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Instance hybriddynamic_varcc
Variable Finite Elements
| Formatsⓘ | ams gms mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 1.53641516 (ANTIGONE) 1.53641516 (BARON) 1.53641516 (COUENNE) 1.53641516 (LINDO) 1.53641405 (SCIP) |
| Referencesⓘ | Baumrucker, Brian and Biegler, L T, MINLP & MPCC Strategies for Optimization of a Class of Hybrid Dynamic Systems, 2009. |
| Sourceⓘ | del_asl_hvar.gms from minlp.org model 27 |
| Applicationⓘ | Hybrid Dynamic Systems |
| Added to libraryⓘ | 18 Aug 2014 |
| Problem typeⓘ | NLP |
| #Variablesⓘ | 151 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 71 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | polynomial |
| Objective curvatureⓘ | indefinite |
| #Nonzeros in Objectiveⓘ | 61 |
| #Nonlinear Nonzeros in Objectiveⓘ | 61 |
| #Constraintsⓘ | 110 |
| #Linear Constraintsⓘ | 90 |
| #Quadratic Constraintsⓘ | 20 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 327 |
| #Nonlinear Nonzeros in Jacobianⓘ | 40 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 91 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 11 |
| #Blocks in Hessian of Lagrangianⓘ | 31 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 1 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 3 |
| Average blocksize in Hessian of Lagrangianⓘ | 2.290323 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e+00 |
| Maximal coefficientⓘ | 1.0000e+03 |
| Infeasibility of initial pointⓘ | 3 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 111 111 0 0 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 152 152 0 0 0 0 0 0
* FX 2
*
* Nonzero counts
* Total const NL DLL
* 389 288 101 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,objvar;
Positive Variables 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;
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;
e1.. -(sqr((-1.66666666666667) + x151) + sqr(x131)*x91 + sqr(x132)*x92 + sqr(
x133)*x93 + sqr(x134)*x94 + sqr(x135)*x95 + sqr(x136)*x96 + sqr(x137)*x97
+ sqr(x138)*x98 + sqr(x139)*x99 + sqr(x140)*x100 + 1000*(x81*x61 + x71*
x51 + x82*x62 + x72*x52 + x83*x63 + x73*x53 + x84*x64 + x74*x54 + x85*x65
+ x75*x55 + x86*x66 + x76*x56 + x87*x67 + x77*x57 + x88*x68 + x78*x58 +
x89*x69 + x79*x59 + x90*x70 + x80*x60)) + objvar =E= 0;
e2.. - x91 - x111 + x121 =E= 0;
e3.. - x92 - x112 + x122 =E= 0;
e4.. - x93 - x113 + x123 =E= 0;
e5.. - x94 - x114 + x124 =E= 0;
e6.. - x95 - x115 + x125 =E= 0;
e7.. - x96 - x116 + x126 =E= 0;
e8.. - x97 - x117 + x127 =E= 0;
e9.. - x98 - x118 + x128 =E= 0;
e10.. - x99 - x119 + x129 =E= 0;
e11.. - x100 - x120 + x130 =E= 0;
e12.. -x91*x141 - x101 + x131 =E= 0;
e13.. -x92*x142 - x102 + x132 =E= 0;
e14.. -x93*x143 - x103 + x133 =E= 0;
e15.. -x94*x144 - x104 + x134 =E= 0;
e16.. -x95*x145 - x105 + x135 =E= 0;
e17.. -x96*x146 - x106 + x136 =E= 0;
e18.. -x97*x147 - x107 + x137 =E= 0;
e19.. -x98*x148 - x108 + x138 =E= 0;
e20.. -x99*x149 - x109 + x139 =E= 0;
e21.. -x100*x150 - x110 + x140 =E= 0;
e22.. - x91 - x111 + x112 =E= 0;
e23.. - x92 - x112 + x113 =E= 0;
e24.. - x93 - x113 + x114 =E= 0;
e25.. - x94 - x114 + x115 =E= 0;
e26.. - x95 - x115 + x116 =E= 0;
e27.. - x96 - x116 + x117 =E= 0;
e28.. - x97 - x117 + x118 =E= 0;
e29.. - x98 - x118 + x119 =E= 0;
e30.. - x99 - x119 + x120 =E= 0;
e31.. -x91*x141 - x101 + x102 =E= 0;
e32.. -x92*x142 - x102 + x103 =E= 0;
e33.. -x93*x143 - x103 + x104 =E= 0;
e34.. -x94*x144 - x104 + x105 =E= 0;
e35.. -x95*x145 - x105 + x106 =E= 0;
e36.. -x96*x146 - x106 + x107 =E= 0;
e37.. -x97*x147 - x107 + x108 =E= 0;
e38.. -x98*x148 - x108 + x109 =E= 0;
e39.. -x99*x149 - x109 + x110 =E= 0;
e40.. -x100*x150 - x110 + x151 =E= 0;
e41.. x1 + x141 =E= 2;
e42.. x2 + x142 =E= 2;
e43.. x3 + x143 =E= 2;
e44.. x4 + x144 =E= 2;
e45.. x5 + x145 =E= 2;
e46.. x6 + x146 =E= 2;
e47.. x7 + x147 =E= 2;
e48.. x8 + x148 =E= 2;
e49.. x9 + x149 =E= 2;
e50.. x10 + x150 =E= 2;
e51.. - x11 + x21 + x131 =E= 0;
e52.. - x12 + x22 + x132 =E= 0;
e53.. - x13 + x23 + x133 =E= 0;
e54.. - x14 + x24 + x134 =E= 0;
e55.. - x15 + x25 + x135 =E= 0;
e56.. - x16 + x26 + x136 =E= 0;
e57.. - x17 + x27 + x137 =E= 0;
e58.. - x18 + x28 + x138 =E= 0;
e59.. - x19 + x29 + x139 =E= 0;
e60.. - x20 + x30 + x140 =E= 0;
e61.. - x31 + x41 + x101 =E= 0;
e62.. - x32 + x42 + x102 =E= 0;
e63.. - x33 + x43 + x103 =E= 0;
e64.. - x34 + x44 + x104 =E= 0;
e65.. - x35 + x45 + x105 =E= 0;
e66.. - x36 + x46 + x106 =E= 0;
e67.. - x37 + x47 + x107 =E= 0;
e68.. - x38 + x48 + x108 =E= 0;
e69.. - x39 + x49 + x109 =E= 0;
e70.. - x40 + x50 + x110 =E= 0;
e71.. - x11 - x31 + x51 =E= 0;
e72.. - x12 - x32 + x52 =E= 0;
e73.. - x13 - x33 + x53 =E= 0;
e74.. - x14 - x34 + x54 =E= 0;
e75.. - x15 - x35 + x55 =E= 0;
e76.. - x16 - x36 + x56 =E= 0;
e77.. - x17 - x37 + x57 =E= 0;
e78.. - x18 - x38 + x58 =E= 0;
e79.. - x19 - x39 + x59 =E= 0;
e80.. - x20 - x40 + x60 =E= 0;
e81.. - x21 - x41 + x61 =E= 0;
e82.. - x22 - x42 + x62 =E= 0;
e83.. - x23 - x43 + x63 =E= 0;
e84.. - x24 - x44 + x64 =E= 0;
e85.. - x25 - x45 + x65 =E= 0;
e86.. - x26 - x46 + x66 =E= 0;
e87.. - x27 - x47 + x67 =E= 0;
e88.. - x28 - x48 + x68 =E= 0;
e89.. - x29 - x49 + x69 =E= 0;
e90.. - x30 - x50 + x70 =E= 0;
e91.. x1 + x71 =E= 1;
e92.. x2 + x72 =E= 1;
e93.. x3 + x73 =E= 1;
e94.. x4 + x74 =E= 1;
e95.. x5 + x75 =E= 1;
e96.. x6 + x76 =E= 1;
e97.. x7 + x77 =E= 1;
e98.. x8 + x78 =E= 1;
e99.. x9 + x79 =E= 1;
e100.. x10 + x80 =E= 1;
e101.. - x1 + x81 =E= 1;
e102.. - x2 + x82 =E= 1;
e103.. - x3 + x83 =E= 1;
e104.. - x4 + x84 =E= 1;
e105.. - x5 + x85 =E= 1;
e106.. - x6 + x86 =E= 1;
e107.. - x7 + x87 =E= 1;
e108.. - x8 + x88 =E= 1;
e109.. - x9 + x89 =E= 1;
e110.. - x10 + x90 =E= 1;
e111.. x91 + x92 + x93 + x94 + x95 + x96 + x97 + x98 + x99 + x100 =E= 2;
* set non-default bounds
x1.lo = -1; x1.up = 1;
x2.lo = -1; x2.up = 1;
x3.lo = -1; x3.up = 1;
x4.lo = -1; x4.up = 1;
x5.lo = -1; x5.up = 1;
x6.lo = -1; x6.up = 1;
x7.lo = -1; x7.up = 1;
x8.lo = -1; x8.up = 1;
x9.lo = -1; x9.up = 1;
x10.lo = -1; x10.up = 1;
x91.lo = 0.16; x91.up = 0.24;
x92.lo = 0.16; x92.up = 0.24;
x93.lo = 0.16; x93.up = 0.24;
x94.lo = 0.16; x94.up = 0.24;
x95.lo = 0.16; x95.up = 0.24;
x96.lo = 0.16; x96.up = 0.24;
x97.lo = 0.16; x97.up = 0.24;
x98.lo = 0.16; x98.up = 0.24;
x99.lo = 0.16; x99.up = 0.24;
x100.lo = 0.16; x100.up = 0.24;
x101.fx = -2;
x111.fx = 0;
* set non-default levels
x1.l = -1;
x2.l = -1;
x3.l = -1;
x4.l = -1;
x5.l = -1;
x6.l = -1;
x7.l = -1;
x8.l = -1;
x9.l = -1;
x10.l = -1;
x11.l = 0.1;
x12.l = 0.1;
x13.l = 0.1;
x14.l = 0.1;
x15.l = 0.1;
x16.l = 0.1;
x17.l = 0.1;
x18.l = 0.1;
x19.l = 0.1;
x20.l = 0.1;
x21.l = 0.1;
x22.l = 0.1;
x23.l = 0.1;
x24.l = 0.1;
x25.l = 0.1;
x26.l = 0.1;
x27.l = 0.1;
x28.l = 0.1;
x29.l = 0.1;
x30.l = 0.1;
x31.l = 0.1;
x32.l = 0.1;
x33.l = 0.1;
x34.l = 0.1;
x35.l = 0.1;
x36.l = 0.1;
x37.l = 0.1;
x38.l = 0.1;
x39.l = 0.1;
x40.l = 0.1;
x41.l = 0.1;
x42.l = 0.1;
x43.l = 0.1;
x44.l = 0.1;
x45.l = 0.1;
x46.l = 0.1;
x47.l = 0.1;
x48.l = 0.1;
x49.l = 0.1;
x50.l = 0.1;
x51.l = 0.1;
x52.l = 0.1;
x53.l = 0.1;
x54.l = 0.1;
x55.l = 0.1;
x56.l = 0.1;
x57.l = 0.1;
x58.l = 0.1;
x59.l = 0.1;
x60.l = 0.1;
x61.l = 0.1;
x62.l = 0.1;
x63.l = 0.1;
x64.l = 0.1;
x65.l = 0.1;
x66.l = 0.1;
x67.l = 0.1;
x68.l = 0.1;
x69.l = 0.1;
x70.l = 0.1;
x71.l = 0.1;
x72.l = 0.1;
x73.l = 0.1;
x74.l = 0.1;
x75.l = 0.1;
x76.l = 0.1;
x77.l = 0.1;
x78.l = 0.1;
x79.l = 0.1;
x80.l = 0.1;
x81.l = 0.1;
x82.l = 0.1;
x83.l = 0.1;
x84.l = 0.1;
x85.l = 0.1;
x86.l = 0.1;
x87.l = 0.1;
x88.l = 0.1;
x89.l = 0.1;
x90.l = 0.1;
x91.l = 0.2;
x92.l = 0.2;
x93.l = 0.2;
x94.l = 0.2;
x95.l = 0.2;
x96.l = 0.2;
x97.l = 0.2;
x98.l = 0.2;
x99.l = 0.2;
x100.l = 0.2;
x102.l = -2;
x103.l = -2;
x104.l = -2;
x105.l = -2;
x106.l = -2;
x107.l = -2;
x108.l = -2;
x109.l = -2;
x110.l = -2;
x112.l = 1;
x113.l = 1;
x114.l = 1;
x115.l = 1;
x116.l = 1;
x117.l = 1;
x118.l = 1;
x119.l = 1;
x120.l = 1;
x121.l = 1;
x122.l = 1;
x123.l = 1;
x124.l = 1;
x125.l = 1;
x126.l = 1;
x127.l = 1;
x128.l = 1;
x129.l = 1;
x130.l = 1;
x131.l = -2;
x132.l = -2;
x133.l = -2;
x134.l = -2;
x135.l = -2;
x136.l = -2;
x137.l = -2;
x138.l = -2;
x139.l = -2;
x140.l = -2;
x151.l = 1;
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