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Instance p_ball_20b_5p_2d_m

Select 5-points in 2-dimensional balls, such that the l1-distance between all points is minimized.
Only one point can be assigned to each ball, and in total there are 20 balls with radius one.
This is a big-M formulation.
Formats ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)
2.43717509 p1 ( gdx sol )
(infeas: 3e-14)
Other points (infeas > 1e-08)  
Dual Bounds
2.43661233 (ALPHAECP)
2.43715272 (ANTIGONE)
2.43717506 (BARON)
2.43717505 (BONMIN)
2.43714878 (COUENNE)
2.43717509 (CPLEX)
2.43716742 (GUROBI)
2.43717509 (LINDO)
2.43717362 (SCIP)
2.43717509 (SHOT)
References Kronqvist, Jan and Misener, Ruth, A disjunctive cut strengthening technique for convex MINLP, Tech. Rep., 2020.
Source p_ball_20b_5p_2d.gms, contributed by Jan Kronqvist and Ruth Misener
Application Geometry
Added to library 26 Aug 2020
Problem type MBQCP
#Variables 130
#Binary Variables 100
#Integer Variables 0
#Nonlinear Variables 10
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 20
#Nonlinear Nonzeros in Objective 0
#Constraints 169
#Linear Constraints 69
#Quadratic Constraints 100
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature convex
#Nonzeros in Jacobian 628
#Nonlinear Nonzeros in Jacobian 200
#Nonzeros in (Upper-Left) Hessian of Lagrangian 10
#Nonzeros in Diagonal of Hessian of Lagrangian 10
#Blocks in Hessian of Lagrangian 10
Minimal blocksize in Hessian of Lagrangian 1
Maximal blocksize in Hessian of Lagrangian 1
Average blocksize in Hessian of Lagrangian 1.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 2.3675e-02
Maximal coefficient 1.3360e+02
Infeasibility of initial point 8.815e-05
Sparsity Jacobian Sparsity of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangian Sparsity of Hessian of Lagrangian

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*        170        6        0      164        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        131       31      100        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        649      449      200        0
*
*  Solve m using MINLP minimizing objvar;


Variables  b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17,b18,b19
          ,b20,b21,b22,b23,b24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34,b35,b36
          ,b37,b38,b39,b40,b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,b51,b52,b53
          ,b54,b55,b56,b57,b58,b59,b60,b61,b62,b63,b64,b65,b66,b67,b68,b69,b70
          ,b71,b72,b73,b74,b75,b76,b77,b78,b79,b80,b81,b82,b83,b84,b85,b86,b87
          ,b88,b89,b90,b91,b92,b93,b94,b95,b96,b97,b98,b99,b100,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,objvar;

Positive Variables  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;

Binary Variables  b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17
          ,b18,b19,b20,b21,b22,b23,b24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34
          ,b35,b36,b37,b38,b39,b40,b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,b51
          ,b52,b53,b54,b55,b56,b57,b58,b59,b60,b61,b62,b63,b64,b65,b66,b67,b68
          ,b69,b70,b71,b72,b73,b74,b75,b76,b77,b78,b79,b80,b81,b82,b83,b84,b85
          ,b86,b87,b88,b89,b90,b91,b92,b93,b94,b95,b96,b97,b98,b99,b100;

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;


e1..    x101 - x102 - x103 =L= 0;

e2..  - x101 + x102 - x103 =L= 0;

e3..    x104 - x105 - x106 =L= 0;

e4..  - x104 + x105 - x106 =L= 0;

e5..    x101 - x107 - x108 =L= 0;

e6..  - x101 + x107 - x108 =L= 0;

e7..    x104 - x109 - x110 =L= 0;

e8..  - x104 + x109 - x110 =L= 0;

e9..    x101 - x111 - x112 =L= 0;

e10..  - x101 + x111 - x112 =L= 0;

e11..    x104 - x113 - x114 =L= 0;

e12..  - x104 + x113 - x114 =L= 0;

e13..    x101 - x115 - x116 =L= 0;

e14..  - x101 + x115 - x116 =L= 0;

e15..    x104 - x117 - x118 =L= 0;

e16..  - x104 + x117 - x118 =L= 0;

e17..    x102 - x107 - x119 =L= 0;

e18..  - x102 + x107 - x119 =L= 0;

e19..    x105 - x109 - x120 =L= 0;

e20..  - x105 + x109 - x120 =L= 0;

e21..    x102 - x111 - x121 =L= 0;

e22..  - x102 + x111 - x121 =L= 0;

e23..    x105 - x113 - x122 =L= 0;

e24..  - x105 + x113 - x122 =L= 0;

e25..    x102 - x115 - x123 =L= 0;

e26..  - x102 + x115 - x123 =L= 0;

e27..    x105 - x117 - x124 =L= 0;

e28..  - x105 + x117 - x124 =L= 0;

e29..    x107 - x111 - x125 =L= 0;

e30..  - x107 + x111 - x125 =L= 0;

e31..    x109 - x113 - x126 =L= 0;

e32..  - x109 + x113 - x126 =L= 0;

e33..    x107 - x115 - x127 =L= 0;

e34..  - x107 + x115 - x127 =L= 0;

e35..    x109 - x117 - x128 =L= 0;

e36..  - x109 + x117 - x128 =L= 0;

e37..    x111 - x115 - x129 =L= 0;

e38..  - x111 + x115 - x129 =L= 0;

e39..    x113 - x117 - x130 =L= 0;

e40..  - x113 + x117 - x130 =L= 0;

e41.. sqr(0.0236753863366035 - x101) + sqr(0.861938468195851 - x104)
       + 133.598318045686*b1 =L= 134.598318045686;

e42.. sqr(1.43095891437813 - x101) + sqr(5.10831625828775 - x104)
       + 94.8544563231416*b2 =L= 95.8544563231416;

e43.. sqr(1.21379363277567 - x101) + sqr(3.00432848540233 - x104)
       + 87.4797735261255*b3 =L= 88.4797735261255;

e44.. sqr(8.84443217821809 - x101) + sqr(0.384566405581435 - x104)
       + 103.126413671578*b4 =L= 104.126413671578;

e45.. sqr(5.88364087295228 - x101) + sqr(7.44470191338639 - x104)
       + 95.2983106051005*b5 =L= 96.2983106051005;

e46.. sqr(8.07096798042338 - x101) + sqr(5.55715186969177 - x104)
       + 105.43767414173*b6 =L= 106.43767414173;

e47.. sqr(9.60611615222079 - x101) + sqr(3.49008429472371 - x104)
       + 118.60294806901*b7 =L= 119.60294806901;

e48.. sqr(3.8828653966979 - x101) + sqr(5.56627471425883 - x104)
       + 65.8153811229109*b8 =L= 66.8153811229109;

e49.. sqr(3.47709171076729 - x101) + sqr(1.01589173470293 - x104)
       + 81.404902491826*b9 =L= 82.404902491826;

e50.. sqr(3.29737974336435 - x101) + sqr(4.14110922298337 - x104)
       + 58.2801217051105*b10 =L= 59.2801217051105;

e51.. sqr(8.28345883424477 - x101) + sqr(7.50806458757389 - x104)
       + 133.598318045686*b11 =L= 134.598318045686;

e52.. sqr(5.4084966970588 - x101) + sqr(7.74684442267358 - x104)
       + 93.8794468182122*b12 =L= 94.8794468182122;

e53.. sqr(3.43292425314245 - x101) + sqr(7.8299358039566 - x104)
       + 103.126413671578*b13 =L= 104.126413671578;

e54.. sqr(8.35004447905012 - x101) + sqr(1.33263454148094 - x104)
       + 86.2293028346251*b14 =L= 87.2293028346251;

e55.. sqr(2.65420450303518 - x101) + sqr(6.31096321892449 - x104)
       + 90.5806541970954*b15 =L= 91.5806541970954;

e56.. sqr(5.8344315991351 - x101) + sqr(8.56684140863644 - x104)
       + 112.431237492188*b16 =L= 113.431237492188;

e57.. sqr(4.10957657319824 - x101) + sqr(7.8233834211224 - x104)
       + 95.3905990097055*b17 =L= 96.3905990097055;

e58.. sqr(7.39474057003054 - x101) + sqr(2.49738552645804 - x104)
       + 72.1079233169562*b18 =L= 73.1079233169562;

e59.. sqr(6.14221519240217 - x101) + sqr(3.03591203112434 - x104)
       + 55.1492512196064*b19 =L= 56.1492512196064;

e60.. sqr(8.26974385940666 - x101) + sqr(4.22323814320874 - x104)
       + 97.1056389080134*b20 =L= 98.1056389080134;

e61..    b1 + b2 + b3 + b4 + b5 + b6 + b7 + b8 + b9 + b10 + b11 + b12 + b13
       + b14 + b15 + b16 + b17 + b18 + b19 + b20 =E= 1;

e62.. sqr(0.0236753863366035 - x102) + sqr(0.861938468195851 - x105)
       + 133.598318045686*b21 =L= 134.598318045686;

e63.. sqr(1.43095891437813 - x102) + sqr(5.10831625828775 - x105)
       + 94.8544563231416*b22 =L= 95.8544563231416;

e64.. sqr(1.21379363277567 - x102) + sqr(3.00432848540233 - x105)
       + 87.4797735261255*b23 =L= 88.4797735261255;

e65.. sqr(8.84443217821809 - x102) + sqr(0.384566405581435 - x105)
       + 103.126413671578*b24 =L= 104.126413671578;

e66.. sqr(5.88364087295228 - x102) + sqr(7.44470191338639 - x105)
       + 95.2983106051005*b25 =L= 96.2983106051005;

e67.. sqr(8.07096798042338 - x102) + sqr(5.55715186969177 - x105)
       + 105.43767414173*b26 =L= 106.43767414173;

e68.. sqr(9.60611615222079 - x102) + sqr(3.49008429472371 - x105)
       + 118.60294806901*b27 =L= 119.60294806901;

e69.. sqr(3.8828653966979 - x102) + sqr(5.56627471425883 - x105)
       + 65.8153811229109*b28 =L= 66.8153811229109;

e70.. sqr(3.47709171076729 - x102) + sqr(1.01589173470293 - x105)
       + 81.404902491826*b29 =L= 82.404902491826;

e71.. sqr(3.29737974336435 - x102) + sqr(4.14110922298337 - x105)
       + 58.2801217051105*b30 =L= 59.2801217051105;

e72.. sqr(8.28345883424477 - x102) + sqr(7.50806458757389 - x105)
       + 133.598318045686*b31 =L= 134.598318045686;

e73.. sqr(5.4084966970588 - x102) + sqr(7.74684442267358 - x105)
       + 93.8794468182122*b32 =L= 94.8794468182122;

e74.. sqr(3.43292425314245 - x102) + sqr(7.8299358039566 - x105)
       + 103.126413671578*b33 =L= 104.126413671578;

e75.. sqr(8.35004447905012 - x102) + sqr(1.33263454148094 - x105)
       + 86.2293028346251*b34 =L= 87.2293028346251;

e76.. sqr(2.65420450303518 - x102) + sqr(6.31096321892449 - x105)
       + 90.5806541970954*b35 =L= 91.5806541970954;

e77.. sqr(5.8344315991351 - x102) + sqr(8.56684140863644 - x105)
       + 112.431237492188*b36 =L= 113.431237492188;

e78.. sqr(4.10957657319824 - x102) + sqr(7.8233834211224 - x105)
       + 95.3905990097055*b37 =L= 96.3905990097055;

e79.. sqr(7.39474057003054 - x102) + sqr(2.49738552645804 - x105)
       + 72.1079233169562*b38 =L= 73.1079233169562;

e80.. sqr(6.14221519240217 - x102) + sqr(3.03591203112434 - x105)
       + 55.1492512196064*b39 =L= 56.1492512196064;

e81.. sqr(8.26974385940666 - x102) + sqr(4.22323814320874 - x105)
       + 97.1056389080134*b40 =L= 98.1056389080134;

e82..    b21 + b22 + b23 + b24 + b25 + b26 + b27 + b28 + b29 + b30 + b31 + b32
       + b33 + b34 + b35 + b36 + b37 + b38 + b39 + b40 =E= 1;

e83.. sqr(0.0236753863366035 - x107) + sqr(0.861938468195851 - x109)
       + 133.598318045686*b41 =L= 134.598318045686;

e84.. sqr(1.43095891437813 - x107) + sqr(5.10831625828775 - x109)
       + 94.8544563231416*b42 =L= 95.8544563231416;

e85.. sqr(1.21379363277567 - x107) + sqr(3.00432848540233 - x109)
       + 87.4797735261255*b43 =L= 88.4797735261255;

e86.. sqr(8.84443217821809 - x107) + sqr(0.384566405581435 - x109)
       + 103.126413671578*b44 =L= 104.126413671578;

e87.. sqr(5.88364087295228 - x107) + sqr(7.44470191338639 - x109)
       + 95.2983106051005*b45 =L= 96.2983106051005;

e88.. sqr(8.07096798042338 - x107) + sqr(5.55715186969177 - x109)
       + 105.43767414173*b46 =L= 106.43767414173;

e89.. sqr(9.60611615222079 - x107) + sqr(3.49008429472371 - x109)
       + 118.60294806901*b47 =L= 119.60294806901;

e90.. sqr(3.8828653966979 - x107) + sqr(5.56627471425883 - x109)
       + 65.8153811229109*b48 =L= 66.8153811229109;

e91.. sqr(3.47709171076729 - x107) + sqr(1.01589173470293 - x109)
       + 81.404902491826*b49 =L= 82.404902491826;

e92.. sqr(3.29737974336435 - x107) + sqr(4.14110922298337 - x109)
       + 58.2801217051105*b50 =L= 59.2801217051105;

e93.. sqr(8.28345883424477 - x107) + sqr(7.50806458757389 - x109)
       + 133.598318045686*b51 =L= 134.598318045686;

e94.. sqr(5.4084966970588 - x107) + sqr(7.74684442267358 - x109)
       + 93.8794468182122*b52 =L= 94.8794468182122;

e95.. sqr(3.43292425314245 - x107) + sqr(7.8299358039566 - x109)
       + 103.126413671578*b53 =L= 104.126413671578;

e96.. sqr(8.35004447905012 - x107) + sqr(1.33263454148094 - x109)
       + 86.2293028346251*b54 =L= 87.2293028346251;

e97.. sqr(2.65420450303518 - x107) + sqr(6.31096321892449 - x109)
       + 90.5806541970954*b55 =L= 91.5806541970954;

e98.. sqr(5.8344315991351 - x107) + sqr(8.56684140863644 - x109)
       + 112.431237492188*b56 =L= 113.431237492188;

e99.. sqr(4.10957657319824 - x107) + sqr(7.8233834211224 - x109)
       + 95.3905990097055*b57 =L= 96.3905990097055;

e100.. sqr(7.39474057003054 - x107) + sqr(2.49738552645804 - x109)
        + 72.1079233169562*b58 =L= 73.1079233169562;

e101.. sqr(6.14221519240217 - x107) + sqr(3.03591203112434 - x109)
        + 55.1492512196064*b59 =L= 56.1492512196064;

e102.. sqr(8.26974385940666 - x107) + sqr(4.22323814320874 - x109)
        + 97.1056389080134*b60 =L= 98.1056389080134;

e103..    b41 + b42 + b43 + b44 + b45 + b46 + b47 + b48 + b49 + b50 + b51 + b52
        + b53 + b54 + b55 + b56 + b57 + b58 + b59 + b60 =E= 1;

e104.. sqr(0.0236753863366035 - x111) + sqr(0.861938468195851 - x113)
        + 133.598318045686*b61 =L= 134.598318045686;

e105.. sqr(1.43095891437813 - x111) + sqr(5.10831625828775 - x113)
        + 94.8544563231416*b62 =L= 95.8544563231416;

e106.. sqr(1.21379363277567 - x111) + sqr(3.00432848540233 - x113)
        + 87.4797735261255*b63 =L= 88.4797735261255;

e107.. sqr(8.84443217821809 - x111) + sqr(0.384566405581435 - x113)
        + 103.126413671578*b64 =L= 104.126413671578;

e108.. sqr(5.88364087295228 - x111) + sqr(7.44470191338639 - x113)
        + 95.2983106051005*b65 =L= 96.2983106051005;

e109.. sqr(8.07096798042338 - x111) + sqr(5.55715186969177 - x113)
        + 105.43767414173*b66 =L= 106.43767414173;

e110.. sqr(9.60611615222079 - x111) + sqr(3.49008429472371 - x113)
        + 118.60294806901*b67 =L= 119.60294806901;

e111.. sqr(3.8828653966979 - x111) + sqr(5.56627471425883 - x113)
        + 65.8153811229109*b68 =L= 66.8153811229109;

e112.. sqr(3.47709171076729 - x111) + sqr(1.01589173470293 - x113)
        + 81.404902491826*b69 =L= 82.404902491826;

e113.. sqr(3.29737974336435 - x111) + sqr(4.14110922298337 - x113)
        + 58.2801217051105*b70 =L= 59.2801217051105;

e114.. sqr(8.28345883424477 - x111) + sqr(7.50806458757389 - x113)
        + 133.598318045686*b71 =L= 134.598318045686;

e115.. sqr(5.4084966970588 - x111) + sqr(7.74684442267358 - x113)
        + 93.8794468182122*b72 =L= 94.8794468182122;

e116.. sqr(3.43292425314245 - x111) + sqr(7.8299358039566 - x113)
        + 103.126413671578*b73 =L= 104.126413671578;

e117.. sqr(8.35004447905012 - x111) + sqr(1.33263454148094 - x113)
        + 86.2293028346251*b74 =L= 87.2293028346251;

e118.. sqr(2.65420450303518 - x111) + sqr(6.31096321892449 - x113)
        + 90.5806541970954*b75 =L= 91.5806541970954;

e119.. sqr(5.8344315991351 - x111) + sqr(8.56684140863644 - x113)
        + 112.431237492188*b76 =L= 113.431237492188;

e120.. sqr(4.10957657319824 - x111) + sqr(7.8233834211224 - x113)
        + 95.3905990097055*b77 =L= 96.3905990097055;

e121.. sqr(7.39474057003054 - x111) + sqr(2.49738552645804 - x113)
        + 72.1079233169562*b78 =L= 73.1079233169562;

e122.. sqr(6.14221519240217 - x111) + sqr(3.03591203112434 - x113)
        + 55.1492512196064*b79 =L= 56.1492512196064;

e123.. sqr(8.26974385940666 - x111) + sqr(4.22323814320874 - x113)
        + 97.1056389080134*b80 =L= 98.1056389080134;

e124..    b61 + b62 + b63 + b64 + b65 + b66 + b67 + b68 + b69 + b70 + b71 + b72
        + b73 + b74 + b75 + b76 + b77 + b78 + b79 + b80 =E= 1;

e125.. sqr(0.0236753863366035 - x115) + sqr(0.861938468195851 - x117)
        + 133.598318045686*b81 =L= 134.598318045686;

e126.. sqr(1.43095891437813 - x115) + sqr(5.10831625828775 - x117)
        + 94.8544563231416*b82 =L= 95.8544563231416;

e127.. sqr(1.21379363277567 - x115) + sqr(3.00432848540233 - x117)
        + 87.4797735261255*b83 =L= 88.4797735261255;

e128.. sqr(8.84443217821809 - x115) + sqr(0.384566405581435 - x117)
        + 103.126413671578*b84 =L= 104.126413671578;

e129.. sqr(5.88364087295228 - x115) + sqr(7.44470191338639 - x117)
        + 95.2983106051005*b85 =L= 96.2983106051005;

e130.. sqr(8.07096798042338 - x115) + sqr(5.55715186969177 - x117)
        + 105.43767414173*b86 =L= 106.43767414173;

e131.. sqr(9.60611615222079 - x115) + sqr(3.49008429472371 - x117)
        + 118.60294806901*b87 =L= 119.60294806901;

e132.. sqr(3.8828653966979 - x115) + sqr(5.56627471425883 - x117)
        + 65.8153811229109*b88 =L= 66.8153811229109;

e133.. sqr(3.47709171076729 - x115) + sqr(1.01589173470293 - x117)
        + 81.404902491826*b89 =L= 82.404902491826;

e134.. sqr(3.29737974336435 - x115) + sqr(4.14110922298337 - x117)
        + 58.2801217051105*b90 =L= 59.2801217051105;

e135.. sqr(8.28345883424477 - x115) + sqr(7.50806458757389 - x117)
        + 133.598318045686*b91 =L= 134.598318045686;

e136.. sqr(5.4084966970588 - x115) + sqr(7.74684442267358 - x117)
        + 93.8794468182122*b92 =L= 94.8794468182122;

e137.. sqr(3.43292425314245 - x115) + sqr(7.8299358039566 - x117)
        + 103.126413671578*b93 =L= 104.126413671578;

e138.. sqr(8.35004447905012 - x115) + sqr(1.33263454148094 - x117)
        + 86.2293028346251*b94 =L= 87.2293028346251;

e139.. sqr(2.65420450303518 - x115) + sqr(6.31096321892449 - x117)
        + 90.5806541970954*b95 =L= 91.5806541970954;

e140.. sqr(5.8344315991351 - x115) + sqr(8.56684140863644 - x117)
        + 112.431237492188*b96 =L= 113.431237492188;

e141.. sqr(4.10957657319824 - x115) + sqr(7.8233834211224 - x117)
        + 95.3905990097055*b97 =L= 96.3905990097055;

e142.. sqr(7.39474057003054 - x115) + sqr(2.49738552645804 - x117)
        + 72.1079233169562*b98 =L= 73.1079233169562;

e143.. sqr(6.14221519240217 - x115) + sqr(3.03591203112434 - x117)
        + 55.1492512196064*b99 =L= 56.1492512196064;

e144.. sqr(8.26974385940666 - x115) + sqr(4.22323814320874 - x117)
        + 97.1056389080134*b100 =L= 98.1056389080134;

e145..    b81 + b82 + b83 + b84 + b85 + b86 + b87 + b88 + b89 + b90 + b91 + b92
        + b93 + b94 + b95 + b96 + b97 + b98 + b99 + b100 =E= 1;

e146..    b1 + b21 + b41 + b61 + b81 =L= 1;

e147..    b2 + b22 + b42 + b62 + b82 =L= 1;

e148..    b3 + b23 + b43 + b63 + b83 =L= 1;

e149..    b4 + b24 + b44 + b64 + b84 =L= 1;

e150..    b5 + b25 + b45 + b65 + b85 =L= 1;

e151..    b6 + b26 + b46 + b66 + b86 =L= 1;

e152..    b7 + b27 + b47 + b67 + b87 =L= 1;

e153..    b8 + b28 + b48 + b68 + b88 =L= 1;

e154..    b9 + b29 + b49 + b69 + b89 =L= 1;

e155..    b10 + b30 + b50 + b70 + b90 =L= 1;

e156..    b11 + b31 + b51 + b71 + b91 =L= 1;

e157..    b12 + b32 + b52 + b72 + b92 =L= 1;

e158..    b13 + b33 + b53 + b73 + b93 =L= 1;

e159..    b14 + b34 + b54 + b74 + b94 =L= 1;

e160..    b15 + b35 + b55 + b75 + b95 =L= 1;

e161..    b16 + b36 + b56 + b76 + b96 =L= 1;

e162..    b17 + b37 + b57 + b77 + b97 =L= 1;

e163..    b18 + b38 + b58 + b78 + b98 =L= 1;

e164..    b19 + b39 + b59 + b79 + b99 =L= 1;

e165..    b20 + b40 + b60 + b80 + b100 =L= 1;

e166..    x101 - x102 =L= 0;

e167..    x102 - x107 =L= 0;

e168..    x107 - x111 =L= 0;

e169..    x111 - x115 =L= 0;

e170..  - x103 - x106 - x108 - x110 - x112 - x114 - x116 - x118 - x119 - x120
        - x121 - x122 - x123 - x124 - x125 - x126 - x127 - x128 - x129 - x130
        + objvar =E= 0;

* set non-default bounds
x101.up = 10;
x102.up = 10;
x103.up = 10;
x104.up = 10;
x105.up = 10;
x106.up = 10;
x107.up = 10;
x108.up = 10;
x109.up = 10;
x110.up = 10;
x111.up = 10;
x112.up = 10;
x113.up = 10;
x114.up = 10;
x115.up = 10;
x116.up = 10;
x117.up = 10;
x118.up = 10;
x119.up = 10;
x120.up = 10;
x121.up = 10;
x122.up = 10;
x123.up = 10;
x124.up = 10;
x125.up = 10;
x126.up = 10;
x127.up = 10;
x128.up = 10;
x129.up = 10;
x130.up = 10;

* set non-default levels
b13.l = 1;
b25.l = 1;
b57.l = 1;
b76.l = 1;
b92.l = 1;
x101.l = 4.42317283955211;
x102.l = 5.03240021704025;
x103.l = 0.609227377488138;
x104.l = 7.96948572261155;
x105.l = 7.96948572261155;
x107.l = 5.03240021704025;
x108.l = 0.609227377488138;
x109.l = 7.96948572261155;
x111.l = 5.03240021704025;
x112.l = 0.609227377488136;
x113.l = 7.96948572261155;
x115.l = 5.03240021704025;
x116.l = 0.609227377488136;
x117.l = 7.96948572261155;

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: 2022-04-26 Git hash: de668763
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