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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) 0.00000000 (BARON) 0.00000000 (COUENNE) 7764.79321700 (GUROBI) 0.00000000 (LINDO) 8081.55017500 (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: 2024-12-17 Git hash: 8eaceb91