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Instance powerflow0014r
Optimal Power Flow problem modeled using quadratic functions (rectangular coordinates)
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 0.00000000 (ANTIGONE) 8082.57377100 (BARON) 0.00000000 (COUENNE) 8080.33129500 (GUROBI) 0.00000000 (LINDO) 8081.61544300 (SCIP) |
| 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ⓘ | 18 Aug 2014 |
| Problem typeⓘ | QCQP |
| #Variablesⓘ | 118 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 113 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | quadratic |
| Objective curvatureⓘ | convex |
| #Nonzeros in Objectiveⓘ | 5 |
| #Nonlinear Nonzeros in Objectiveⓘ | 5 |
| #Constraintsⓘ | 197 |
| #Linear Constraintsⓘ | 49 |
| #Quadratic Constraintsⓘ | 148 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 647 |
| #Nonlinear Nonzeros in Jacobianⓘ | 456 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 273 |
| #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ⓘ | 28 |
| Average blocksize in Hessian of Lagrangianⓘ | 1.313953 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 5.1295e-01 |
| 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
* 198 110 24 64 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 119 119 0 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 653 192 461 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,x103
,x104,x105,x106,x107,x108,x109,x110,x111,x112,x113,x114,x115,x116
,x117,x118,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,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;
e1.. 430.293*sqr(x109) + 2000*x109 + 2500*sqr(x110) + 2000*x110 + 100*sqr(x111)
+ 4000*x111 + 100*sqr(x112) + 4000*x112 + 100*sqr(x113) + 4000*x113
- objvar =E= 0;
e2.. 0.567509596153698*x82*x83 - 1.1350191923074*sqr(x82) - 2.39093157587886*
x82*x97 + 0.567509596153698*x83*x82 + 2.39093157587886*x83*x96 +
2.39093157587886*x96*x83 - 1.1350191923074*sqr(x96) + 0.567509596153698*
x96*x97 - 2.39093157587886*x97*x82 + 0.567509596153698*x97*x96 + x1 =E= 0;
e3.. 0.567509596153698*x82*x83 + 2.39093157587886*x82*x97 + 0.567509596153698*
x83*x82 - 1.1350191923074*sqr(x83) - 2.39093157587886*x83*x96 -
2.39093157587886*x96*x83 + 0.567509596153698*x96*x97 + 2.39093157587886*
x97*x82 + 0.567509596153698*x97*x96 - 1.1350191923074*sqr(x97) + x2 =E= 0;
e4.. 4.54504135987637*x89*x101 - 4.54504135987637*x87*x103 + 4.54504135987637*
x101*x89 - 4.54504135987637*x103*x87 + x3 =E= 0;
e5.. 4.54504135987637*x87*x103 - 4.54504135987637*x89*x101 - 4.54504135987637*
x101*x89 + 4.54504135987637*x103*x87 + x4 =E= 0;
e6.. 0.9404423768502*x90*x91 - 1.8808847537004*sqr(x90) - 2.20147187473026*x90*
x105 + 0.9404423768502*x91*x90 + 2.20147187473026*x91*x104 +
2.20147187473026*x104*x91 - 1.8808847537004*sqr(x104) + 0.9404423768502*
x104*x105 - 2.20147187473026*x105*x90 + 0.9404423768502*x105*x104 + x5
=E= 0;
e7.. 0.9404423768502*x90*x91 + 2.20147187473026*x90*x105 + 0.9404423768502*x91*
x90 - 1.8808847537004*sqr(x91) - 2.20147187473026*x91*x104 -
2.20147187473026*x104*x91 + 0.9404423768502*x104*x105 + 2.20147187473026*
x105*x90 + 0.9404423768502*x105*x104 - 1.8808847537004*sqr(x105) + x6
=E= 0;
e8.. 2.39097169089518*x87*x98 - 2.39097169089518*x84*x101 + 2.39097169089518*
x98*x87 - 2.39097169089518*x101*x84 + x7 =E= 0;
e9.. 2.39097169089518*x84*x101 - 2.39097169089518*x87*x98 - 2.39097169089518*
x98*x87 + 2.39097169089518*x101*x84 + x8 =E= 0;
e10.. 1.98396952622808*x86*x99 - 1.98396952622808*x85*x100 + 1.98396952622808*
x99*x86 - 1.98396952622808*x100*x85 + x9 =E= 0;
e11.. 1.98396952622808*x85*x100 - 1.98396952622808*x86*x99 - 1.98396952622808*
x99*x86 + 1.98396952622808*x100*x85 + x10 =E= 0;
e12.. 0.712002743509966*x89*x94 - 1.42400548701993*sqr(x89) - 1.5145252284653*
x89*x108 + 0.712002743509966*x94*x89 + 1.5145252284653*x94*x103 +
1.5145252284653*x103*x94 - 1.42400548701993*sqr(x103) + 0.712002743509966
*x103*x108 - 1.5145252284653*x108*x89 + 0.712002743509966*x108*x103 + x11
=E= 0;
e13.. 0.712002743509966*x89*x94 + 1.5145252284653*x89*x108 + 0.712002743509966*
x94*x89 - 1.42400548701993*sqr(x94) - 1.5145252284653*x94*x103 -
1.5145252284653*x103*x94 + 0.712002743509966*x103*x108 + 1.5145252284653*
x108*x89 + 0.712002743509966*x108*x103 - 1.42400548701993*sqr(x108) + x12
=E= 0;
e14.. 3.42049033074784*x84*x85 - 6.84098066149567*sqr(x84) - 10.7892769908458*
x84*x99 + 3.42049033074784*x85*x84 + 10.7892769908458*x85*x98 +
10.7892769908458*x98*x85 - 6.84098066149567*sqr(x98) + 3.42049033074784*
x98*x99 - 10.7892769908458*x99*x84 + 3.42049033074784*x99*x98 + x13 =E= 0
;
e15.. 3.42049033074784*x84*x85 + 10.7892769908458*x84*x99 + 3.42049033074784*
x85*x84 - 6.84098066149567*sqr(x85) - 10.7892769908458*x85*x98 -
10.7892769908458*x98*x85 + 3.42049033074784*x98*x99 + 10.7892769908458*
x99*x84 + 3.42049033074784*x99*x98 - 6.84098066149567*sqr(x99) + x14
=E= 0;
e16.. 1.54946370191899*x86*x93 - 3.09892740383799*sqr(x86) - 3.05137772409656*
x86*x107 + 1.54946370191899*x93*x86 + 3.05137772409656*x93*x100 +
3.05137772409656*x100*x93 - 3.09892740383799*sqr(x100) + 1.54946370191899
*x100*x107 - 3.05137772409656*x107*x86 + 1.54946370191899*x107*x100 + x15
=E= 0;
e17.. 1.54946370191899*x86*x93 + 3.05137772409656*x86*x107 + 1.54946370191899*
x93*x86 - 3.09892740383799*sqr(x93) - 3.05137772409656*x93*x100 -
3.05137772409656*x100*x93 + 1.54946370191899*x100*x107 + 3.05137772409656
*x107*x86 + 1.54946370191899*x107*x100 - 3.09892740383799*sqr(x107) + x16
=E= 0;
e18.. 2.83848992336077*x88*x101 - 2.83848992336077*x87*x102 + 2.83848992336077*
x101*x88 - 2.83848992336077*x102*x87 + x17 =E= 0;
e19.. 2.83848992336077*x87*x102 - 2.83848992336077*x88*x101 - 2.83848992336077*
x101*x88 + 2.83848992336077*x102*x87 + x18 =E= 0;
e20.. 0.568497078903163*x93*x94 - 1.13699415780633*sqr(x93) - 1.15748173755268*
x93*x108 + 0.568497078903163*x94*x93 + 1.15748173755268*x94*x107 +
1.15748173755268*x107*x94 - 1.13699415780633*sqr(x107) +
0.568497078903163*x107*x108 - 1.15748173755268*x108*x93 +
0.568497078903163*x108*x107 + x19 =E= 0;
e21.. 0.568497078903163*x93*x94 + 1.15748173755268*x93*x108 + 0.568497078903163
*x94*x93 - 1.13699415780633*sqr(x94) - 1.15748173755268*x94*x107 -
1.15748173755268*x107*x94 + 0.568497078903163*x107*x108 +
1.15748173755268*x108*x93 + 0.568497078903163*x108*x107 -
1.13699415780633*sqr(x108) + x20 =E= 0;
e22.. 0.762983720225487*x86*x92 - 1.52596744045097*sqr(x86) - 1.5879819825147*
x86*x106 + 0.762983720225487*x92*x86 + 1.5879819825147*x92*x100 +
1.5879819825147*x100*x92 - 1.52596744045097*sqr(x100) + 0.762983720225487
*x100*x106 - 1.5879819825147*x106*x86 + 0.762983720225487*x106*x100 + x21
=E= 0;
e23.. 0.762983720225487*x86*x92 + 1.5879819825147*x86*x106 + 0.762983720225487*
x92*x86 - 1.52596744045097*sqr(x92) - 1.5879819825147*x92*x100 -
1.5879819825147*x100*x92 + 0.762983720225487*x100*x106 + 1.5879819825147*
x106*x86 + 0.762983720225487*x106*x100 - 1.52596744045097*sqr(x106) + x22
=E= 0;
e24.. 0.97751428158863*x86*x91 - 1.95502856317726*sqr(x86) - 2.04703717212022*
x86*x105 + 0.97751428158863*x91*x86 + 2.04703717212022*x91*x100 +
2.04703717212022*x100*x91 - 1.95502856317726*sqr(x100) + 0.97751428158863
*x100*x105 - 2.04703717212022*x105*x86 + 0.97751428158863*x105*x100 + x23
=E= 0;
e25.. 0.97751428158863*x86*x91 + 2.04703717212022*x86*x105 + 0.97751428158863*
x91*x86 - 1.95502856317726*sqr(x91) - 2.04703717212022*x91*x100 -
2.04703717212022*x100*x91 + 0.97751428158863*x100*x105 + 2.04703717212022
*x105*x86 + 0.97751428158863*x105*x100 - 1.95502856317726*sqr(x105) + x24
=E= 0;
e26.. 1.24451229341096*x92*x93 - 2.48902458682192*sqr(x92) - 1.12598731308611*
x92*x107 + 1.24451229341096*x93*x92 + 1.12598731308611*x93*x106 +
1.12598731308611*x106*x93 - 2.48902458682192*sqr(x106) + 1.24451229341096
*x106*x107 - 1.12598731308611*x107*x92 + 1.24451229341096*x107*x106 + x25
=E= 0;
e27.. 1.24451229341096*x92*x93 + 1.12598731308611*x92*x107 + 1.24451229341096*
x93*x92 - 2.48902458682192*sqr(x93) - 1.12598731308611*x93*x106 -
1.12598731308611*x106*x93 + 1.24451229341096*x106*x107 + 1.12598731308611
*x107*x92 + 1.24451229341096*x107*x106 - 2.48902458682192*sqr(x107) + x26
=E= 0;
e28.. 0.512948727485094*x81*x85 - 1.02589745497019*sqr(x81) - 2.11749184116742*
x81*x99 + 0.512948727485094*x85*x81 + 2.11749184116742*x85*x95 +
2.11749184116742*x95*x85 - 1.02589745497019*sqr(x95) + 0.512948727485094*
x95*x99 - 2.11749184116742*x99*x81 + 0.512948727485094*x99*x95 + x27
=E= 0;
e29.. 0.512948727485094*x81*x85 + 2.11749184116742*x81*x99 + 0.512948727485094*
x85*x81 - 1.02589745497019*sqr(x85) - 2.11749184116742*x85*x95 -
2.11749184116742*x95*x85 + 0.512948727485094*x95*x99 + 2.11749184116742*
x99*x81 + 0.512948727485094*x99*x95 - 1.02589745497019*sqr(x99) + x28
=E= 0;
e30.. 1.95102477622371*x89*x90 - 3.90204955244743*sqr(x89) - 5.18269706353046*
x89*x104 + 1.95102477622371*x90*x89 + 5.18269706353046*x90*x103 +
5.18269706353046*x103*x90 - 3.90204955244743*sqr(x103) + 1.95102477622371
*x103*x104 - 5.18269706353046*x104*x89 + 1.95102477622371*x104*x103 + x29
=E= 0;
e31.. 1.95102477622371*x89*x90 + 5.18269706353046*x89*x104 + 1.95102477622371*
x90*x89 - 3.90204955244743*sqr(x90) - 5.18269706353046*x90*x103 -
5.18269706353046*x103*x90 + 1.95102477622371*x103*x104 + 5.18269706353046
*x104*x89 + 1.95102477622371*x104*x103 - 3.90204955244743*sqr(x104) + x30
=E= 0;
e32.. 2.49956580039902*x81*x82 - 4.99913160079803*sqr(x81) - 7.63154326158978*
x81*x96 + 2.49956580039902*x82*x81 + 7.63154326158978*x82*x95 +
7.63154326158978*x95*x82 - 4.99913160079803*sqr(x95) + 2.49956580039902*
x95*x96 - 7.63154326158978*x96*x81 + 2.49956580039902*x96*x95 + x31 =E= 0
;
e33.. 2.49956580039902*x81*x82 + 7.63154326158978*x81*x96 + 2.49956580039902*
x82*x81 - 4.99913160079803*sqr(x82) - 7.63154326158978*x82*x95 -
7.63154326158978*x95*x82 + 2.49956580039902*x95*x96 + 7.63154326158978*
x96*x81 + 2.49956580039902*x96*x95 - 4.99913160079803*sqr(x96) + x32
=E= 0;
e34.. 0.850569833547202*x82*x85 - 1.7011396670944*sqr(x82) - 2.59696369898486*
x82*x99 + 0.850569833547202*x85*x82 + 2.59696369898486*x85*x96 +
2.59696369898486*x96*x85 - 1.7011396670944*sqr(x96) + 0.850569833547202*
x96*x99 - 2.59696369898486*x99*x82 + 0.850569833547202*x99*x96 + x33
=E= 0;
e35.. 0.850569833547202*x82*x85 + 2.59696369898486*x82*x99 + 0.850569833547202*
x85*x82 - 1.7011396670944*sqr(x85) - 2.59696369898486*x85*x96 -
2.59696369898486*x96*x85 + 0.850569833547202*x96*x99 + 2.59696369898486*
x99*x82 + 0.850569833547202*x99*x96 - 1.7011396670944*sqr(x99) + x34
=E= 0;
e36.. 0.99298785496278*x83*x84 - 1.98597570992556*sqr(x83) - 2.53440848879696*
x83*x98 + 0.99298785496278*x84*x83 + 2.53440848879696*x84*x97 +
2.53440848879696*x97*x84 - 1.98597570992556*sqr(x97) + 0.99298785496278*
x97*x98 - 2.53440848879696*x98*x83 + 0.99298785496278*x98*x97 + x35 =E= 0
;
e37.. 0.99298785496278*x83*x84 + 2.53440848879696*x83*x98 + 0.99298785496278*
x84*x83 - 1.98597570992556*sqr(x84) - 2.53440848879696*x84*x97 -
2.53440848879696*x97*x84 + 0.99298785496278*x97*x98 + 2.53440848879696*
x98*x83 + 0.99298785496278*x98*x97 - 1.98597570992556*sqr(x98) + x36
=E= 0;
e38.. 0.898989535761804*x89*x98 - 0.898989535761804*x84*x103 +
0.898989535761804*x98*x89 - 0.898989535761804*x103*x84 + x37 =E= 0;
e39.. 0.898989535761804*x84*x103 - 0.898989535761804*x89*x98 -
0.898989535761804*x98*x89 + 0.898989535761804*x103*x84 + x38 =E= 0;
e40.. 0.843016575307471*x82*x84 - 1.68603315061494*sqr(x82) - 2.55791916293604*
x82*x98 + 0.843016575307471*x84*x82 + 2.55791916293604*x84*x96 +
2.55791916293604*x96*x84 - 1.68603315061494*sqr(x96) + 0.843016575307471*
x96*x98 - 2.55791916293604*x98*x82 + 0.843016575307471*x98*x96 + x39
=E= 0;
e41.. 0.843016575307471*x82*x84 + 2.55791916293604*x82*x98 + 0.843016575307471*
x84*x82 - 1.68603315061494*sqr(x84) - 2.55791916293604*x84*x96 -
2.55791916293604*x96*x84 + 0.843016575307471*x96*x98 + 2.55791916293604*
x98*x82 + 0.843016575307471*x98*x96 - 1.68603315061494*sqr(x98) + x40
=E= 0;
e42.. 2.39093157587886*x82*x83 - 4.75996315175772*sqr(x82) + 0.567509596153698*
x82*x97 + 2.39093157587886*x83*x82 - 0.567509596153698*x83*x96 -
0.567509596153698*x96*x83 - 4.75996315175772*sqr(x96) + 2.39093157587886*
x96*x97 + 0.567509596153698*x97*x82 + 2.39093157587886*x97*x96 + x41
=E= 0;
e43.. 2.39093157587886*x82*x83 - 0.567509596153698*x82*x97 + 2.39093157587886*
x83*x82 - 4.75996315175772*sqr(x83) + 0.567509596153698*x83*x96 +
0.567509596153698*x96*x83 + 2.39093157587886*x96*x97 - 0.567509596153698*
x97*x82 + 2.39093157587886*x97*x96 - 4.75996315175772*sqr(x97) + x42
=E= 0;
e44.. 4.54504135987637*x87*x89 - 9.09008271975275*sqr(x87) + 4.54504135987637*
x89*x87 - 9.09008271975275*sqr(x101) + 4.54504135987637*x101*x103 +
4.54504135987637*x103*x101 + x43 =E= 0;
e45.. 4.54504135987637*x87*x89 + 4.54504135987637*x89*x87 - 9.09008271975275*
sqr(x89) + 4.54504135987637*x101*x103 + 4.54504135987637*x103*x101 -
9.09008271975275*sqr(x103) + x44 =E= 0;
e46.. 2.20147187473026*x90*x91 - 4.40294374946052*sqr(x90) + 0.9404423768502*
x90*x105 + 2.20147187473026*x91*x90 - 0.9404423768502*x91*x104 -
0.9404423768502*x104*x91 - 4.40294374946052*sqr(x104) + 2.20147187473026*
x104*x105 + 0.9404423768502*x105*x90 + 2.20147187473026*x105*x104 + x45
=E= 0;
e47.. 2.20147187473026*x90*x91 - 0.9404423768502*x90*x105 + 2.20147187473026*
x91*x90 - 4.40294374946052*sqr(x91) + 0.9404423768502*x91*x104 +
0.9404423768502*x104*x91 + 2.20147187473026*x104*x105 - 0.9404423768502*
x105*x90 + 2.20147187473026*x105*x104 - 4.40294374946052*sqr(x105) + x46
=E= 0;
e48.. 2.39097169089518*x84*x87 - 4.78194338179036*sqr(x84) + 2.39097169089518*
x87*x84 - 4.78194338179036*sqr(x98) + 2.39097169089518*x98*x101 +
2.39097169089518*x101*x98 + x47 =E= 0;
e49.. 2.39097169089518*x84*x87 + 2.39097169089518*x87*x84 - 4.78194338179036*
sqr(x87) + 2.39097169089518*x98*x101 + 2.39097169089518*x101*x98 -
4.78194338179036*sqr(x101) + x48 =E= 0;
e50.. 1.98396952622808*x85*x86 - 3.96793905245615*sqr(x85) + 1.98396952622808*
x86*x85 - 3.96793905245615*sqr(x99) + 1.98396952622808*x99*x100 +
1.98396952622808*x100*x99 + x49 =E= 0;
e51.. 1.98396952622808*x85*x86 + 1.98396952622808*x86*x85 - 3.96793905245615*
sqr(x86) + 1.98396952622808*x99*x100 + 1.98396952622808*x100*x99 -
3.96793905245615*sqr(x100) + x50 =E= 0;
e52.. 1.5145252284653*x89*x94 - 3.0290504569306*sqr(x89) + 0.712002743509966*
x89*x108 + 1.5145252284653*x94*x89 - 0.712002743509966*x94*x103 -
0.712002743509966*x103*x94 - 3.0290504569306*sqr(x103) + 1.5145252284653*
x103*x108 + 0.712002743509966*x108*x89 + 1.5145252284653*x108*x103 + x51
=E= 0;
e53.. 1.5145252284653*x89*x94 - 0.712002743509966*x89*x108 + 1.5145252284653*
x94*x89 - 3.0290504569306*sqr(x94) + 0.712002743509966*x94*x103 +
0.712002743509966*x103*x94 + 1.5145252284653*x103*x108 -
0.712002743509966*x108*x89 + 1.5145252284653*x108*x103 - 3.0290504569306*
sqr(x108) + x52 =E= 0;
e54.. 10.7892769908458*x84*x85 - 21.5785539816916*sqr(x84) + 3.42049033074784*
x84*x99 + 10.7892769908458*x85*x84 - 3.42049033074784*x85*x98 -
3.42049033074784*x98*x85 - 21.5785539816916*sqr(x98) + 10.7892769908458*
x98*x99 + 3.42049033074784*x99*x84 + 10.7892769908458*x99*x98 + x53 =E= 0
;
e55.. 10.7892769908458*x84*x85 - 3.42049033074784*x84*x99 + 10.7892769908458*
x85*x84 - 21.5785539816916*sqr(x85) + 3.42049033074784*x85*x98 +
3.42049033074784*x98*x85 + 10.7892769908458*x98*x99 - 3.42049033074784*
x99*x84 + 10.7892769908458*x99*x98 - 21.5785539816916*sqr(x99) + x54
=E= 0;
e56.. 3.05137772409656*x86*x93 - 6.10275544819311*sqr(x86) + 1.54946370191899*
x86*x107 + 3.05137772409656*x93*x86 - 1.54946370191899*x93*x100 -
1.54946370191899*x100*x93 - 6.10275544819311*sqr(x100) + 3.05137772409656
*x100*x107 + 1.54946370191899*x107*x86 + 3.05137772409656*x107*x100 + x55
=E= 0;
e57.. 3.05137772409656*x86*x93 - 1.54946370191899*x86*x107 + 3.05137772409656*
x93*x86 - 6.10275544819311*sqr(x93) + 1.54946370191899*x93*x100 +
1.54946370191899*x100*x93 + 3.05137772409656*x100*x107 - 1.54946370191899
*x107*x86 + 3.05137772409656*x107*x100 - 6.10275544819311*sqr(x107) + x56
=E= 0;
e58.. 2.83848992336077*x87*x88 - 5.67697984672154*sqr(x87) + 2.83848992336077*
x88*x87 - 5.67697984672154*sqr(x101) + 2.83848992336077*x101*x102 +
2.83848992336077*x102*x101 + x57 =E= 0;
e59.. 2.83848992336077*x87*x88 + 2.83848992336077*x88*x87 - 5.67697984672154*
sqr(x88) + 2.83848992336077*x101*x102 + 2.83848992336077*x102*x101 -
5.67697984672154*sqr(x102) + x58 =E= 0;
e60.. 1.15748173755268*x93*x94 - 2.31496347510535*sqr(x93) + 0.568497078903163*
x93*x108 + 1.15748173755268*x94*x93 - 0.568497078903163*x94*x107 -
0.568497078903163*x107*x94 - 2.31496347510535*sqr(x107) +
1.15748173755268*x107*x108 + 0.568497078903163*x108*x93 +
1.15748173755268*x108*x107 + x59 =E= 0;
e61.. 1.15748173755268*x93*x94 - 0.568497078903163*x93*x108 + 1.15748173755268*
x94*x93 - 2.31496347510535*sqr(x94) + 0.568497078903163*x94*x107 +
0.568497078903163*x107*x94 + 1.15748173755268*x107*x108 -
0.568497078903163*x108*x93 + 1.15748173755268*x108*x107 -
2.31496347510535*sqr(x108) + x60 =E= 0;
e62.. 1.5879819825147*x86*x92 - 3.1759639650294*sqr(x86) + 0.762983720225487*
x86*x106 + 1.5879819825147*x92*x86 - 0.762983720225487*x92*x100 -
0.762983720225487*x100*x92 - 3.1759639650294*sqr(x100) + 1.5879819825147*
x100*x106 + 0.762983720225487*x106*x86 + 1.5879819825147*x106*x100 + x61
=E= 0;
e63.. 1.5879819825147*x86*x92 - 0.762983720225487*x86*x106 + 1.5879819825147*
x92*x86 - 3.1759639650294*sqr(x92) + 0.762983720225487*x92*x100 +
0.762983720225487*x100*x92 + 1.5879819825147*x100*x106 -
0.762983720225487*x106*x86 + 1.5879819825147*x106*x100 - 3.1759639650294*
sqr(x106) + x62 =E= 0;
e64.. 2.04703717212022*x86*x91 - 4.09407434424044*sqr(x86) + 0.97751428158863*
x86*x105 + 2.04703717212022*x91*x86 - 0.97751428158863*x91*x100 -
0.97751428158863*x100*x91 - 4.09407434424044*sqr(x100) + 2.04703717212022
*x100*x105 + 0.97751428158863*x105*x86 + 2.04703717212022*x105*x100 + x63
=E= 0;
e65.. 2.04703717212022*x86*x91 - 0.97751428158863*x86*x105 + 2.04703717212022*
x91*x86 - 4.09407434424044*sqr(x91) + 0.97751428158863*x91*x100 +
0.97751428158863*x100*x91 + 2.04703717212022*x100*x105 - 0.97751428158863
*x105*x86 + 2.04703717212022*x105*x100 - 4.09407434424044*sqr(x105) + x64
=E= 0;
e66.. 1.12598731308611*x92*x93 - 2.25197462617221*sqr(x92) + 1.24451229341096*
x92*x107 + 1.12598731308611*x93*x92 - 1.24451229341096*x93*x106 -
1.24451229341096*x106*x93 - 2.25197462617221*sqr(x106) + 1.12598731308611
*x106*x107 + 1.24451229341096*x107*x92 + 1.12598731308611*x107*x106 + x65
=E= 0;
e67.. 1.12598731308611*x92*x93 - 1.24451229341096*x92*x107 + 1.12598731308611*
x93*x92 - 2.25197462617221*sqr(x93) + 1.24451229341096*x93*x106 +
1.24451229341096*x106*x93 + 1.12598731308611*x106*x107 - 1.24451229341096
*x107*x92 + 1.12598731308611*x107*x106 - 2.25197462617221*sqr(x107) + x66
=E= 0;
e68.. 2.11749184116742*x81*x85 - 4.21038368233483*sqr(x81) + 0.512948727485094*
x81*x99 + 2.11749184116742*x85*x81 - 0.512948727485094*x85*x95 -
0.512948727485094*x95*x85 - 4.21038368233483*sqr(x95) + 2.11749184116742*
x95*x99 + 0.512948727485094*x99*x81 + 2.11749184116742*x99*x95 + x67
=E= 0;
e69.. 2.11749184116742*x81*x85 - 0.512948727485094*x81*x99 + 2.11749184116742*
x85*x81 - 4.21038368233483*sqr(x85) + 0.512948727485094*x85*x95 +
0.512948727485094*x95*x85 + 2.11749184116742*x95*x99 - 0.512948727485094*
x99*x81 + 2.11749184116742*x99*x95 - 4.21038368233483*sqr(x99) + x68
=E= 0;
e70.. 5.18269706353046*x89*x90 - 10.3653941270609*sqr(x89) + 1.95102477622371*
x89*x104 + 5.18269706353046*x90*x89 - 1.95102477622371*x90*x103 -
1.95102477622371*x103*x90 - 10.3653941270609*sqr(x103) + 5.18269706353046
*x103*x104 + 1.95102477622371*x104*x89 + 5.18269706353046*x104*x103 + x69
=E= 0;
e71.. 5.18269706353046*x89*x90 - 1.95102477622371*x89*x104 + 5.18269706353046*
x90*x89 - 10.3653941270609*sqr(x90) + 1.95102477622371*x90*x103 +
1.95102477622371*x103*x90 + 5.18269706353046*x103*x104 - 1.95102477622371
*x104*x89 + 5.18269706353046*x104*x103 - 10.3653941270609*sqr(x104) + x70
=E= 0;
e72.. 7.63154326158978*x81*x82 - 15.2366865231796*sqr(x81) + 2.49956580039902*
x81*x96 + 7.63154326158978*x82*x81 - 2.49956580039902*x82*x95 -
2.49956580039902*x95*x82 - 15.2366865231796*sqr(x95) + 7.63154326158978*
x95*x96 + 2.49956580039902*x96*x81 + 7.63154326158978*x96*x95 + x71 =E= 0
;
e73.. 7.63154326158978*x81*x82 - 2.49956580039902*x81*x96 + 7.63154326158978*
x82*x81 - 15.2366865231796*sqr(x82) + 2.49956580039902*x82*x95 +
2.49956580039902*x95*x82 + 7.63154326158978*x95*x96 - 2.49956580039902*
x96*x81 + 7.63154326158978*x96*x95 - 15.2366865231796*sqr(x96) + x72
=E= 0;
e74.. 2.59696369898486*x82*x85 - 5.17662739796971*sqr(x82) + 0.850569833547202*
x82*x99 + 2.59696369898486*x85*x82 - 0.850569833547202*x85*x96 -
0.850569833547202*x96*x85 - 5.17662739796971*sqr(x96) + 2.59696369898486*
x96*x99 + 0.850569833547202*x99*x82 + 2.59696369898486*x99*x96 + x73
=E= 0;
e75.. 2.59696369898486*x82*x85 - 0.850569833547202*x82*x99 + 2.59696369898486*
x85*x82 - 5.17662739796971*sqr(x85) + 0.850569833547202*x85*x96 +
0.850569833547202*x96*x85 + 2.59696369898486*x96*x99 - 0.850569833547202*
x99*x82 + 2.59696369898486*x99*x96 - 5.17662739796971*sqr(x99) + x74
=E= 0;
e76.. 2.53440848879696*x83*x84 - 5.06241697759392*sqr(x83) + 0.99298785496278*
x83*x98 + 2.53440848879696*x84*x83 - 0.99298785496278*x84*x97 -
0.99298785496278*x97*x84 - 5.06241697759392*sqr(x97) + 2.53440848879696*
x97*x98 + 0.99298785496278*x98*x83 + 2.53440848879696*x98*x97 + x75 =E= 0
;
e77.. 2.53440848879696*x83*x84 - 0.99298785496278*x83*x98 + 2.53440848879696*
x84*x83 - 5.06241697759392*sqr(x84) + 0.99298785496278*x84*x97 +
0.99298785496278*x97*x84 + 2.53440848879696*x97*x98 - 0.99298785496278*
x98*x83 + 2.53440848879696*x98*x97 - 5.06241697759392*sqr(x98) + x76
=E= 0;
e78.. 0.898989535761804*x84*x89 - 1.79797907152361*sqr(x84) + 0.898989535761804
*x89*x84 - 1.79797907152361*sqr(x98) + 0.898989535761804*x98*x103 +
0.898989535761804*x103*x98 + x77 =E= 0;
e79.. 0.898989535761804*x84*x89 + 0.898989535761804*x89*x84 - 1.79797907152361*
sqr(x89) + 0.898989535761804*x98*x103 + 0.898989535761804*x103*x98 -
1.79797907152361*sqr(x103) + x78 =E= 0;
e80.. 2.55791916293604*x82*x84 - 5.09883832587208*sqr(x82) + 0.843016575307471*
x82*x98 + 2.55791916293604*x84*x82 - 0.843016575307471*x84*x96 -
0.843016575307471*x96*x84 - 5.09883832587208*sqr(x96) + 2.55791916293604*
x96*x98 + 0.843016575307471*x98*x82 + 2.55791916293604*x98*x96 + x79
=E= 0;
e81.. 2.55791916293604*x82*x84 - 0.843016575307471*x82*x98 + 2.55791916293604*
x84*x82 - 5.09883832587208*sqr(x84) + 0.843016575307471*x84*x96 +
0.843016575307471*x96*x84 + 2.55791916293604*x96*x98 - 0.843016575307471*
x98*x82 + 2.55791916293604*x98*x96 - 5.09883832587208*sqr(x98) + x80
=E= 0;
e82.. sqr(x1) + sqr(x41) =L= 9801;
e83.. sqr(x2) + sqr(x42) =L= 9801;
e84.. sqr(x3) + sqr(x43) =L= 9801;
e85.. sqr(x4) + sqr(x44) =L= 9801;
e86.. sqr(x5) + sqr(x45) =L= 9801;
e87.. sqr(x6) + sqr(x46) =L= 9801;
e88.. sqr(x7) + sqr(x47) =L= 9801;
e89.. sqr(x8) + sqr(x48) =L= 9801;
e90.. sqr(x9) + sqr(x49) =L= 9801;
e91.. sqr(x10) + sqr(x50) =L= 9801;
e92.. sqr(x11) + sqr(x51) =L= 9801;
e93.. sqr(x12) + sqr(x52) =L= 9801;
e94.. sqr(x13) + sqr(x53) =L= 9801;
e95.. sqr(x14) + sqr(x54) =L= 9801;
e96.. sqr(x15) + sqr(x55) =L= 9801;
e97.. sqr(x16) + sqr(x56) =L= 9801;
e98.. sqr(x17) + sqr(x57) =L= 9801;
e99.. sqr(x18) + sqr(x58) =L= 9801;
e100.. sqr(x19) + sqr(x59) =L= 9801;
e101.. sqr(x20) + sqr(x60) =L= 9801;
e102.. sqr(x21) + sqr(x61) =L= 9801;
e103.. sqr(x22) + sqr(x62) =L= 9801;
e104.. sqr(x23) + sqr(x63) =L= 9801;
e105.. sqr(x24) + sqr(x64) =L= 9801;
e106.. sqr(x25) + sqr(x65) =L= 9801;
e107.. sqr(x26) + sqr(x66) =L= 9801;
e108.. sqr(x27) + sqr(x67) =L= 9801;
e109.. sqr(x28) + sqr(x68) =L= 9801;
e110.. sqr(x29) + sqr(x69) =L= 9801;
e111.. sqr(x30) + sqr(x70) =L= 9801;
e112.. sqr(x31) + sqr(x71) =L= 9801;
e113.. sqr(x32) + sqr(x72) =L= 9801;
e114.. sqr(x33) + sqr(x73) =L= 9801;
e115.. sqr(x34) + sqr(x74) =L= 9801;
e116.. sqr(x35) + sqr(x75) =L= 9801;
e117.. sqr(x36) + sqr(x76) =L= 9801;
e118.. sqr(x37) + sqr(x77) =L= 9801;
e119.. sqr(x38) + sqr(x78) =L= 9801;
e120.. sqr(x39) + sqr(x79) =L= 9801;
e121.. sqr(x40) + sqr(x80) =L= 9801;
e122.. sqr(x81) + sqr(x95) =L= 1.1236;
e123.. sqr(x82) + sqr(x96) =L= 1.1236;
e124.. sqr(x83) + sqr(x97) =L= 1.1236;
e125.. sqr(x84) + sqr(x98) =L= 1.1236;
e126.. sqr(x85) + sqr(x99) =L= 1.1236;
e127.. sqr(x86) + sqr(x100) =L= 1.1236;
e128.. sqr(x87) + sqr(x101) =L= 1.1236;
e129.. sqr(x88) + sqr(x102) =L= 1.1236;
e130.. sqr(x89) + sqr(x103) =L= 1.1236;
e131.. sqr(x90) + sqr(x104) =L= 1.1236;
e132.. sqr(x91) + sqr(x105) =L= 1.1236;
e133.. sqr(x92) + sqr(x106) =L= 1.1236;
e134.. sqr(x93) + sqr(x107) =L= 1.1236;
e135.. sqr(x94) + sqr(x108) =L= 1.1236;
e136.. sqr(x81) + sqr(x95) =G= 0.8836;
e137.. sqr(x82) + sqr(x96) =G= 0.8836;
e138.. sqr(x83) + sqr(x97) =G= 0.8836;
e139.. sqr(x84) + sqr(x98) =G= 0.8836;
e140.. sqr(x85) + sqr(x99) =G= 0.8836;
e141.. sqr(x86) + sqr(x100) =G= 0.8836;
e142.. sqr(x87) + sqr(x101) =G= 0.8836;
e143.. sqr(x88) + sqr(x102) =G= 0.8836;
e144.. sqr(x89) + sqr(x103) =G= 0.8836;
e145.. sqr(x90) + sqr(x104) =G= 0.8836;
e146.. sqr(x91) + sqr(x105) =G= 0.8836;
e147.. sqr(x92) + sqr(x106) =G= 0.8836;
e148.. sqr(x93) + sqr(x107) =G= 0.8836;
e149.. sqr(x94) + sqr(x108) =G= 0.8836;
e150.. x109 =L= 3.324;
e151.. x110 =L= 1.4;
e152.. x111 =L= 1;
e153.. x112 =L= 1;
e154.. x113 =L= 1;
e155.. x109 =G= 0;
e156.. x110 =G= 0;
e157.. x111 =G= 0;
e158.. x112 =G= 0;
e159.. x113 =G= 0;
e160.. x114 =L= 0.1;
e161.. x115 =L= 0.5;
e162.. x116 =L= 0.4;
e163.. x117 =L= 0.24;
e164.. x118 =L= 0.24;
e165.. x114 =G= 0;
e166.. x115 =G= -0.4;
e167.. x116 =G= 0;
e168.. x117 =G= -0.06;
e169.. x118 =G= -0.06;
e170.. x95 =E= 0;
e171.. x27 + x31 - x109 =E= 0;
e172.. x1 + x32 + x33 + x39 - x110 =E= -0.217;
e173.. x2 + x35 - x111 =E= -0.942;
e174.. x10 + x15 + x21 + x23 - x112 =E= -0.112;
e175.. x18 - x113 =E= 0;
e176.. x67 + x71 - x114 =E= 0;
e177.. x41 + x72 + x73 + x79 - x115 =E= -0.127;
e178.. x42 + x75 - x116 =E= -0.19;
e179.. x50 + x55 + x61 + x63 - x117 =E= -0.075;
e180.. x58 - x118 =E= 0;
e181.. x7 + x13 + x36 + x37 + x40 =E= -0.478;
e182.. x9 + x14 + x28 + x34 =E= -0.076;
e183.. x3 + x8 + x17 =E= 0;
e184.. x4 + x11 + x29 + x38 =E= -0.295;
e185.. x5 + x30 =E= -0.09;
e186.. x6 + x24 =E= -0.035;
e187.. x22 + x25 =E= -0.061;
e188.. x16 + x19 + x26 =E= -0.135;
e189.. x12 + x20 =E= -0.149;
e190.. x47 + x53 + x76 + x77 + x80 =E= 0.039;
e191.. x49 + x54 + x68 + x74 =E= -0.016;
e192.. x43 + x48 + x57 =E= 0;
e193.. x44 + x51 + x69 + x78 =E= -0.166;
e194.. x45 + x70 =E= -0.058;
e195.. x46 + x64 =E= -0.018;
e196.. x62 + x65 =E= -0.016;
e197.. x56 + x59 + x66 =E= -0.058;
e198.. x52 + x60 =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 NLP $set NLP NLP
Solve m using %NLP% minimizing objvar;
Last updated: 2025-08-07 Git hash: e62cedfc