MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance chain100
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 0.09367008 (ANTIGONE) -173.12294830 (BARON) -106.89896800 (COUENNE) -77.45596407 (GUROBI) -72.89931543 (LINDO) -183.97942720 (SCIP) |
| Referencesⓘ | Cesari, L, Optimization - Theory and Applications, Springer Verlag, 1983. 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 chain, Constrained Optimization Problem Set (COPS) |
| Applicationⓘ | Hanging Chain |
| Added to libraryⓘ | 31 Jul 2001 |
| Problem typeⓘ | NLP |
| #Variablesⓘ | 202 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 202 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | nonlinear |
| Objective curvatureⓘ | indefinite |
| #Nonzeros in Objectiveⓘ | 202 |
| #Nonlinear Nonzeros in Objectiveⓘ | 202 |
| #Constraintsⓘ | 101 |
| #Linear Constraintsⓘ | 100 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 1 |
| Operands in Gen. Nonlin. Functionsⓘ | mul sqr sqrt |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 501 |
| #Nonlinear Nonzeros in Jacobianⓘ | 101 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 303 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 101 |
| #Blocks in Hessian of Lagrangianⓘ | 101 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 2 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 2 |
| Average blocksize in Hessian of Lagrangianⓘ | 2.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 5.0000e-03 |
| Maximal coefficientⓘ | 1.0000e+00 |
| Infeasibility of initial pointⓘ | 1.193 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 102 102 0 0 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 203 203 0 0 0 0 0 0
* FX 2
*
* Nonzero counts
* Total const NL DLL
* 704 401 303 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,x119,x120,x121,x122,x123,x124,x125,x126,x127,x128,x129
,x130,x131,x132,x133,x134,x135,x136,x137,x138,x139,x140,x141,x142
,x143,x144,x145,x146,x147,x148,x149,x150,x151,x152,x153,x154,x155
,x156,x157,x158,x159,x160,x161,x162,x163,x164,x165,x166,x167,x168
,x169,x170,x171,x172,x173,x174,x175,x176,x177,x178,x179,x180,x181
,x182,x183,x184,x185,x186,x187,x188,x189,x190,x191,x192,x193,x194
,x195,x196,x197,x198,x199,x200,x201,x202,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;
e1.. -0.005*(sqrt(1 + sqr(x102))*x1 + sqrt(1 + sqr(x103))*x2 + sqrt(1 + sqr(
x103))*x2 + sqrt(1 + sqr(x104))*x3 + sqrt(1 + sqr(x104))*x3 + sqrt(1 +
sqr(x105))*x4 + sqrt(1 + sqr(x105))*x4 + sqrt(1 + sqr(x106))*x5 + sqrt(1
+ sqr(x106))*x5 + sqrt(1 + sqr(x107))*x6 + sqrt(1 + sqr(x107))*x6 + sqrt(
1 + sqr(x108))*x7 + sqrt(1 + sqr(x108))*x7 + sqrt(1 + sqr(x109))*x8 +
sqrt(1 + sqr(x109))*x8 + sqrt(1 + sqr(x110))*x9 + sqrt(1 + sqr(x110))*x9
+ sqrt(1 + sqr(x111))*x10 + sqrt(1 + sqr(x111))*x10 + sqrt(1 + sqr(x112))
*x11 + sqrt(1 + sqr(x112))*x11 + sqrt(1 + sqr(x113))*x12 + sqrt(1 + sqr(
x113))*x12 + sqrt(1 + sqr(x114))*x13 + sqrt(1 + sqr(x114))*x13 + sqrt(1 +
sqr(x115))*x14 + sqrt(1 + sqr(x115))*x14 + sqrt(1 + sqr(x116))*x15 + sqrt(
1 + sqr(x116))*x15 + sqrt(1 + sqr(x117))*x16 + sqrt(1 + sqr(x117))*x16 +
sqrt(1 + sqr(x118))*x17 + sqrt(1 + sqr(x118))*x17 + sqrt(1 + sqr(x119))*
x18 + sqrt(1 + sqr(x119))*x18 + sqrt(1 + sqr(x120))*x19 + sqrt(1 + sqr(
x120))*x19 + sqrt(1 + sqr(x121))*x20 + sqrt(1 + sqr(x121))*x20 + sqrt(1 +
sqr(x122))*x21 + sqrt(1 + sqr(x122))*x21 + sqrt(1 + sqr(x123))*x22 + sqrt(
1 + sqr(x123))*x22 + sqrt(1 + sqr(x124))*x23 + sqrt(1 + sqr(x124))*x23 +
sqrt(1 + sqr(x125))*x24 + sqrt(1 + sqr(x125))*x24 + sqrt(1 + sqr(x126))*
x25 + sqrt(1 + sqr(x126))*x25 + sqrt(1 + sqr(x127))*x26 + sqrt(1 + sqr(
x127))*x26 + sqrt(1 + sqr(x128))*x27 + sqrt(1 + sqr(x128))*x27 + sqrt(1 +
sqr(x129))*x28 + sqrt(1 + sqr(x129))*x28 + sqrt(1 + sqr(x130))*x29 + sqrt(
1 + sqr(x130))*x29 + sqrt(1 + sqr(x131))*x30 + sqrt(1 + sqr(x131))*x30 +
sqrt(1 + sqr(x132))*x31 + sqrt(1 + sqr(x132))*x31 + sqrt(1 + sqr(x133))*
x32 + sqrt(1 + sqr(x133))*x32 + sqrt(1 + sqr(x134))*x33 + sqrt(1 + sqr(
x134))*x33 + sqrt(1 + sqr(x135))*x34 + sqrt(1 + sqr(x135))*x34 + sqrt(1 +
sqr(x136))*x35 + sqrt(1 + sqr(x136))*x35 + sqrt(1 + sqr(x137))*x36 + sqrt(
1 + sqr(x137))*x36 + sqrt(1 + sqr(x138))*x37 + sqrt(1 + sqr(x138))*x37 +
sqrt(1 + sqr(x139))*x38 + sqrt(1 + sqr(x139))*x38 + sqrt(1 + sqr(x140))*
x39 + sqrt(1 + sqr(x140))*x39 + sqrt(1 + sqr(x141))*x40 + sqrt(1 + sqr(
x141))*x40 + sqrt(1 + sqr(x142))*x41 + sqrt(1 + sqr(x142))*x41 + sqrt(1 +
sqr(x143))*x42 + sqrt(1 + sqr(x143))*x42 + sqrt(1 + sqr(x144))*x43 + sqrt(
1 + sqr(x144))*x43 + sqrt(1 + sqr(x145))*x44 + sqrt(1 + sqr(x145))*x44 +
sqrt(1 + sqr(x146))*x45 + sqrt(1 + sqr(x146))*x45 + sqrt(1 + sqr(x147))*
x46 + sqrt(1 + sqr(x147))*x46 + sqrt(1 + sqr(x148))*x47 + sqrt(1 + sqr(
x148))*x47 + sqrt(1 + sqr(x149))*x48 + sqrt(1 + sqr(x149))*x48 + sqrt(1 +
sqr(x150))*x49 + sqrt(1 + sqr(x150))*x49 + sqrt(1 + sqr(x151))*x50 + sqrt(
1 + sqr(x151))*x50 + sqrt(1 + sqr(x152))*x51 + sqrt(1 + sqr(x152))*x51 +
sqrt(1 + sqr(x153))*x52 + sqrt(1 + sqr(x153))*x52 + sqrt(1 + sqr(x154))*
x53 + sqrt(1 + sqr(x154))*x53 + sqrt(1 + sqr(x155))*x54 + sqrt(1 + sqr(
x155))*x54 + sqrt(1 + sqr(x156))*x55 + sqrt(1 + sqr(x156))*x55 + sqrt(1 +
sqr(x157))*x56 + sqrt(1 + sqr(x157))*x56 + sqrt(1 + sqr(x158))*x57 + sqrt(
1 + sqr(x158))*x57 + sqrt(1 + sqr(x159))*x58 + sqrt(1 + sqr(x159))*x58 +
sqrt(1 + sqr(x160))*x59 + sqrt(1 + sqr(x160))*x59 + sqrt(1 + sqr(x161))*
x60 + sqrt(1 + sqr(x161))*x60 + sqrt(1 + sqr(x162))*x61 + sqrt(1 + sqr(
x162))*x61 + sqrt(1 + sqr(x163))*x62 + sqrt(1 + sqr(x163))*x62 + sqrt(1 +
sqr(x164))*x63 + sqrt(1 + sqr(x164))*x63 + sqrt(1 + sqr(x165))*x64 + sqrt(
1 + sqr(x165))*x64 + sqrt(1 + sqr(x166))*x65 + sqrt(1 + sqr(x166))*x65 +
sqrt(1 + sqr(x167))*x66 + sqrt(1 + sqr(x167))*x66 + sqrt(1 + sqr(x168))*
x67 + sqrt(1 + sqr(x168))*x67 + sqrt(1 + sqr(x169))*x68 + sqrt(1 + sqr(
x169))*x68 + sqrt(1 + sqr(x170))*x69 + sqrt(1 + sqr(x170))*x69 + sqrt(1 +
sqr(x171))*x70 + sqrt(1 + sqr(x171))*x70 + sqrt(1 + sqr(x172))*x71 + sqrt(
1 + sqr(x172))*x71 + sqrt(1 + sqr(x173))*x72 + sqrt(1 + sqr(x173))*x72 +
sqrt(1 + sqr(x174))*x73 + sqrt(1 + sqr(x174))*x73 + sqrt(1 + sqr(x175))*
x74 + sqrt(1 + sqr(x175))*x74 + sqrt(1 + sqr(x176))*x75 + sqrt(1 + sqr(
x176))*x75 + sqrt(1 + sqr(x177))*x76 + sqrt(1 + sqr(x177))*x76 + sqrt(1 +
sqr(x178))*x77 + sqrt(1 + sqr(x178))*x77 + sqrt(1 + sqr(x179))*x78 + sqrt(
1 + sqr(x179))*x78 + sqrt(1 + sqr(x180))*x79 + sqrt(1 + sqr(x180))*x79 +
sqrt(1 + sqr(x181))*x80 + sqrt(1 + sqr(x181))*x80 + sqrt(1 + sqr(x182))*
x81 + sqrt(1 + sqr(x182))*x81 + sqrt(1 + sqr(x183))*x82 + sqrt(1 + sqr(
x183))*x82 + sqrt(1 + sqr(x184))*x83 + sqrt(1 + sqr(x184))*x83 + sqrt(1 +
sqr(x185))*x84 + sqrt(1 + sqr(x185))*x84 + sqrt(1 + sqr(x186))*x85 + sqrt(
1 + sqr(x186))*x85 + sqrt(1 + sqr(x187))*x86 + sqrt(1 + sqr(x187))*x86 +
sqrt(1 + sqr(x188))*x87 + sqrt(1 + sqr(x188))*x87 + sqrt(1 + sqr(x189))*
x88 + sqrt(1 + sqr(x189))*x88 + sqrt(1 + sqr(x190))*x89 + sqrt(1 + sqr(
x190))*x89 + sqrt(1 + sqr(x191))*x90 + sqrt(1 + sqr(x191))*x90 + sqrt(1 +
sqr(x192))*x91 + sqrt(1 + sqr(x192))*x91 + sqrt(1 + sqr(x193))*x92 + sqrt(
1 + sqr(x193))*x92 + sqrt(1 + sqr(x194))*x93 + sqrt(1 + sqr(x194))*x93 +
sqrt(1 + sqr(x195))*x94 + sqrt(1 + sqr(x195))*x94 + sqrt(1 + sqr(x196))*
x95 + sqrt(1 + sqr(x196))*x95 + sqrt(1 + sqr(x197))*x96 + sqrt(1 + sqr(
x197))*x96 + sqrt(1 + sqr(x198))*x97 + sqrt(1 + sqr(x198))*x97 + sqrt(1 +
sqr(x199))*x98 + sqrt(1 + sqr(x199))*x98 + sqrt(1 + sqr(x200))*x99 + sqrt(
1 + sqr(x200))*x99 + sqrt(1 + sqr(x201))*x100 + sqrt(1 + sqr(x201))*x100
+ sqrt(1 + sqr(x202))*x101) + objvar =E= 0;
e2.. - x1 + x2 - 0.005*x102 - 0.005*x103 =E= 0;
e3.. - x2 + x3 - 0.005*x103 - 0.005*x104 =E= 0;
e4.. - x3 + x4 - 0.005*x104 - 0.005*x105 =E= 0;
e5.. - x4 + x5 - 0.005*x105 - 0.005*x106 =E= 0;
e6.. - x5 + x6 - 0.005*x106 - 0.005*x107 =E= 0;
e7.. - x6 + x7 - 0.005*x107 - 0.005*x108 =E= 0;
e8.. - x7 + x8 - 0.005*x108 - 0.005*x109 =E= 0;
e9.. - x8 + x9 - 0.005*x109 - 0.005*x110 =E= 0;
e10.. - x9 + x10 - 0.005*x110 - 0.005*x111 =E= 0;
e11.. - x10 + x11 - 0.005*x111 - 0.005*x112 =E= 0;
e12.. - x11 + x12 - 0.005*x112 - 0.005*x113 =E= 0;
e13.. - x12 + x13 - 0.005*x113 - 0.005*x114 =E= 0;
e14.. - x13 + x14 - 0.005*x114 - 0.005*x115 =E= 0;
e15.. - x14 + x15 - 0.005*x115 - 0.005*x116 =E= 0;
e16.. - x15 + x16 - 0.005*x116 - 0.005*x117 =E= 0;
e17.. - x16 + x17 - 0.005*x117 - 0.005*x118 =E= 0;
e18.. - x17 + x18 - 0.005*x118 - 0.005*x119 =E= 0;
e19.. - x18 + x19 - 0.005*x119 - 0.005*x120 =E= 0;
e20.. - x19 + x20 - 0.005*x120 - 0.005*x121 =E= 0;
e21.. - x20 + x21 - 0.005*x121 - 0.005*x122 =E= 0;
e22.. - x21 + x22 - 0.005*x122 - 0.005*x123 =E= 0;
e23.. - x22 + x23 - 0.005*x123 - 0.005*x124 =E= 0;
e24.. - x23 + x24 - 0.005*x124 - 0.005*x125 =E= 0;
e25.. - x24 + x25 - 0.005*x125 - 0.005*x126 =E= 0;
e26.. - x25 + x26 - 0.005*x126 - 0.005*x127 =E= 0;
e27.. - x26 + x27 - 0.005*x127 - 0.005*x128 =E= 0;
e28.. - x27 + x28 - 0.005*x128 - 0.005*x129 =E= 0;
e29.. - x28 + x29 - 0.005*x129 - 0.005*x130 =E= 0;
e30.. - x29 + x30 - 0.005*x130 - 0.005*x131 =E= 0;
e31.. - x30 + x31 - 0.005*x131 - 0.005*x132 =E= 0;
e32.. - x31 + x32 - 0.005*x132 - 0.005*x133 =E= 0;
e33.. - x32 + x33 - 0.005*x133 - 0.005*x134 =E= 0;
e34.. - x33 + x34 - 0.005*x134 - 0.005*x135 =E= 0;
e35.. - x34 + x35 - 0.005*x135 - 0.005*x136 =E= 0;
e36.. - x35 + x36 - 0.005*x136 - 0.005*x137 =E= 0;
e37.. - x36 + x37 - 0.005*x137 - 0.005*x138 =E= 0;
e38.. - x37 + x38 - 0.005*x138 - 0.005*x139 =E= 0;
e39.. - x38 + x39 - 0.005*x139 - 0.005*x140 =E= 0;
e40.. - x39 + x40 - 0.005*x140 - 0.005*x141 =E= 0;
e41.. - x40 + x41 - 0.005*x141 - 0.005*x142 =E= 0;
e42.. - x41 + x42 - 0.005*x142 - 0.005*x143 =E= 0;
e43.. - x42 + x43 - 0.005*x143 - 0.005*x144 =E= 0;
e44.. - x43 + x44 - 0.005*x144 - 0.005*x145 =E= 0;
e45.. - x44 + x45 - 0.005*x145 - 0.005*x146 =E= 0;
e46.. - x45 + x46 - 0.005*x146 - 0.005*x147 =E= 0;
e47.. - x46 + x47 - 0.005*x147 - 0.005*x148 =E= 0;
e48.. - x47 + x48 - 0.005*x148 - 0.005*x149 =E= 0;
e49.. - x48 + x49 - 0.005*x149 - 0.005*x150 =E= 0;
e50.. - x49 + x50 - 0.005*x150 - 0.005*x151 =E= 0;
e51.. - x50 + x51 - 0.005*x151 - 0.005*x152 =E= 0;
e52.. - x51 + x52 - 0.005*x152 - 0.005*x153 =E= 0;
e53.. - x52 + x53 - 0.005*x153 - 0.005*x154 =E= 0;
e54.. - x53 + x54 - 0.005*x154 - 0.005*x155 =E= 0;
e55.. - x54 + x55 - 0.005*x155 - 0.005*x156 =E= 0;
e56.. - x55 + x56 - 0.005*x156 - 0.005*x157 =E= 0;
e57.. - x56 + x57 - 0.005*x157 - 0.005*x158 =E= 0;
e58.. - x57 + x58 - 0.005*x158 - 0.005*x159 =E= 0;
e59.. - x58 + x59 - 0.005*x159 - 0.005*x160 =E= 0;
e60.. - x59 + x60 - 0.005*x160 - 0.005*x161 =E= 0;
e61.. - x60 + x61 - 0.005*x161 - 0.005*x162 =E= 0;
e62.. - x61 + x62 - 0.005*x162 - 0.005*x163 =E= 0;
e63.. - x62 + x63 - 0.005*x163 - 0.005*x164 =E= 0;
e64.. - x63 + x64 - 0.005*x164 - 0.005*x165 =E= 0;
e65.. - x64 + x65 - 0.005*x165 - 0.005*x166 =E= 0;
e66.. - x65 + x66 - 0.005*x166 - 0.005*x167 =E= 0;
e67.. - x66 + x67 - 0.005*x167 - 0.005*x168 =E= 0;
e68.. - x67 + x68 - 0.005*x168 - 0.005*x169 =E= 0;
e69.. - x68 + x69 - 0.005*x169 - 0.005*x170 =E= 0;
e70.. - x69 + x70 - 0.005*x170 - 0.005*x171 =E= 0;
e71.. - x70 + x71 - 0.005*x171 - 0.005*x172 =E= 0;
e72.. - x71 + x72 - 0.005*x172 - 0.005*x173 =E= 0;
e73.. - x72 + x73 - 0.005*x173 - 0.005*x174 =E= 0;
e74.. - x73 + x74 - 0.005*x174 - 0.005*x175 =E= 0;
e75.. - x74 + x75 - 0.005*x175 - 0.005*x176 =E= 0;
e76.. - x75 + x76 - 0.005*x176 - 0.005*x177 =E= 0;
e77.. - x76 + x77 - 0.005*x177 - 0.005*x178 =E= 0;
e78.. - x77 + x78 - 0.005*x178 - 0.005*x179 =E= 0;
e79.. - x78 + x79 - 0.005*x179 - 0.005*x180 =E= 0;
e80.. - x79 + x80 - 0.005*x180 - 0.005*x181 =E= 0;
e81.. - x80 + x81 - 0.005*x181 - 0.005*x182 =E= 0;
e82.. - x81 + x82 - 0.005*x182 - 0.005*x183 =E= 0;
e83.. - x82 + x83 - 0.005*x183 - 0.005*x184 =E= 0;
e84.. - x83 + x84 - 0.005*x184 - 0.005*x185 =E= 0;
e85.. - x84 + x85 - 0.005*x185 - 0.005*x186 =E= 0;
e86.. - x85 + x86 - 0.005*x186 - 0.005*x187 =E= 0;
e87.. - x86 + x87 - 0.005*x187 - 0.005*x188 =E= 0;
e88.. - x87 + x88 - 0.005*x188 - 0.005*x189 =E= 0;
e89.. - x88 + x89 - 0.005*x189 - 0.005*x190 =E= 0;
e90.. - x89 + x90 - 0.005*x190 - 0.005*x191 =E= 0;
e91.. - x90 + x91 - 0.005*x191 - 0.005*x192 =E= 0;
e92.. - x91 + x92 - 0.005*x192 - 0.005*x193 =E= 0;
e93.. - x92 + x93 - 0.005*x193 - 0.005*x194 =E= 0;
e94.. - x93 + x94 - 0.005*x194 - 0.005*x195 =E= 0;
e95.. - x94 + x95 - 0.005*x195 - 0.005*x196 =E= 0;
e96.. - x95 + x96 - 0.005*x196 - 0.005*x197 =E= 0;
e97.. - x96 + x97 - 0.005*x197 - 0.005*x198 =E= 0;
e98.. - x97 + x98 - 0.005*x198 - 0.005*x199 =E= 0;
e99.. - x98 + x99 - 0.005*x199 - 0.005*x200 =E= 0;
e100.. - x99 + x100 - 0.005*x200 - 0.005*x201 =E= 0;
e101.. - x100 + x101 - 0.005*x201 - 0.005*x202 =E= 0;
e102.. 0.005*(sqrt(1 + sqr(x102)) + sqrt(1 + sqr(x103)) + sqrt(1 + sqr(x103))
+ sqrt(1 + sqr(x104)) + sqrt(1 + sqr(x104)) + sqrt(1 + sqr(x105)) +
sqrt(1 + sqr(x105)) + sqrt(1 + sqr(x106)) + sqrt(1 + sqr(x106)) + sqrt(1
+ sqr(x107)) + sqrt(1 + sqr(x107)) + sqrt(1 + sqr(x108)) + sqrt(1 +
sqr(x108)) + sqrt(1 + sqr(x109)) + sqrt(1 + sqr(x109)) + sqrt(1 + sqr(
x110)) + sqrt(1 + sqr(x110)) + sqrt(1 + sqr(x111)) + sqrt(1 + sqr(x111))
+ sqrt(1 + sqr(x112)) + sqrt(1 + sqr(x112)) + sqrt(1 + sqr(x113)) +
sqrt(1 + sqr(x113)) + sqrt(1 + sqr(x114)) + sqrt(1 + sqr(x114)) + sqrt(1
+ sqr(x115)) + sqrt(1 + sqr(x115)) + sqrt(1 + sqr(x116)) + sqrt(1 +
sqr(x116)) + sqrt(1 + sqr(x117)) + sqrt(1 + sqr(x117)) + sqrt(1 + sqr(
x118)) + sqrt(1 + sqr(x118)) + sqrt(1 + sqr(x119)) + sqrt(1 + sqr(x119))
+ sqrt(1 + sqr(x120)) + sqrt(1 + sqr(x120)) + sqrt(1 + sqr(x121)) +
sqrt(1 + sqr(x121)) + sqrt(1 + sqr(x122)) + sqrt(1 + sqr(x122)) + sqrt(1
+ sqr(x123)) + sqrt(1 + sqr(x123)) + sqrt(1 + sqr(x124)) + sqrt(1 +
sqr(x124)) + sqrt(1 + sqr(x125)) + sqrt(1 + sqr(x125)) + sqrt(1 + sqr(
x126)) + sqrt(1 + sqr(x126)) + sqrt(1 + sqr(x127)) + sqrt(1 + sqr(x127))
+ sqrt(1 + sqr(x128)) + sqrt(1 + sqr(x128)) + sqrt(1 + sqr(x129)) +
sqrt(1 + sqr(x129)) + sqrt(1 + sqr(x130)) + sqrt(1 + sqr(x130)) + sqrt(1
+ sqr(x131)) + sqrt(1 + sqr(x131)) + sqrt(1 + sqr(x132)) + sqrt(1 +
sqr(x132)) + sqrt(1 + sqr(x133)) + sqrt(1 + sqr(x133)) + sqrt(1 + sqr(
x134)) + sqrt(1 + sqr(x134)) + sqrt(1 + sqr(x135)) + sqrt(1 + sqr(x135))
+ sqrt(1 + sqr(x136)) + sqrt(1 + sqr(x136)) + sqrt(1 + sqr(x137)) +
sqrt(1 + sqr(x137)) + sqrt(1 + sqr(x138)) + sqrt(1 + sqr(x138)) + sqrt(1
+ sqr(x139)) + sqrt(1 + sqr(x139)) + sqrt(1 + sqr(x140)) + sqrt(1 +
sqr(x140)) + sqrt(1 + sqr(x141)) + sqrt(1 + sqr(x141)) + sqrt(1 + sqr(
x142)) + sqrt(1 + sqr(x142)) + sqrt(1 + sqr(x143)) + sqrt(1 + sqr(x143))
+ sqrt(1 + sqr(x144)) + sqrt(1 + sqr(x144)) + sqrt(1 + sqr(x145)) +
sqrt(1 + sqr(x145)) + sqrt(1 + sqr(x146)) + sqrt(1 + sqr(x146)) + sqrt(1
+ sqr(x147)) + sqrt(1 + sqr(x147)) + sqrt(1 + sqr(x148)) + sqrt(1 +
sqr(x148)) + sqrt(1 + sqr(x149)) + sqrt(1 + sqr(x149)) + sqrt(1 + sqr(
x150)) + sqrt(1 + sqr(x150)) + sqrt(1 + sqr(x151)) + sqrt(1 + sqr(x151))
+ sqrt(1 + sqr(x152)) + sqrt(1 + sqr(x152)) + sqrt(1 + sqr(x153)) +
sqrt(1 + sqr(x153)) + sqrt(1 + sqr(x154)) + sqrt(1 + sqr(x154)) + sqrt(1
+ sqr(x155)) + sqrt(1 + sqr(x155)) + sqrt(1 + sqr(x156)) + sqrt(1 +
sqr(x156)) + sqrt(1 + sqr(x157)) + sqrt(1 + sqr(x157)) + sqrt(1 + sqr(
x158)) + sqrt(1 + sqr(x158)) + sqrt(1 + sqr(x159)) + sqrt(1 + sqr(x159))
+ sqrt(1 + sqr(x160)) + sqrt(1 + sqr(x160)) + sqrt(1 + sqr(x161)) +
sqrt(1 + sqr(x161)) + sqrt(1 + sqr(x162)) + sqrt(1 + sqr(x162)) + sqrt(1
+ sqr(x163)) + sqrt(1 + sqr(x163)) + sqrt(1 + sqr(x164)) + sqrt(1 +
sqr(x164)) + sqrt(1 + sqr(x165)) + sqrt(1 + sqr(x165)) + sqrt(1 + sqr(
x166)) + sqrt(1 + sqr(x166)) + sqrt(1 + sqr(x167)) + sqrt(1 + sqr(x167))
+ sqrt(1 + sqr(x168)) + sqrt(1 + sqr(x168)) + sqrt(1 + sqr(x169)) +
sqrt(1 + sqr(x169)) + sqrt(1 + sqr(x170)) + sqrt(1 + sqr(x170)) + sqrt(1
+ sqr(x171)) + sqrt(1 + sqr(x171)) + sqrt(1 + sqr(x172)) + sqrt(1 +
sqr(x172)) + sqrt(1 + sqr(x173)) + sqrt(1 + sqr(x173)) + sqrt(1 + sqr(
x174)) + sqrt(1 + sqr(x174)) + sqrt(1 + sqr(x175)) + sqrt(1 + sqr(x175))
+ sqrt(1 + sqr(x176)) + sqrt(1 + sqr(x176)) + sqrt(1 + sqr(x177)) +
sqrt(1 + sqr(x177)) + sqrt(1 + sqr(x178)) + sqrt(1 + sqr(x178)) + sqrt(1
+ sqr(x179)) + sqrt(1 + sqr(x179)) + sqrt(1 + sqr(x180)) + sqrt(1 +
sqr(x180)) + sqrt(1 + sqr(x181)) + sqrt(1 + sqr(x181)) + sqrt(1 + sqr(
x182)) + sqrt(1 + sqr(x182)) + sqrt(1 + sqr(x183)) + sqrt(1 + sqr(x183))
+ sqrt(1 + sqr(x184)) + sqrt(1 + sqr(x184)) + sqrt(1 + sqr(x185)) +
sqrt(1 + sqr(x185)) + sqrt(1 + sqr(x186)) + sqrt(1 + sqr(x186)) + sqrt(1
+ sqr(x187)) + sqrt(1 + sqr(x187)) + sqrt(1 + sqr(x188)) + sqrt(1 +
sqr(x188)) + sqrt(1 + sqr(x189)) + sqrt(1 + sqr(x189)) + sqrt(1 + sqr(
x190)) + sqrt(1 + sqr(x190)) + sqrt(1 + sqr(x191)) + sqrt(1 + sqr(x191))
+ sqrt(1 + sqr(x192)) + sqrt(1 + sqr(x192)) + sqrt(1 + sqr(x193)) +
sqrt(1 + sqr(x193)) + sqrt(1 + sqr(x194)) + sqrt(1 + sqr(x194)) + sqrt(1
+ sqr(x195)) + sqrt(1 + sqr(x195)) + sqrt(1 + sqr(x196)) + sqrt(1 +
sqr(x196)) + sqrt(1 + sqr(x197)) + sqrt(1 + sqr(x197)) + sqrt(1 + sqr(
x198)) + sqrt(1 + sqr(x198)) + sqrt(1 + sqr(x199)) + sqrt(1 + sqr(x199))
+ sqrt(1 + sqr(x200)) + sqrt(1 + sqr(x200)) + sqrt(1 + sqr(x201)) +
sqrt(1 + sqr(x201)) + sqrt(1 + sqr(x202))) =E= 4;
* set non-default bounds
x1.fx = 1;
x101.fx = 3;
* set non-default levels
x2.l = 0.9804;
x3.l = 0.9616;
x4.l = 0.9436;
x5.l = 0.9264;
x6.l = 0.91;
x7.l = 0.8944;
x8.l = 0.8796;
x9.l = 0.8656;
x10.l = 0.8524;
x11.l = 0.84;
x12.l = 0.8284;
x13.l = 0.8176;
x14.l = 0.8076;
x15.l = 0.7984;
x16.l = 0.79;
x17.l = 0.7824;
x18.l = 0.7756;
x19.l = 0.7696;
x20.l = 0.7644;
x21.l = 0.76;
x22.l = 0.7564;
x23.l = 0.7536;
x24.l = 0.7516;
x25.l = 0.7504;
x26.l = 0.75;
x27.l = 0.7504;
x28.l = 0.7516;
x29.l = 0.7536;
x30.l = 0.7564;
x31.l = 0.76;
x32.l = 0.7644;
x33.l = 0.7696;
x34.l = 0.7756;
x35.l = 0.7824;
x36.l = 0.79;
x37.l = 0.7984;
x38.l = 0.8076;
x39.l = 0.8176;
x40.l = 0.8284;
x41.l = 0.84;
x42.l = 0.8524;
x43.l = 0.8656;
x44.l = 0.8796;
x45.l = 0.8944;
x46.l = 0.91;
x47.l = 0.9264;
x48.l = 0.9436;
x49.l = 0.9616;
x50.l = 0.9804;
x51.l = 1;
x52.l = 1.0204;
x53.l = 1.0416;
x54.l = 1.0636;
x55.l = 1.0864;
x56.l = 1.11;
x57.l = 1.1344;
x58.l = 1.1596;
x59.l = 1.1856;
x60.l = 1.2124;
x61.l = 1.24;
x62.l = 1.2684;
x63.l = 1.2976;
x64.l = 1.3276;
x65.l = 1.3584;
x66.l = 1.39;
x67.l = 1.4224;
x68.l = 1.4556;
x69.l = 1.4896;
x70.l = 1.5244;
x71.l = 1.56;
x72.l = 1.5964;
x73.l = 1.6336;
x74.l = 1.6716;
x75.l = 1.7104;
x76.l = 1.75;
x77.l = 1.7904;
x78.l = 1.8316;
x79.l = 1.8736;
x80.l = 1.9164;
x81.l = 1.96;
x82.l = 2.0044;
x83.l = 2.0496;
x84.l = 2.0956;
x85.l = 2.1424;
x86.l = 2.19;
x87.l = 2.2384;
x88.l = 2.2876;
x89.l = 2.3376;
x90.l = 2.3884;
x91.l = 2.44;
x92.l = 2.4924;
x93.l = 2.5456;
x94.l = 2.5996;
x95.l = 2.6544;
x96.l = 2.71;
x97.l = 2.7664;
x98.l = 2.8236;
x99.l = 2.8816;
x100.l = 2.9404;
x102.l = -2;
x103.l = -1.92;
x104.l = -1.84;
x105.l = -1.76;
x106.l = -1.68;
x107.l = -1.6;
x108.l = -1.52;
x109.l = -1.44;
x110.l = -1.36;
x111.l = -1.28;
x112.l = -1.2;
x113.l = -1.12;
x114.l = -1.04;
x115.l = -0.96;
x116.l = -0.88;
x117.l = -0.8;
x118.l = -0.72;
x119.l = -0.64;
x120.l = -0.56;
x121.l = -0.48;
x122.l = -0.4;
x123.l = -0.32;
x124.l = -0.24;
x125.l = -0.16;
x126.l = -0.0800000000000001;
x128.l = 0.0800000000000001;
x129.l = 0.16;
x130.l = 0.24;
x131.l = 0.32;
x132.l = 0.4;
x133.l = 0.48;
x134.l = 0.56;
x135.l = 0.64;
x136.l = 0.72;
x137.l = 0.8;
x138.l = 0.88;
x139.l = 0.96;
x140.l = 1.04;
x141.l = 1.12;
x142.l = 1.2;
x143.l = 1.28;
x144.l = 1.36;
x145.l = 1.44;
x146.l = 1.52;
x147.l = 1.6;
x148.l = 1.68;
x149.l = 1.76;
x150.l = 1.84;
x151.l = 1.92;
x152.l = 2;
x153.l = 2.08;
x154.l = 2.16;
x155.l = 2.24;
x156.l = 2.32;
x157.l = 2.4;
x158.l = 2.48;
x159.l = 2.56;
x160.l = 2.64;
x161.l = 2.72;
x162.l = 2.8;
x163.l = 2.88;
x164.l = 2.96;
x165.l = 3.04;
x166.l = 3.12;
x167.l = 3.2;
x168.l = 3.28;
x169.l = 3.36;
x170.l = 3.44;
x171.l = 3.52;
x172.l = 3.6;
x173.l = 3.68;
x174.l = 3.76;
x175.l = 3.84;
x176.l = 3.92;
x177.l = 4;
x178.l = 4.08;
x179.l = 4.16;
x180.l = 4.24;
x181.l = 4.32;
x182.l = 4.4;
x183.l = 4.48;
x184.l = 4.56;
x185.l = 4.64;
x186.l = 4.72;
x187.l = 4.8;
x188.l = 4.88;
x189.l = 4.96;
x190.l = 5.04;
x191.l = 5.12;
x192.l = 5.2;
x193.l = 5.28;
x194.l = 5.36;
x195.l = 5.44;
x196.l = 5.52;
x197.l = 5.6;
x198.l = 5.68;
x199.l = 5.76;
x200.l = 5.84;
x201.l = 5.92;
x202.l = 6;
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