b124 + x85 =E= 0;
e73.. -(15.2366865231796*sqr(x2) - 15.2630865231796*x2*x1*cos(x96 - x95) -
4.99913160079803*x2*x1*sin(x96 - x95))*b124 + x86 =E= 0;
e74.. -(5.17662739796971*sqr(x2) - 5.19392739796971*x2*x5*cos(x96 - x99) -
1.7011396670944*x2*x5*sin(x96 - x99))*b125 + x87 =E= 0;
e75.. -(5.17662739796971*sqr(x5) - 5.19392739796971*x5*x2*cos(x99 - x96) -
1.7011396670944*x5*x2*sin(x99 - x96))*b125 + x88 =E= 0;
e76.. -(5.06241697759392*sqr(x3) - 5.06881697759392*x3*x4*cos(x97 - x98) -
1.98597570992556*x3*x4*sin(x97 - x98))*b126 + x89 =E= 0;
e77.. -(5.06241697759392*sqr(x4) - 5.06881697759392*x4*x3*cos(x98 - x97) -
1.98597570992556*x4*x3*sin(x98 - x97))*b126 + x90 =E= 0;
e78.. -(1.79797907152361*sqr(x4) - 1.79797907152361*x4*x9*cos(x98 - x103))*b127
+ x91 =E= 0;
e79.. -(1.79797907152361*sqr(x9) - 1.79797907152361*x9*x4*cos(x103 - x98))*b127
+ x92 =E= 0;
e80.. -(5.09883832587208*sqr(x2) - 5.11583832587208*x2*x4*cos(x96 - x98) -
1.68603315061494*x2*x4*sin(x96 - x98))*b128 + x93 =E= 0;
e81.. -(5.09883832587208*sqr(x4) - 5.11583832587208*x4*x2*cos(x98 - x96) -
1.68603315061494*x4*x2*sin(x98 - x96))*b128 + x94 =E= 0;
e82.. sqr(x15) + sqr(x55) =L= 9801;
e83.. sqr(x16) + sqr(x56) =L= 9801;
e84.. sqr(x17) + sqr(x57) =L= 9801;
e85.. sqr(x18) + sqr(x58) =L= 9801;
e86.. sqr(x19) + sqr(x59) =L= 9801;
e87.. sqr(x20) + sqr(x60) =L= 9801;
e88.. sqr(x21) + sqr(x61) =L= 9801;
e89.. sqr(x22) + sqr(x62) =L= 9801;
e90.. sqr(x23) + sqr(x63) =L= 9801;
e91.. sqr(x24) + sqr(x64) =L= 9801;
e92.. sqr(x25) + sqr(x65) =L= 9801;
e93.. sqr(x26) + sqr(x66) =L= 9801;
e94.. sqr(x27) + sqr(x67) =L= 9801;
e95.. sqr(x28) + sqr(x68) =L= 9801;
e96.. sqr(x29) + sqr(x69) =L= 9801;
e97.. sqr(x30) + sqr(x70) =L= 9801;
e98.. sqr(x31) + sqr(x71) =L= 9801;
e99.. sqr(x32) + sqr(x72) =L= 9801;
e100.. sqr(x33) + sqr(x73) =L= 9801;
e101.. sqr(x34) + sqr(x74) =L= 9801;
e102.. sqr(x35) + sqr(x75) =L= 9801;
e103.. sqr(x36) + sqr(x76) =L= 9801;
e104.. sqr(x37) + sqr(x77) =L= 9801;
e105.. sqr(x38) + sqr(x78) =L= 9801;
e106.. sqr(x39) + sqr(x79) =L= 9801;
e107.. sqr(x40) + sqr(x80) =L= 9801;
e108.. sqr(x41) + sqr(x81) =L= 9801;
e109.. sqr(x42) + sqr(x82) =L= 9801;
e110.. sqr(x43) + sqr(x83) =L= 9801;
e111.. sqr(x44) + sqr(x84) =L= 9801;
e112.. sqr(x45) + sqr(x85) =L= 9801;
e113.. sqr(x46) + sqr(x86) =L= 9801;
e114.. sqr(x47) + sqr(x87) =L= 9801;
e115.. sqr(x48) + sqr(x88) =L= 9801;
e116.. sqr(x49) + sqr(x89) =L= 9801;
e117.. sqr(x50) + sqr(x90) =L= 9801;
e118.. sqr(x51) + sqr(x91) =L= 9801;
e119.. sqr(x52) + sqr(x92) =L= 9801;
e120.. sqr(x53) + sqr(x93) =L= 9801;
e121.. sqr(x54) + sqr(x94) =L= 9801;
e122.. x129 =L= 3.324;
e123.. x130 =L= 1.4;
e124.. x131 =L= 1;
e125.. x132 =L= 1;
e126.. x133 =L= 1;
e127.. x129 =G= 0;
e128.. x130 =G= 0;
e129.. x131 =G= 0;
e130.. x132 =G= 0;
e131.. x133 =G= 0;
e132.. x134 =L= 0.1;
e133.. x135 =L= 0.5;
e134.. x136 =L= 0.4;
e135.. x137 =L= 0.24;
e136.. x138 =L= 0.24;
e137.. x134 =G= 0;
e138.. x135 =G= -0.4;
e139.. x136 =G= 0;
e140.. x137 =G= -0.06;
e141.. x138 =G= -0.06;
e142.. x1 =L= 1.06;
e143.. x2 =L= 1.06;
e144.. x3 =L= 1.06;
e145.. x4 =L= 1.06;
e146.. x5 =L= 1.06;
e147.. x6 =L= 1.06;
e148.. x7 =L= 1.06;
e149.. x8 =L= 1.06;
e150.. x9 =L= 1.06;
e151.. x10 =L= 1.06;
e152.. x11 =L= 1.06;
e153.. x12 =L= 1.06;
e154.. x13 =L= 1.06;
e155.. x14 =L= 1.06;
e156.. x1 =G= 0.94;
e157.. x2 =G= 0.94;
e158.. x3 =G= 0.94;
e159.. x4 =G= 0.94;
e160.. x5 =G= 0.94;
e161.. x6 =G= 0.94;
e162.. x7 =G= 0.94;
e163.. x8 =G= 0.94;
e164.. x9 =G= 0.94;
e165.. x10 =G= 0.94;
e166.. x11 =G= 0.94;
e167.. x12 =G= 0.94;
e168.. x13 =G= 0.94;
e169.. x14 =G= 0.94;
e170.. x96 - x97 =G= -0.26;
e171.. - x96 + x97 =G= -0.26;
e172.. x101 - x103 =G= -0.26;
e173.. - x101 + x103 =G= -0.26;
e174.. x104 - x105 =G= -0.26;
e175.. - x104 + x105 =G= -0.26;
e176.. x98 - x101 =G= -0.26;
e177.. - x98 + x101 =G= -0.26;
e178.. x99 - x100 =G= -0.26;
e179.. - x99 + x100 =G= -0.26;
e180.. x103 - x108 =G= -0.26;
e181.. - x103 + x108 =G= -0.26;
e182.. x98 - x99 =G= -0.26;
e183.. - x98 + x99 =G= -0.26;
e184.. x100 - x107 =G= -0.26;
e185.. - x100 + x107 =G= -0.26;
e186.. x101 - x102 =G= -0.26;
e187.. - x101 + x102 =G= -0.26;
e188.. x107 - x108 =G= -0.26;
e189.. - x107 + x108 =G= -0.26;
e190.. x100 - x106 =G= -0.26;
e191.. - x100 + x106 =G= -0.26;
e192.. x100 - x105 =G= -0.26;
e193.. - x100 + x105 =G= -0.26;
e194.. x106 - x107 =G= -0.26;
e195.. - x106 + x107 =G= -0.26;
e196.. x95 - x99 =G= -0.26;
e197.. - x95 + x99 =G= -0.26;
e198.. x103 - x104 =G= -0.26;
e199.. - x103 + x104 =G= -0.26;
e200.. x95 - x96 =G= -0.26;
e201.. - x95 + x96 =G= -0.26;
e202.. x96 - x99 =G= -0.26;
e203.. - x96 + x99 =G= -0.26;
e204.. x97 - x98 =G= -0.26;
e205.. - x97 + x98 =G= -0.26;
e206.. x98 - x103 =G= -0.26;
e207.. - x98 + x103 =G= -0.26;
e208.. x96 - x98 =G= -0.26;
e209.. - x96 + x98 =G= -0.26;
e210.. x96 - x97 =L= 0.26;
e211.. - x96 + x97 =L= 0.26;
e212.. x101 - x103 =L= 0.26;
e213.. - x101 + x103 =L= 0.26;
e214.. x104 - x105 =L= 0.26;
e215.. - x104 + x105 =L= 0.26;
e216.. x98 - x101 =L= 0.26;
e217.. - x98 + x101 =L= 0.26;
e218.. x99 - x100 =L= 0.26;
e219.. - x99 + x100 =L= 0.26;
e220.. x103 - x108 =L= 0.26;
e221.. - x103 + x108 =L= 0.26;
e222.. x98 - x99 =L= 0.26;
e223.. - x98 + x99 =L= 0.26;
e224.. x100 - x107 =L= 0.26;
e225.. - x100 + x107 =L= 0.26;
e226.. x101 - x102 =L= 0.26;
e227.. - x101 + x102 =L= 0.26;
e228.. x107 - x108 =L= 0.26;
e229.. - x107 + x108 =L= 0.26;
e230.. x100 - x106 =L= 0.26;
e231.. - x100 + x106 =L= 0.26;
e232.. x100 - x105 =L= 0.26;
e233.. - x100 + x105 =L= 0.26;
e234.. x106 - x107 =L= 0.26;
e235.. - x106 + x107 =L= 0.26;
e236.. x95 - x99 =L= 0.26;
e237.. - x95 + x99 =L= 0.26;
e238.. x103 - x104 =L= 0.26;
e239.. - x103 + x104 =L= 0.26;
e240.. x95 - x96 =L= 0.26;
e241.. - x95 + x96 =L= 0.26;
e242.. x96 - x99 =L= 0.26;
e243.. - x96 + x99 =L= 0.26;
e244.. x97 - x98 =L= 0.26;
e245.. - x97 + x98 =L= 0.26;
e246.. x98 - x103 =L= 0.26;
e247.. - x98 + x103 =L= 0.26;
e248.. x96 - x98 =L= 0.26;
e249.. - x96 + x98 =L= 0.26;
e250.. x95 =E= 0;
e251.. x41 + x45 - x129 =E= 0;
e252.. x15 + x46 + x47 + x53 - x130 =E= -0.217;
e253.. x16 + x49 - x131 =E= -0.942;
e254.. x24 + x29 + x35 + x37 - x132 =E= -0.112;
e255.. x32 - x133 =E= 0;
e256.. x81 + x85 - x134 =E= 0;
e257.. x55 + x86 + x87 + x93 - x135 =E= -0.127;
e258.. x56 + x89 - x136 =E= -0.19;
e259.. x64 + x69 + x75 + x77 - x137 =E= -0.075;
e260.. x72 - x138 =E= 0;
e261.. x21 + x27 + x50 + x51 + x54 =E= -0.478;
e262.. x23 + x28 + x42 + x48 =E= -0.076;
e263.. x17 + x22 + x31 =E= 0;
e264.. x18 + x25 + x43 + x52 =E= -0.295;
e265.. x19 + x44 =E= -0.09;
e266.. x20 + x38 =E= -0.035;
e267.. x36 + x39 =E= -0.061;
e268.. x30 + x33 + x40 =E= -0.135;
e269.. x26 + x34 =E= -0.149;
e270.. x61 + x67 + x90 + x91 + x94 =E= 0.039;
e271.. x63 + x68 + x82 + x88 =E= -0.016;
e272.. x57 + x62 + x71 =E= 0;
e273.. x58 + x65 + x83 + x92 =E= -0.166;
e274.. x59 + x84 =E= -0.058;
e275.. x60 + x78 =E= -0.018;
e276.. x76 + x79 =E= -0.016;
e277.. x70 + x73 + x80 =E= -0.058;
e278.. x66 + x74 =E= -0.05;
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