MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance transswitch0014r
Optimal Transmission Switching problem modeled using quadratic functions (rectangular coordinates)
| Formatsⓘ | ams gms 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) 0.00000000 (GUROBI) 0.00000000 (LINDO) 0.00000000 (SCIP) 0.00000000 (SHOT) 0.00000050 (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ⓘ | 197 |
| #Linear Constraintsⓘ | 49 |
| #Quadratic Constraintsⓘ | 68 |
| #Polynomial Constraintsⓘ | 80 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 727 |
| #Nonlinear Nonzeros in Jacobianⓘ | 536 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 433 |
| #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
* 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
* 139 119 20 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 733 192 541 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;
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(x82) + sqr(x96)) - 1.1350191923074*(x82*x83 + x96*
x97) + 4.78186315175772*(x82*x97 - x83*x96))*b109 + x1 =E= 0;
e3.. -(1.1350191923074*(sqr(x83) + sqr(x97)) - 1.1350191923074*(x83*x82 + x97*
x96) + 4.78186315175772*(x83*x96 - x82*x97))*b109 + x2 =E= 0;
e4.. -9.09008271975275*(x87*x103 - x89*x101)*b110 + x3 =E= 0;
e5.. -9.09008271975275*(x89*x101 - x87*x103)*b110 + x4 =E= 0;
e6.. -(1.8808847537004*(sqr(x90) + sqr(x104)) - 1.8808847537004*(x90*x91 + x104
*x105) + 4.40294374946052*(x90*x105 - x91*x104))*b111 + x5 =E= 0;
e7.. -(1.8808847537004*(sqr(x91) + sqr(x105)) - 1.8808847537004*(x91*x90 + x105
*x104) + 4.40294374946052*(x91*x104 - x90*x105))*b111 + x6 =E= 0;
e8.. -4.78194338179036*(x84*x101 - x87*x98)*b112 + x7 =E= 0;
e9.. -4.78194338179036*(x87*x98 - x84*x101)*b112 + x8 =E= 0;
e10.. -3.96793905245615*(x85*x100 - x86*x99)*b113 + x9 =E= 0;
e11.. -3.96793905245615*(x86*x99 - x85*x100)*b113 + x10 =E= 0;
e12.. -(1.42400548701993*(sqr(x89) + sqr(x103)) - 1.42400548701993*(x89*x94 +
x103*x108) + 3.0290504569306*(x89*x108 - x94*x103))*b114 + x11 =E= 0;
e13.. -(1.42400548701993*(sqr(x94) + sqr(x108)) - 1.42400548701993*(x94*x89 +
x108*x103) + 3.0290504569306*(x94*x103 - x89*x108))*b114 + x12 =E= 0;
e14.. -(6.84098066149567*(sqr(x84) + sqr(x98)) - 6.84098066149567*(x84*x85 +
x98*x99) + 21.5785539816916*(x84*x99 - x85*x98))*b115 + x13 =E= 0;
e15.. -(6.84098066149567*(sqr(x85) + sqr(x99)) - 6.84098066149567*(x85*x84 +
x99*x98) + 21.5785539816916*(x85*x98 - x84*x99))*b115 + x14 =E= 0;
e16.. -(3.09892740383799*(sqr(x86) + sqr(x100)) - 3.09892740383799*(x86*x93 +
x100*x107) + 6.10275544819311*(x86*x107 - x93*x100))*b116 + x15 =E= 0;
e17.. -(3.09892740383799*(sqr(x93) + sqr(x107)) - 3.09892740383799*(x93*x86 +
x107*x100) + 6.10275544819311*(x93*x100 - x86*x107))*b116 + x16 =E= 0;
e18.. -5.67697984672154*(x87*x102 - x88*x101)*b117 + x17 =E= 0;
e19.. -5.67697984672154*(x88*x101 - x87*x102)*b117 + x18 =E= 0;
e20.. -(1.13699415780633*(sqr(x93) + sqr(x107)) - 1.13699415780633*(x93*x94 +
x107*x108) + 2.31496347510535*(x93*x108 - x94*x107))*b118 + x19 =E= 0;
e21.. -(1.13699415780633*(sqr(x94) + sqr(x108)) - 1.13699415780633*(x94*x93 +
x108*x107) + 2.31496347510535*(x94*x107 - x93*x108))*b118 + x20 =E= 0;
e22.. -(1.52596744045097*(sqr(x86) + sqr(x100)) - 1.52596744045097*(x86*x92 +
x100*x106) + 3.1759639650294*(x86*x106 - x92*x100))*b119 + x21 =E= 0;
e23.. -(1.52596744045097*(sqr(x92) + sqr(x106)) - 1.52596744045097*(x92*x86 +
x106*x100) + 3.1759639650294*(x92*x100 - x86*x106))*b119 + x22 =E= 0;
e24.. -(1.95502856317726*(sqr(x86) + sqr(x100)) - 1.95502856317726*(x86*x91 +
x100*x105) + 4.09407434424044*(x86*x105 - x91*x100))*b120 + x23 =E= 0;
e25.. -(1.95502856317726*(sqr(x91) + sqr(x105)) - 1.95502856317726*(x91*x86 +
x105*x100) + 4.09407434424044*(x91*x100 - x86*x105))*b120 + x24 =E= 0;
e26.. -(2.48902458682192*(sqr(x92) + sqr(x106)) - 2.48902458682192*(x92*x93 +
x106*x107) + 2.25197462617221*(x92*x107 - x93*x106))*b121 + x25 =E= 0;
e27.. -(2.48902458682192*(sqr(x93) + sqr(x107)) - 2.48902458682192*(x93*x92 +
x107*x106) + 2.25197462617221*(x93*x106 - x92*x107))*b121 + x26 =E= 0;
e28.. -(1.02589745497019*(sqr(x81) + sqr(x95)) - 1.02589745497019*(x81*x85 +
x95*x99) + 4.23498368233483*(x81*x99 - x85*x95))*b122 + x27 =E= 0;
e29.. -(1.02589745497019*(sqr(x85) + sqr(x99)) - 1.02589745497019*(x85*x81 +
x99*x95) + 4.23498368233483*(x85*x95 - x81*x99))*b122 + x28 =E= 0;
e30.. -(3.90204955244743*(sqr(x89) + sqr(x103)) - 3.90204955244743*(x89*x90 +
x103*x104) + 10.3653941270609*(x89*x104 - x90*x103))*b123 + x29 =E= 0;
e31.. -(3.90204955244743*(sqr(x90) + sqr(x104)) - 3.90204955244743*(x90*x89 +
x104*x103) + 10.3653941270609*(x90*x103 - x89*x104))*b123 + x30 =E= 0;
e32.. -(4.99913160079803*(sqr(x81) + sqr(x95)) - 4.99913160079803*(x81*x82 +
x95*x96) + 15.2630865231796*(x81*x96 - x82*x95))*b124 + x31 =E= 0;
e33.. -(4.99913160079803*(sqr(x82) + sqr(x96)) - 4.99913160079803*(x82*x81 +
x96*x95) + 15.2630865231796*(x82*x95 - x81*x96))*b124 + x32 =E= 0;
e34.. -(1.7011396670944*(sqr(x82) + sqr(x96)) - 1.7011396670944*(x82*x85 + x96*
x99) + 5.19392739796971*(x82*x99 - x85*x96))*b125 + x33 =E= 0;
e35.. -(1.7011396670944*(sqr(x85) + sqr(x99)) - 1.7011396670944*(x85*x82 + x99*
x96) + 5.19392739796971*(x85*x96 - x82*x99))*b125 + x34 =E= 0;
e36.. -(1.98597570992556*(sqr(x83) + sqr(x97)) - 1.98597570992556*(x83*x84 +
x97*x98) + 5.06881697759392*(x83*x98 - x84*x97))*b126 + x35 =E= 0;
e37.. -(1.98597570992556*(sqr(x84) + sqr(x98)) - 1.98597570992556*(x84*x83 +
x98*x97) + 5.06881697759392*(x84*x97 - x83*x98))*b126 + x36 =E= 0;
e38.. -1.79797907152361*(x84*x103 - x89*x98)*b127 + x37 =E= 0;
e39.. -1.79797907152361*(x89*x98 - x84*x103)*b127 + x38 =E= 0;
e40.. -(1.68603315061494*(sqr(x82) + sqr(x96)) - 1.68603315061494*(x82*x84 +
x96*x98) + 5.11583832587208*(x82*x98 - x84*x96))*b128 + x39 =E= 0;
e41.. -(1.68603315061494*(sqr(x84) + sqr(x98)) - 1.68603315061494*(x84*x82 +
x98*x96) + 5.11583832587208*(x84*x96 - x82*x98))*b128 + x40 =E= 0;
e42.. -(4.75996315175772*(sqr(x82) + sqr(x96)) - 4.78186315175772*(x82*x83 +
x96*x97) - 1.1350191923074*(x82*x97 - x83*x96))*b109 + x41 =E= 0;
e43.. -(4.75996315175772*(sqr(x83) + sqr(x97)) - 4.78186315175772*(x83*x82 +
x97*x96) - 1.1350191923074*(x83*x96 - x82*x97))*b109 + x42 =E= 0;
e44.. -(9.09008271975275*(sqr(x87) + sqr(x101)) - 9.09008271975275*(x87*x89 +
x101*x103))*b110 + x43 =E= 0;
e45.. -(9.09008271975275*(sqr(x89) + sqr(x103)) - 9.09008271975275*(x89*x87 +
x103*x101))*b110 + x44 =E= 0;
e46.. -(4.40294374946052*(sqr(x90) + sqr(x104)) - 4.40294374946052*(x90*x91 +
x104*x105) - 1.8808847537004*(x90*x105 - x91*x104))*b111 + x45 =E= 0;
e47.. -(4.40294374946052*(sqr(x91) + sqr(x105)) - 4.40294374946052*(x91*x90 +
x105*x104) - 1.8808847537004*(x91*x104 - x90*x105))*b111 + x46 =E= 0;
e48.. -(4.78194338179036*(sqr(x84) + sqr(x98)) - 4.78194338179036*(x84*x87 +
x98*x101))*b112 + x47 =E= 0;
e49.. -(4.78194338179036*(sqr(x87) + sqr(x101)) - 4.78194338179036*(x87*x84 +
x101*x98))*b112 + x48 =E= 0;
e50.. -(3.96793905245615*(sqr(x85) + sqr(x99)) - 3.96793905245615*(x85*x86 +
x99*x100))*b113 + x49 =E= 0;
e51.. -(3.96793905245615*(sqr(x86) + sqr(x100)) - 3.96793905245615*(x86*x85 +
x100*x99))*b113 + x50 =E= 0;
e52.. -(3.0290504569306*(sqr(x89) + sqr(x103)) - 3.0290504569306*(x89*x94 +
x103*x108) - 1.42400548701993*(x89*x108 - x94*x103))*b114 + x51 =E= 0;
e53.. -(3.0290504569306*(sqr(x94) + sqr(x108)) - 3.0290504569306*(x94*x89 +
x108*x103) - 1.42400548701993*(x94*x103 - x89*x108))*b114 + x52 =E= 0;
e54.. -(21.5785539816916*(sqr(x84) + sqr(x98)) - 21.5785539816916*(x84*x85 +
x98*x99) - 6.84098066149567*(x84*x99 - x85*x98))*b115 + x53 =E= 0;
e55.. -(21.5785539816916*(sqr(x85) + sqr(x99)) - 21.5785539816916*(x85*x84 +
x99*x98) - 6.84098066149567*(x85*x98 - x84*x99))*b115 + x54 =E= 0;
e56.. -(6.10275544819311*(sqr(x86) + sqr(x100)) - 6.10275544819311*(x86*x93 +
x100*x107) - 3.09892740383799*(x86*x107 - x93*x100))*b116 + x55 =E= 0;
e57.. -(6.10275544819311*(sqr(x93) + sqr(x107)) - 6.10275544819311*(x93*x86 +
x107*x100) - 3.09892740383799*(x93*x100 - x86*x107))*b116 + x56 =E= 0;
e58.. -(5.67697984672154*(sqr(x87) + sqr(x101)) - 5.67697984672154*(x87*x88 +
x101*x102))*b117 + x57 =E= 0;
e59.. -(5.67697984672154*(sqr(x88) + sqr(x102)) - 5.67697984672154*(x88*x87 +
x102*x101))*b117 + x58 =E= 0;
e60.. -(2.31496347510535*(sqr(x93) + sqr(x107)) - 2.31496347510535*(x93*x94 +
x107*x108) - 1.13699415780633*(x93*x108 - x94*x107))*b118 + x59 =E= 0;
e61.. -(2.31496347510535*(sqr(x94) + sqr(x108)) - 2.31496347510535*(x94*x93 +
x108*x107) - 1.13699415780633*(x94*x107 - x93*x108))*b118 + x60 =E= 0;
e62.. -(3.1759639650294*(sqr(x86) + sqr(x100)) - 3.1759639650294*(x86*x92 +
x100*x106) - 1.52596744045097*(x86*x106 - x92*x100))*b119 + x61 =E= 0;
e63.. -(3.1759639650294*(sqr(x92) + sqr(x106)) - 3.1759639650294*(x92*x86 +
x106*x100) - 1.52596744045097*(x92*x100 - x86*x106))*b119 + x62 =E= 0;
e64.. -(4.09407434424044*(sqr(x86) + sqr(x100)) - 4.09407434424044*(x86*x91 +
x100*x105) - 1.95502856317726*(x86*x105 - x91*x100))*b120 + x63 =E= 0;
e65.. -(4.09407434424044*(sqr(x91) + sqr(x105)) - 4.09407434424044*(x91*x86 +
x105*x100) - 1.95502856317726*(x91*x100 - x86*x105))*b120 + x64 =E= 0;
e66.. -(2.25197462617221*(sqr(x92) + sqr(x106)) - 2.25197462617221*(x92*x93 +
x106*x107) - 2.48902458682192*(x92*x107 - x93*x106))*b121 + x65 =E= 0;
e67.. -(2.25197462617221*(sqr(x93) + sqr(x107)) - 2.25197462617221*(x93*x92 +
x107*x106) - 2.48902458682192*(x93*x106 - x92*x107))*b121 + x66 =E= 0;
e68.. -(4.21038368233483*(sqr(x81) + sqr(x95)) - 4.23498368233483*(x81*x85 +
x95*x99) - 1.02589745497019*(x81*x99 - x85*x95))*b122 + x67 =E= 0;
e69.. -(4.21038368233483*(sqr(x85) + sqr(x99)) - 4.23498368233483*(x85*x81 +
x99*x95) - 1.02589745497019*(x85*x95 - x81*x99))*b122 + x68 =E= 0;
e70.. -(10.3653941270609*(sqr(x89) + sqr(x103)) - 10.3653941270609*(x89*x90 +
x103*x104) - 3.90204955244743*(x89*x104 - x90*x103))*b123 + x69 =E= 0;
e71.. -(10.3653941270609*(sqr(x90) + sqr(x104)) - 10.3653941270609*(x90*x89 +
x104*x103) - 3.90204955244743*(x90*x103 - x89*x104))*b123 + x70 =E= 0;
e72.. -(15.2366865231796*(sqr(x81) + sqr(x95)) - 15.2630865231796*(x81*x82 +
x95*x96) - 4.99913160079803*(x81*x96 - x82*x95))*b124 + x71 =E= 0;
e73.. -(15.2366865231796*(sqr(x82) + sqr(x96)) - 15.2630865231796*(x82*x81 +
x96*x95) - 4.99913160079803*(x82*x95 - x81*x96))*b124 + x72 =E= 0;
e74.. -(5.17662739796971*(sqr(x82) + sqr(x96)) - 5.19392739796971*(x82*x85 +
x96*x99) - 1.7011396670944*(x82*x99 - x85*x96))*b125 + x73 =E= 0;
e75.. -(5.17662739796971*(sqr(x85) + sqr(x99)) - 5.19392739796971*(x85*x82 +
x99*x96) - 1.7011396670944*(x85*x96 - x82*x99))*b125 + x74 =E= 0;
e76.. -(5.06241697759392*(sqr(x83) + sqr(x97)) - 5.06881697759392*(x83*x84 +
x97*x98) - 1.98597570992556*(x83*x98 - x84*x97))*b126 + x75 =E= 0;
e77.. -(5.06241697759392*(sqr(x84) + sqr(x98)) - 5.06881697759392*(x84*x83 +
x98*x97) - 1.98597570992556*(x84*x97 - x83*x98))*b126 + x76 =E= 0;
e78.. -(1.79797907152361*(sqr(x84) + sqr(x98)) - 1.79797907152361*(x84*x89 +
x98*x103))*b127 + x77 =E= 0;
e79.. -(1.79797907152361*(sqr(x89) + sqr(x103)) - 1.79797907152361*(x89*x84 +
x103*x98))*b127 + x78 =E= 0;
e80.. -(5.09883832587208*(sqr(x82) + sqr(x96)) - 5.11583832587208*(x82*x84 +
x96*x98) - 1.68603315061494*(x82*x98 - x84*x96))*b128 + x79 =E= 0;
e81.. -(5.09883832587208*(sqr(x84) + sqr(x98)) - 5.11583832587208*(x84*x82 +
x98*x96) - 1.68603315061494*(x84*x96 - x82*x98))*b128 + 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.. x129 =L= 3.324;
e151.. x130 =L= 1.4;
e152.. x131 =L= 1;
e153.. x132 =L= 1;
e154.. x133 =L= 1;
e155.. x129 =G= 0;
e156.. x130 =G= 0;
e157.. x131 =G= 0;
e158.. x132 =G= 0;
e159.. x133 =G= 0;
e160.. x134 =L= 0.1;
e161.. x135 =L= 0.5;
e162.. x136 =L= 0.4;
e163.. x137 =L= 0.24;
e164.. x138 =L= 0.24;
e165.. x134 =G= 0;
e166.. x135 =G= -0.4;
e167.. x136 =G= 0;
e168.. x137 =G= -0.06;
e169.. x138 =G= -0.06;
e170.. x95 =E= 0;
e171.. x27 + x31 - x129 =E= 0;
e172.. x1 + x32 + x33 + x39 - x130 =E= -0.217;
e173.. x2 + x35 - x131 =E= -0.942;
e174.. x10 + x15 + x21 + x23 - x132 =E= -0.112;
e175.. x18 - x133 =E= 0;
e176.. x67 + x71 - x134 =E= 0;
e177.. x41 + x72 + x73 + x79 - x135 =E= -0.127;
e178.. x42 + x75 - x136 =E= -0.19;
e179.. x50 + x55 + x61 + x63 - x137 =E= -0.075;
e180.. x58 - x138 =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 MINLP $set MINLP MINLP
Solve m using %MINLP% minimizing objvar;
Last updated: 2025-08-07 Git hash: e62cedfc