MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
Home // Instances // Documentation // Download // Statistics
Instance elec25
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 87.21562003 (ANTIGONE) 90.22758027 (BARON) 86.66541259 (COUENNE) 86.88895946 (GUROBI) 243.81276030 (LINDO) 152.71358790 (SCIP) |
| Referencesⓘ | Morris, J R, Deaven, D M, and Ho, K M, Genetic Algorithm Energy Minimization for Point Charges on a Sphere, Physical Review B, 53:4-15, 1996, R1740-R1743. Saff, E B and Kuijlaars, A, Distributing Many Points on a Sphere, The Mathematical Intelligencer, 19:1, 1997, 5-11. Dolan, E D and More, J J, Benchmarking Optimization Software with COPS, Tech. Rep. ANL/MCS-246, Mathematics and Computer Science Division, 2000. |
| Sourceⓘ | GAMS Model Library model elec, Constrained Optimization Problem Set (COPS) |
| Applicationⓘ | Electrons on a Sphere |
| Added to libraryⓘ | 31 Jul 2001 |
| Problem typeⓘ | NLP |
| #Variablesⓘ | 75 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 75 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | nonlinear |
| Objective curvatureⓘ | indefinite |
| #Nonzeros in Objectiveⓘ | 75 |
| #Nonlinear Nonzeros in Objectiveⓘ | 75 |
| #Constraintsⓘ | 25 |
| #Linear Constraintsⓘ | 0 |
| #Quadratic Constraintsⓘ | 25 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | div sqr sqrt |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 75 |
| #Nonlinear Nonzeros in Jacobianⓘ | 75 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 5625 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 75 |
| #Blocks in Hessian of Lagrangianⓘ | 1 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 75 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 75 |
| Average blocksize in Hessian of Lagrangianⓘ | 75.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e+00 |
| Maximal coefficientⓘ | 1.0000e+00 |
| Infeasibility of initial pointⓘ | 1.11e-15 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 26 26 0 0 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 76 76 0 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 151 1 150 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,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;
e1.. -(1/sqrt(sqr(x1 - x2) + sqr(x26 - x27) + sqr(x51 - x52)) + 1/sqrt(sqr(x1
- x3) + sqr(x26 - x28) + sqr(x51 - x53)) + 1/sqrt(sqr(x1 - x4) + sqr(x26
- x29) + sqr(x51 - x54)) + 1/sqrt(sqr(x1 - x5) + sqr(x26 - x30) + sqr(x51
- x55)) + 1/sqrt(sqr(x1 - x6) + sqr(x26 - x31) + sqr(x51 - x56)) + 1/
sqrt(sqr(x1 - x7) + sqr(x26 - x32) + sqr(x51 - x57)) + 1/sqrt(sqr(x1 - x8)
+ sqr(x26 - x33) + sqr(x51 - x58)) + 1/sqrt(sqr(x1 - x9) + sqr(x26 - x34)
+ sqr(x51 - x59)) + 1/sqrt(sqr(x1 - x10) + sqr(x26 - x35) + sqr(x51 - x60
)) + 1/sqrt(sqr(x1 - x11) + sqr(x26 - x36) + sqr(x51 - x61)) + 1/sqrt(sqr(
x1 - x12) + sqr(x26 - x37) + sqr(x51 - x62)) + 1/sqrt(sqr(x1 - x13) + sqr(
x26 - x38) + sqr(x51 - x63)) + 1/sqrt(sqr(x1 - x14) + sqr(x26 - x39) +
sqr(x51 - x64)) + 1/sqrt(sqr(x1 - x15) + sqr(x26 - x40) + sqr(x51 - x65))
+ 1/sqrt(sqr(x1 - x16) + sqr(x26 - x41) + sqr(x51 - x66)) + 1/sqrt(sqr(x1
- x17) + sqr(x26 - x42) + sqr(x51 - x67)) + 1/sqrt(sqr(x1 - x18) + sqr(
x26 - x43) + sqr(x51 - x68)) + 1/sqrt(sqr(x1 - x19) + sqr(x26 - x44) +
sqr(x51 - x69)) + 1/sqrt(sqr(x1 - x20) + sqr(x26 - x45) + sqr(x51 - x70))
+ 1/sqrt(sqr(x1 - x21) + sqr(x26 - x46) + sqr(x51 - x71)) + 1/sqrt(sqr(x1
- x22) + sqr(x26 - x47) + sqr(x51 - x72)) + 1/sqrt(sqr(x1 - x23) + sqr(
x26 - x48) + sqr(x51 - x73)) + 1/sqrt(sqr(x1 - x24) + sqr(x26 - x49) +
sqr(x51 - x74)) + 1/sqrt(sqr(x1 - x25) + sqr(x26 - x50) + sqr(x51 - x75))
+ 1/sqrt(sqr(x2 - x3) + sqr(x27 - x28) + sqr(x52 - x53)) + 1/sqrt(sqr(x2
- x4) + sqr(x27 - x29) + sqr(x52 - x54)) + 1/sqrt(sqr(x2 - x5) + sqr(x27
- x30) + sqr(x52 - x55)) + 1/sqrt(sqr(x2 - x6) + sqr(x27 - x31) + sqr(x52
- x56)) + 1/sqrt(sqr(x2 - x7) + sqr(x27 - x32) + sqr(x52 - x57)) + 1/
sqrt(sqr(x2 - x8) + sqr(x27 - x33) + sqr(x52 - x58)) + 1/sqrt(sqr(x2 - x9)
+ sqr(x27 - x34) + sqr(x52 - x59)) + 1/sqrt(sqr(x2 - x10) + sqr(x27 - x35
) + sqr(x52 - x60)) + 1/sqrt(sqr(x2 - x11) + sqr(x27 - x36) + sqr(x52 -
x61)) + 1/sqrt(sqr(x2 - x12) + sqr(x27 - x37) + sqr(x52 - x62)) + 1/sqrt(
sqr(x2 - x13) + sqr(x27 - x38) + sqr(x52 - x63)) + 1/sqrt(sqr(x2 - x14) +
sqr(x27 - x39) + sqr(x52 - x64)) + 1/sqrt(sqr(x2 - x15) + sqr(x27 - x40)
+ sqr(x52 - x65)) + 1/sqrt(sqr(x2 - x16) + sqr(x27 - x41) + sqr(x52 - x66
)) + 1/sqrt(sqr(x2 - x17) + sqr(x27 - x42) + sqr(x52 - x67)) + 1/sqrt(sqr(
x2 - x18) + sqr(x27 - x43) + sqr(x52 - x68)) + 1/sqrt(sqr(x2 - x19) + sqr(
x27 - x44) + sqr(x52 - x69)) + 1/sqrt(sqr(x2 - x20) + sqr(x27 - x45) +
sqr(x52 - x70)) + 1/sqrt(sqr(x2 - x21) + sqr(x27 - x46) + sqr(x52 - x71))
+ 1/sqrt(sqr(x2 - x22) + sqr(x27 - x47) + sqr(x52 - x72)) + 1/sqrt(sqr(x2
- x23) + sqr(x27 - x48) + sqr(x52 - x73)) + 1/sqrt(sqr(x2 - x24) + sqr(
x27 - x49) + sqr(x52 - x74)) + 1/sqrt(sqr(x2 - x25) + sqr(x27 - x50) +
sqr(x52 - x75)) + 1/sqrt(sqr(x3 - x4) + sqr(x28 - x29) + sqr(x53 - x54))
+ 1/sqrt(sqr(x3 - x5) + sqr(x28 - x30) + sqr(x53 - x55)) + 1/sqrt(sqr(x3
- x6) + sqr(x28 - x31) + sqr(x53 - x56)) + 1/sqrt(sqr(x3 - x7) + sqr(x28
- x32) + sqr(x53 - x57)) + 1/sqrt(sqr(x3 - x8) + sqr(x28 - x33) + sqr(x53
- x58)) + 1/sqrt(sqr(x3 - x9) + sqr(x28 - x34) + sqr(x53 - x59)) + 1/
sqrt(sqr(x3 - x10) + sqr(x28 - x35) + sqr(x53 - x60)) + 1/sqrt(sqr(x3 -
x11) + sqr(x28 - x36) + sqr(x53 - x61)) + 1/sqrt(sqr(x3 - x12) + sqr(x28
- x37) + sqr(x53 - x62)) + 1/sqrt(sqr(x3 - x13) + sqr(x28 - x38) + sqr(
x53 - x63)) + 1/sqrt(sqr(x3 - x14) + sqr(x28 - x39) + sqr(x53 - x64)) + 1/
sqrt(sqr(x3 - x15) + sqr(x28 - x40) + sqr(x53 - x65)) + 1/sqrt(sqr(x3 -
x16) + sqr(x28 - x41) + sqr(x53 - x66)) + 1/sqrt(sqr(x3 - x17) + sqr(x28
- x42) + sqr(x53 - x67)) + 1/sqrt(sqr(x3 - x18) + sqr(x28 - x43) + sqr(
x53 - x68)) + 1/sqrt(sqr(x3 - x19) + sqr(x28 - x44) + sqr(x53 - x69)) + 1/
sqrt(sqr(x3 - x20) + sqr(x28 - x45) + sqr(x53 - x70)) + 1/sqrt(sqr(x3 -
x21) + sqr(x28 - x46) + sqr(x53 - x71)) + 1/sqrt(sqr(x3 - x22) + sqr(x28
- x47) + sqr(x53 - x72)) + 1/sqrt(sqr(x3 - x23) + sqr(x28 - x48) + sqr(
x53 - x73)) + 1/sqrt(sqr(x3 - x24) + sqr(x28 - x49) + sqr(x53 - x74)) + 1/
sqrt(sqr(x3 - x25) + sqr(x28 - x50) + sqr(x53 - x75)) + 1/sqrt(sqr(x4 - x5
) + sqr(x29 - x30) + sqr(x54 - x55)) + 1/sqrt(sqr(x4 - x6) + sqr(x29 - x31
) + sqr(x54 - x56)) + 1/sqrt(sqr(x4 - x7) + sqr(x29 - x32) + sqr(x54 - x57
)) + 1/sqrt(sqr(x4 - x8) + sqr(x29 - x33) + sqr(x54 - x58)) + 1/sqrt(sqr(
x4 - x9) + sqr(x29 - x34) + sqr(x54 - x59)) + 1/sqrt(sqr(x4 - x10) + sqr(
x29 - x35) + sqr(x54 - x60)) + 1/sqrt(sqr(x4 - x11) + sqr(x29 - x36) +
sqr(x54 - x61)) + 1/sqrt(sqr(x4 - x12) + sqr(x29 - x37) + sqr(x54 - x62))
+ 1/sqrt(sqr(x4 - x13) + sqr(x29 - x38) + sqr(x54 - x63)) + 1/sqrt(sqr(x4
- x14) + sqr(x29 - x39) + sqr(x54 - x64)) + 1/sqrt(sqr(x4 - x15) + sqr(
x29 - x40) + sqr(x54 - x65)) + 1/sqrt(sqr(x4 - x16) + sqr(x29 - x41) +
sqr(x54 - x66)) + 1/sqrt(sqr(x4 - x17) + sqr(x29 - x42) + sqr(x54 - x67))
+ 1/sqrt(sqr(x4 - x18) + sqr(x29 - x43) + sqr(x54 - x68)) + 1/sqrt(sqr(x4
- x19) + sqr(x29 - x44) + sqr(x54 - x69)) + 1/sqrt(sqr(x4 - x20) + sqr(
x29 - x45) + sqr(x54 - x70)) + 1/sqrt(sqr(x4 - x21) + sqr(x29 - x46) +
sqr(x54 - x71)) + 1/sqrt(sqr(x4 - x22) + sqr(x29 - x47) + sqr(x54 - x72))
+ 1/sqrt(sqr(x4 - x23) + sqr(x29 - x48) + sqr(x54 - x73)) + 1/sqrt(sqr(x4
- x24) + sqr(x29 - x49) + sqr(x54 - x74)) + 1/sqrt(sqr(x4 - x25) + sqr(
x29 - x50) + sqr(x54 - x75)) + 1/sqrt(sqr(x5 - x6) + sqr(x30 - x31) + sqr(
x55 - x56)) + 1/sqrt(sqr(x5 - x7) + sqr(x30 - x32) + sqr(x55 - x57)) + 1/
sqrt(sqr(x5 - x8) + sqr(x30 - x33) + sqr(x55 - x58)) + 1/sqrt(sqr(x5 - x9)
+ sqr(x30 - x34) + sqr(x55 - x59)) + 1/sqrt(sqr(x5 - x10) + sqr(x30 - x35
) + sqr(x55 - x60)) + 1/sqrt(sqr(x5 - x11) + sqr(x30 - x36) + sqr(x55 -
x61)) + 1/sqrt(sqr(x5 - x12) + sqr(x30 - x37) + sqr(x55 - x62)) + 1/sqrt(
sqr(x5 - x13) + sqr(x30 - x38) + sqr(x55 - x63)) + 1/sqrt(sqr(x5 - x14) +
sqr(x30 - x39) + sqr(x55 - x64)) + 1/sqrt(sqr(x5 - x15) + sqr(x30 - x40)
+ sqr(x55 - x65)) + 1/sqrt(sqr(x5 - x16) + sqr(x30 - x41) + sqr(x55 - x66
)) + 1/sqrt(sqr(x5 - x17) + sqr(x30 - x42) + sqr(x55 - x67)) + 1/sqrt(sqr(
x5 - x18) + sqr(x30 - x43) + sqr(x55 - x68)) + 1/sqrt(sqr(x5 - x19) + sqr(
x30 - x44) + sqr(x55 - x69)) + 1/sqrt(sqr(x5 - x20) + sqr(x30 - x45) +
sqr(x55 - x70)) + 1/sqrt(sqr(x5 - x21) + sqr(x30 - x46) + sqr(x55 - x71))
+ 1/sqrt(sqr(x5 - x22) + sqr(x30 - x47) + sqr(x55 - x72)) + 1/sqrt(sqr(x5
- x23) + sqr(x30 - x48) + sqr(x55 - x73)) + 1/sqrt(sqr(x5 - x24) + sqr(
x30 - x49) + sqr(x55 - x74)) + 1/sqrt(sqr(x5 - x25) + sqr(x30 - x50) +
sqr(x55 - x75)) + 1/sqrt(sqr(x6 - x7) + sqr(x31 - x32) + sqr(x56 - x57))
+ 1/sqrt(sqr(x6 - x8) + sqr(x31 - x33) + sqr(x56 - x58)) + 1/sqrt(sqr(x6
- x9) + sqr(x31 - x34) + sqr(x56 - x59)) + 1/sqrt(sqr(x6 - x10) + sqr(x31
- x35) + sqr(x56 - x60)) + 1/sqrt(sqr(x6 - x11) + sqr(x31 - x36) + sqr(
x56 - x61)) + 1/sqrt(sqr(x6 - x12) + sqr(x31 - x37) + sqr(x56 - x62)) + 1/
sqrt(sqr(x6 - x13) + sqr(x31 - x38) + sqr(x56 - x63)) + 1/sqrt(sqr(x6 -
x14) + sqr(x31 - x39) + sqr(x56 - x64)) + 1/sqrt(sqr(x6 - x15) + sqr(x31
- x40) + sqr(x56 - x65)) + 1/sqrt(sqr(x6 - x16) + sqr(x31 - x41) + sqr(
x56 - x66)) + 1/sqrt(sqr(x6 - x17) + sqr(x31 - x42) + sqr(x56 - x67)) + 1/
sqrt(sqr(x6 - x18) + sqr(x31 - x43) + sqr(x56 - x68)) + 1/sqrt(sqr(x6 -
x19) + sqr(x31 - x44) + sqr(x56 - x69)) + 1/sqrt(sqr(x6 - x20) + sqr(x31
- x45) + sqr(x56 - x70)) + 1/sqrt(sqr(x6 - x21) + sqr(x31 - x46) + sqr(
x56 - x71)) + 1/sqrt(sqr(x6 - x22) + sqr(x31 - x47) + sqr(x56 - x72)) + 1/
sqrt(sqr(x6 - x23) + sqr(x31 - x48) + sqr(x56 - x73)) + 1/sqrt(sqr(x6 -
x24) + sqr(x31 - x49) + sqr(x56 - x74)) + 1/sqrt(sqr(x6 - x25) + sqr(x31
- x50) + sqr(x56 - x75)) + 1/sqrt(sqr(x7 - x8) + sqr(x32 - x33) + sqr(x57
- x58)) + 1/sqrt(sqr(x7 - x9) + sqr(x32 - x34) + sqr(x57 - x59)) + 1/
sqrt(sqr(x7 - x10) + sqr(x32 - x35) + sqr(x57 - x60)) + 1/sqrt(sqr(x7 -
x11) + sqr(x32 - x36) + sqr(x57 - x61)) + 1/sqrt(sqr(x7 - x12) + sqr(x32
- x37) + sqr(x57 - x62)) + 1/sqrt(sqr(x7 - x13) + sqr(x32 - x38) + sqr(
x57 - x63)) + 1/sqrt(sqr(x7 - x14) + sqr(x32 - x39) + sqr(x57 - x64)) + 1/
sqrt(sqr(x7 - x15) + sqr(x32 - x40) + sqr(x57 - x65)) + 1/sqrt(sqr(x7 -
x16) + sqr(x32 - x41) + sqr(x57 - x66)) + 1/sqrt(sqr(x7 - x17) + sqr(x32
- x42) + sqr(x57 - x67)) + 1/sqrt(sqr(x7 - x18) + sqr(x32 - x43) + sqr(
x57 - x68)) + 1/sqrt(sqr(x7 - x19) + sqr(x32 - x44) + sqr(x57 - x69)) + 1/
sqrt(sqr(x7 - x20) + sqr(x32 - x45) + sqr(x57 - x70)) + 1/sqrt(sqr(x7 -
x21) + sqr(x32 - x46) + sqr(x57 - x71)) + 1/sqrt(sqr(x7 - x22) + sqr(x32
- x47) + sqr(x57 - x72)) + 1/sqrt(sqr(x7 - x23) + sqr(x32 - x48) + sqr(
x57 - x73)) + 1/sqrt(sqr(x7 - x24) + sqr(x32 - x49) + sqr(x57 - x74)) + 1/
sqrt(sqr(x7 - x25) + sqr(x32 - x50) + sqr(x57 - x75)) + 1/sqrt(sqr(x8 - x9
) + sqr(x33 - x34) + sqr(x58 - x59)) + 1/sqrt(sqr(x8 - x10) + sqr(x33 -
x35) + sqr(x58 - x60)) + 1/sqrt(sqr(x8 - x11) + sqr(x33 - x36) + sqr(x58
- x61)) + 1/sqrt(sqr(x8 - x12) + sqr(x33 - x37) + sqr(x58 - x62)) + 1/
sqrt(sqr(x8 - x13) + sqr(x33 - x38) + sqr(x58 - x63)) + 1/sqrt(sqr(x8 -
x14) + sqr(x33 - x39) + sqr(x58 - x64)) + 1/sqrt(sqr(x8 - x15) + sqr(x33
- x40) + sqr(x58 - x65)) + 1/sqrt(sqr(x8 - x16) + sqr(x33 - x41) + sqr(
x58 - x66)) + 1/sqrt(sqr(x8 - x17) + sqr(x33 - x42) + sqr(x58 - x67)) + 1/
sqrt(sqr(x8 - x18) + sqr(x33 - x43) + sqr(x58 - x68)) + 1/sqrt(sqr(x8 -
x19) + sqr(x33 - x44) + sqr(x58 - x69)) + 1/sqrt(sqr(x8 - x20) + sqr(x33
- x45) + sqr(x58 - x70)) + 1/sqrt(sqr(x8 - x21) + sqr(x33 - x46) + sqr(
x58 - x71)) + 1/sqrt(sqr(x8 - x22) + sqr(x33 - x47) + sqr(x58 - x72)) + 1/
sqrt(sqr(x8 - x23) + sqr(x33 - x48) + sqr(x58 - x73)) + 1/sqrt(sqr(x8 -
x24) + sqr(x33 - x49) + sqr(x58 - x74)) + 1/sqrt(sqr(x8 - x25) + sqr(x33
- x50) + sqr(x58 - x75)) + 1/sqrt(sqr(x9 - x10) + sqr(x34 - x35) + sqr(
x59 - x60)) + 1/sqrt(sqr(x9 - x11) + sqr(x34 - x36) + sqr(x59 - x61)) + 1/
sqrt(sqr(x9 - x12) + sqr(x34 - x37) + sqr(x59 - x62)) + 1/sqrt(sqr(x9 -
x13) + sqr(x34 - x38) + sqr(x59 - x63)) + 1/sqrt(sqr(x9 - x14) + sqr(x34
- x39) + sqr(x59 - x64)) + 1/sqrt(sqr(x9 - x15) + sqr(x34 - x40) + sqr(
x59 - x65)) + 1/sqrt(sqr(x9 - x16) + sqr(x34 - x41) + sqr(x59 - x66)) + 1/
sqrt(sqr(x9 - x17) + sqr(x34 - x42) + sqr(x59 - x67)) + 1/sqrt(sqr(x9 -
x18) + sqr(x34 - x43) + sqr(x59 - x68)) + 1/sqrt(sqr(x9 - x19) + sqr(x34
- x44) + sqr(x59 - x69)) + 1/sqrt(sqr(x9 - x20) + sqr(x34 - x45) + sqr(
x59 - x70)) + 1/sqrt(sqr(x9 - x21) + sqr(x34 - x46) + sqr(x59 - x71)) + 1/
sqrt(sqr(x9 - x22) + sqr(x34 - x47) + sqr(x59 - x72)) + 1/sqrt(sqr(x9 -
x23) + sqr(x34 - x48) + sqr(x59 - x73)) + 1/sqrt(sqr(x9 - x24) + sqr(x34
- x49) + sqr(x59 - x74)) + 1/sqrt(sqr(x9 - x25) + sqr(x34 - x50) + sqr(
x59 - x75)) + 1/sqrt(sqr(x10 - x11) + sqr(x35 - x36) + sqr(x60 - x61)) + 1
/sqrt(sqr(x10 - x12) + sqr(x35 - x37) + sqr(x60 - x62)) + 1/sqrt(sqr(x10
- x13) + sqr(x35 - x38) + sqr(x60 - x63)) + 1/sqrt(sqr(x10 - x14) + sqr(
x35 - x39) + sqr(x60 - x64)) + 1/sqrt(sqr(x10 - x15) + sqr(x35 - x40) +
sqr(x60 - x65)) + 1/sqrt(sqr(x10 - x16) + sqr(x35 - x41) + sqr(x60 - x66))
+ 1/sqrt(sqr(x10 - x17) + sqr(x35 - x42) + sqr(x60 - x67)) + 1/sqrt(sqr(
x10 - x18) + sqr(x35 - x43) + sqr(x60 - x68)) + 1/sqrt(sqr(x10 - x19) +
sqr(x35 - x44) + sqr(x60 - x69)) + 1/sqrt(sqr(x10 - x20) + sqr(x35 - x45)
+ sqr(x60 - x70)) + 1/sqrt(sqr(x10 - x21) + sqr(x35 - x46) + sqr(x60 -
x71)) + 1/sqrt(sqr(x10 - x22) + sqr(x35 - x47) + sqr(x60 - x72)) + 1/sqrt(
sqr(x10 - x23) + sqr(x35 - x48) + sqr(x60 - x73)) + 1/sqrt(sqr(x10 - x24)
+ sqr(x35 - x49) + sqr(x60 - x74)) + 1/sqrt(sqr(x10 - x25) + sqr(x35 -
x50) + sqr(x60 - x75)) + 1/sqrt(sqr(x11 - x12) + sqr(x36 - x37) + sqr(x61
- x62)) + 1/sqrt(sqr(x11 - x13) + sqr(x36 - x38) + sqr(x61 - x63)) + 1/
sqrt(sqr(x11 - x14) + sqr(x36 - x39) + sqr(x61 - x64)) + 1/sqrt(sqr(x11 -
x15) + sqr(x36 - x40) + sqr(x61 - x65)) + 1/sqrt(sqr(x11 - x16) + sqr(x36
- x41) + sqr(x61 - x66)) + 1/sqrt(sqr(x11 - x17) + sqr(x36 - x42) + sqr(
x61 - x67)) + 1/sqrt(sqr(x11 - x18) + sqr(x36 - x43) + sqr(x61 - x68)) + 1
/sqrt(sqr(x11 - x19) + sqr(x36 - x44) + sqr(x61 - x69)) + 1/sqrt(sqr(x11
- x20) + sqr(x36 - x45) + sqr(x61 - x70)) + 1/sqrt(sqr(x11 - x21) + sqr(
x36 - x46) + sqr(x61 - x71)) + 1/sqrt(sqr(x11 - x22) + sqr(x36 - x47) +
sqr(x61 - x72)) + 1/sqrt(sqr(x11 - x23) + sqr(x36 - x48) + sqr(x61 - x73))
+ 1/sqrt(sqr(x11 - x24) + sqr(x36 - x49) + sqr(x61 - x74)) + 1/sqrt(sqr(
x11 - x25) + sqr(x36 - x50) + sqr(x61 - x75)) + 1/sqrt(sqr(x12 - x13) +
sqr(x37 - x38) + sqr(x62 - x63)) + 1/sqrt(sqr(x12 - x14) + sqr(x37 - x39)
+ sqr(x62 - x64)) + 1/sqrt(sqr(x12 - x15) + sqr(x37 - x40) + sqr(x62 -
x65)) + 1/sqrt(sqr(x12 - x16) + sqr(x37 - x41) + sqr(x62 - x66)) + 1/sqrt(
sqr(x12 - x17) + sqr(x37 - x42) + sqr(x62 - x67)) + 1/sqrt(sqr(x12 - x18)
+ sqr(x37 - x43) + sqr(x62 - x68)) + 1/sqrt(sqr(x12 - x19) + sqr(x37 -
x44) + sqr(x62 - x69)) + 1/sqrt(sqr(x12 - x20) + sqr(x37 - x45) + sqr(x62
- x70)) + 1/sqrt(sqr(x12 - x21) + sqr(x37 - x46) + sqr(x62 - x71)) + 1/
sqrt(sqr(x12 - x22) + sqr(x37 - x47) + sqr(x62 - x72)) + 1/sqrt(sqr(x12 -
x23) + sqr(x37 - x48) + sqr(x62 - x73)) + 1/sqrt(sqr(x12 - x24) + sqr(x37
- x49) + sqr(x62 - x74)) + 1/sqrt(sqr(x12 - x25) + sqr(x37 - x50) + sqr(
x62 - x75)) + 1/sqrt(sqr(x13 - x14) + sqr(x38 - x39) + sqr(x63 - x64)) + 1
/sqrt(sqr(x13 - x15) + sqr(x38 - x40) + sqr(x63 - x65)) + 1/sqrt(sqr(x13
- x16) + sqr(x38 - x41) + sqr(x63 - x66)) + 1/sqrt(sqr(x13 - x17) + sqr(
x38 - x42) + sqr(x63 - x67)) + 1/sqrt(sqr(x13 - x18) + sqr(x38 - x43) +
sqr(x63 - x68)) + 1/sqrt(sqr(x13 - x19) + sqr(x38 - x44) + sqr(x63 - x69))
+ 1/sqrt(sqr(x13 - x20) + sqr(x38 - x45) + sqr(x63 - x70)) + 1/sqrt(sqr(
x13 - x21) + sqr(x38 - x46) + sqr(x63 - x71)) + 1/sqrt(sqr(x13 - x22) +
sqr(x38 - x47) + sqr(x63 - x72)) + 1/sqrt(sqr(x13 - x23) + sqr(x38 - x48)
+ sqr(x63 - x73)) + 1/sqrt(sqr(x13 - x24) + sqr(x38 - x49) + sqr(x63 -
x74)) + 1/sqrt(sqr(x13 - x25) + sqr(x38 - x50) + sqr(x63 - x75)) + 1/sqrt(
sqr(x14 - x15) + sqr(x39 - x40) + sqr(x64 - x65)) + 1/sqrt(sqr(x14 - x16)
+ sqr(x39 - x41) + sqr(x64 - x66)) + 1/sqrt(sqr(x14 - x17) + sqr(x39 -
x42) + sqr(x64 - x67)) + 1/sqrt(sqr(x14 - x18) + sqr(x39 - x43) + sqr(x64
- x68)) + 1/sqrt(sqr(x14 - x19) + sqr(x39 - x44) + sqr(x64 - x69)) + 1/
sqrt(sqr(x14 - x20) + sqr(x39 - x45) + sqr(x64 - x70)) + 1/sqrt(sqr(x14 -
x21) + sqr(x39 - x46) + sqr(x64 - x71)) + 1/sqrt(sqr(x14 - x22) + sqr(x39
- x47) + sqr(x64 - x72)) + 1/sqrt(sqr(x14 - x23) + sqr(x39 - x48) + sqr(
x64 - x73)) + 1/sqrt(sqr(x14 - x24) + sqr(x39 - x49) + sqr(x64 - x74)) + 1
/sqrt(sqr(x14 - x25) + sqr(x39 - x50) + sqr(x64 - x75)) + 1/sqrt(sqr(x15
- x16) + sqr(x40 - x41) + sqr(x65 - x66)) + 1/sqrt(sqr(x15 - x17) + sqr(
x40 - x42) + sqr(x65 - x67)) + 1/sqrt(sqr(x15 - x18) + sqr(x40 - x43) +
sqr(x65 - x68)) + 1/sqrt(sqr(x15 - x19) + sqr(x40 - x44) + sqr(x65 - x69))
+ 1/sqrt(sqr(x15 - x20) + sqr(x40 - x45) + sqr(x65 - x70)) + 1/sqrt(sqr(
x15 - x21) + sqr(x40 - x46) + sqr(x65 - x71)) + 1/sqrt(sqr(x15 - x22) +
sqr(x40 - x47) + sqr(x65 - x72)) + 1/sqrt(sqr(x15 - x23) + sqr(x40 - x48)
+ sqr(x65 - x73)) + 1/sqrt(sqr(x15 - x24) + sqr(x40 - x49) + sqr(x65 -
x74)) + 1/sqrt(sqr(x15 - x25) + sqr(x40 - x50) + sqr(x65 - x75)) + 1/sqrt(
sqr(x16 - x17) + sqr(x41 - x42) + sqr(x66 - x67)) + 1/sqrt(sqr(x16 - x18)
+ sqr(x41 - x43) + sqr(x66 - x68)) + 1/sqrt(sqr(x16 - x19) + sqr(x41 -
x44) + sqr(x66 - x69)) + 1/sqrt(sqr(x16 - x20) + sqr(x41 - x45) + sqr(x66
- x70)) + 1/sqrt(sqr(x16 - x21) + sqr(x41 - x46) + sqr(x66 - x71)) + 1/
sqrt(sqr(x16 - x22) + sqr(x41 - x47) + sqr(x66 - x72)) + 1/sqrt(sqr(x16 -
x23) + sqr(x41 - x48) + sqr(x66 - x73)) + 1/sqrt(sqr(x16 - x24) + sqr(x41
- x49) + sqr(x66 - x74)) + 1/sqrt(sqr(x16 - x25) + sqr(x41 - x50) + sqr(
x66 - x75)) + 1/sqrt(sqr(x17 - x18) + sqr(x42 - x43) + sqr(x67 - x68)) + 1
/sqrt(sqr(x17 - x19) + sqr(x42 - x44) + sqr(x67 - x69)) + 1/sqrt(sqr(x17
- x20) + sqr(x42 - x45) + sqr(x67 - x70)) + 1/sqrt(sqr(x17 - x21) + sqr(
x42 - x46) + sqr(x67 - x71)) + 1/sqrt(sqr(x17 - x22) + sqr(x42 - x47) +
sqr(x67 - x72)) + 1/sqrt(sqr(x17 - x23) + sqr(x42 - x48) + sqr(x67 - x73))
+ 1/sqrt(sqr(x17 - x24) + sqr(x42 - x49) + sqr(x67 - x74)) + 1/sqrt(sqr(
x17 - x25) + sqr(x42 - x50) + sqr(x67 - x75)) + 1/sqrt(sqr(x18 - x19) +
sqr(x43 - x44) + sqr(x68 - x69)) + 1/sqrt(sqr(x18 - x20) + sqr(x43 - x45)
+ sqr(x68 - x70)) + 1/sqrt(sqr(x18 - x21) + sqr(x43 - x46) + sqr(x68 -
x71)) + 1/sqrt(sqr(x18 - x22) + sqr(x43 - x47) + sqr(x68 - x72)) + 1/sqrt(
sqr(x18 - x23) + sqr(x43 - x48) + sqr(x68 - x73)) + 1/sqrt(sqr(x18 - x24)
+ sqr(x43 - x49) + sqr(x68 - x74)) + 1/sqrt(sqr(x18 - x25) + sqr(x43 -
x50) + sqr(x68 - x75)) + 1/sqrt(sqr(x19 - x20) + sqr(x44 - x45) + sqr(x69
- x70)) + 1/sqrt(sqr(x19 - x21) + sqr(x44 - x46) + sqr(x69 - x71)) + 1/
sqrt(sqr(x19 - x22) + sqr(x44 - x47) + sqr(x69 - x72)) + 1/sqrt(sqr(x19 -
x23) + sqr(x44 - x48) + sqr(x69 - x73)) + 1/sqrt(sqr(x19 - x24) + sqr(x44
- x49) + sqr(x69 - x74)) + 1/sqrt(sqr(x19 - x25) + sqr(x44 - x50) + sqr(
x69 - x75)) + 1/sqrt(sqr(x20 - x21) + sqr(x45 - x46) + sqr(x70 - x71)) + 1
/sqrt(sqr(x20 - x22) + sqr(x45 - x47) + sqr(x70 - x72)) + 1/sqrt(sqr(x20
- x23) + sqr(x45 - x48) + sqr(x70 - x73)) + 1/sqrt(sqr(x20 - x24) + sqr(
x45 - x49) + sqr(x70 - x74)) + 1/sqrt(sqr(x20 - x25) + sqr(x45 - x50) +
sqr(x70 - x75)) + 1/sqrt(sqr(x21 - x22) + sqr(x46 - x47) + sqr(x71 - x72))
+ 1/sqrt(sqr(x21 - x23) + sqr(x46 - x48) + sqr(x71 - x73)) + 1/sqrt(sqr(
x21 - x24) + sqr(x46 - x49) + sqr(x71 - x74)) + 1/sqrt(sqr(x21 - x25) +
sqr(x46 - x50) + sqr(x71 - x75)) + 1/sqrt(sqr(x22 - x23) + sqr(x47 - x48)
+ sqr(x72 - x73)) + 1/sqrt(sqr(x22 - x24) + sqr(x47 - x49) + sqr(x72 -
x74)) + 1/sqrt(sqr(x22 - x25) + sqr(x47 - x50) + sqr(x72 - x75)) + 1/sqrt(
sqr(x23 - x24) + sqr(x48 - x49) + sqr(x73 - x74)) + 1/sqrt(sqr(x23 - x25)
+ sqr(x48 - x50) + sqr(x73 - x75)) + 1/sqrt(sqr(x24 - x25) + sqr(x49 -
x50) + sqr(x74 - x75))) + objvar =E= 0;
e2.. sqr(x1) + sqr(x26) + sqr(x51) =E= 1;
e3.. sqr(x2) + sqr(x27) + sqr(x52) =E= 1;
e4.. sqr(x3) + sqr(x28) + sqr(x53) =E= 1;
e5.. sqr(x4) + sqr(x29) + sqr(x54) =E= 1;
e6.. sqr(x5) + sqr(x30) + sqr(x55) =E= 1;
e7.. sqr(x6) + sqr(x31) + sqr(x56) =E= 1;
e8.. sqr(x7) + sqr(x32) + sqr(x57) =E= 1;
e9.. sqr(x8) + sqr(x33) + sqr(x58) =E= 1;
e10.. sqr(x9) + sqr(x34) + sqr(x59) =E= 1;
e11.. sqr(x10) + sqr(x35) + sqr(x60) =E= 1;
e12.. sqr(x11) + sqr(x36) + sqr(x61) =E= 1;
e13.. sqr(x12) + sqr(x37) + sqr(x62) =E= 1;
e14.. sqr(x13) + sqr(x38) + sqr(x63) =E= 1;
e15.. sqr(x14) + sqr(x39) + sqr(x64) =E= 1;
e16.. sqr(x15) + sqr(x40) + sqr(x65) =E= 1;
e17.. sqr(x16) + sqr(x41) + sqr(x66) =E= 1;
e18.. sqr(x17) + sqr(x42) + sqr(x67) =E= 1;
e19.. sqr(x18) + sqr(x43) + sqr(x68) =E= 1;
e20.. sqr(x19) + sqr(x44) + sqr(x69) =E= 1;
e21.. sqr(x20) + sqr(x45) + sqr(x70) =E= 1;
e22.. sqr(x21) + sqr(x46) + sqr(x71) =E= 1;
e23.. sqr(x22) + sqr(x47) + sqr(x72) =E= 1;
e24.. sqr(x23) + sqr(x48) + sqr(x73) =E= 1;
e25.. sqr(x24) + sqr(x49) + sqr(x74) =E= 1;
e26.. sqr(x25) + sqr(x50) + sqr(x75) =E= 1;
* set non-default levels
x1.l = 0.239180341590991;
x2.l = 0.366795705695488;
x3.l = -0.824393694345008;
x4.l = -0.20445364152556;
x5.l = -0.213822736723748;
x6.l = 0.0552164684243268;
x7.l = -0.586906863272324;
x8.l = 0.298593602647523;
x9.l = 0.355869249309419;
x10.l = -0.739872584978883;
x11.l = 0.781972693719759;
x12.l = -0.842050067383099;
x13.l = 0.763853183973836;
x14.l = 0.0707385883845137;
x15.l = 0.676966872258273;
x16.l = -0.615239159391388;
x17.l = 0.194562217624882;
x18.l = -0.000422232856522465;
x19.l = -0.0710616666815774;
x20.l = -0.802987831773153;
x21.l = -0.344305154696255;
x22.l = -0.533805829063186;
x23.l = 0.665382373979989;
x24.l = 0.388420087049812;
x25.l = -0.682029983840943;
x26.l = 0.446611486489583;
x27.l = -0.552573627870873;
x28.l = -0.270012939754188;
x29.l = 0.614265045675796;
x30.l = 0.787195952709942;
x31.l = 0.335681675744966;
x32.l = 0.809619787722586;
x33.l = -0.378664598119689;
x34.l = 0.159642467758326;
x35.l = -0.000979349466686923;
x36.l = -0.00924905564272029;
x37.l = -0.454232023429031;
x38.l = -0.042600453543173;
x39.l = -0.91720202046222;
x40.l = 0.727211440768476;
x41.l = -0.741026339314474;
x42.l = 0.304537885768853;
x43.l = 0.834446009909628;
x44.l = -0.127224428134585;
x45.l = 0.34535116139819;
x46.l = 0.417792969107124;
x47.l = 0.720899917808122;
x48.l = 0.72200222898579;
x49.l = 0.535334038601125;
x50.l = -0.427520073559083;
x51.l = -0.862166424962131;
x52.l = 0.748413853469436;
x53.l = -0.497461605643582;
x54.l = -0.762152978166359;
x55.l = 0.578448242539515;
x56.l = 0.940355759371844;
x57.l = -0.00749220741006433;
x58.l = 0.876045080226371;
x59.l = -0.920799304888955;
x60.l = 0.672746310931013;
x61.l = 0.623244062343463;
x62.l = -0.290903683221246;
x63.l = -0.643982542225292;
x64.l = -0.392092470947082;
x65.l = 0.113487330924153;
x66.l = 0.268999518946722;
x67.l = 0.932417406317752;
x68.l = 0.551089537430458;
x69.l = 0.989325115628965;
x70.l = 0.485739762985462;
x71.l = 0.840775234776954;
x72.l = -0.441989417704098;
x73.l = -0.189681516591112;
x74.l = -0.750031534731191;
x75.l = 0.593347864111736;
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