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Instance hybriddynamic_fixedcc
Fixed Finite Elements
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 1.47377775 (ANTIGONE) 1.47377778 (BARON) 1.47377778 (COUENNE) 1.47377778 (CPLEX) 1.47377776 (GUROBI) 1.47377778 (LINDO) 1.47377778 (SCIP) |
| Referencesⓘ | Baumrucker, Brian and Biegler, L T, MINLP & MPCC Strategies for Optimization of a Class of Hybrid Dynamic Systems, 2009. |
| Sourceⓘ | del_asl_hfix.gms from minlp.org model 27 |
| Applicationⓘ | Hybrid Dynamic Systems |
| Added to libraryⓘ | 18 Aug 2014 |
| Problem typeⓘ | QP |
| #Variablesⓘ | 121 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 51 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | quadratic |
| Objective curvatureⓘ | indefinite |
| #Nonzeros in Objectiveⓘ | 51 |
| #Nonlinear Nonzeros in Objectiveⓘ | 51 |
| #Constraintsⓘ | 99 |
| #Linear Constraintsⓘ | 99 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | linear |
| #Nonzeros in Jacobianⓘ | 228 |
| #Nonlinear Nonzeros in Jacobianⓘ | 0 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 51 |
| #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ⓘ | 2 |
| Average blocksize in Hessian of Lagrangianⓘ | 1.645161 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 2.0000e-01 |
| 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
* 100 100 0 0 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 122 122 0 0 0 0 0 0
* FX 2
*
* Nonzero counts
* Total const NL DLL
* 280 229 51 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,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;
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;
e1.. -(sqr((-1.66666666666667) + x121) + 0.2*sqr(x101) + 0.2*sqr(x102) + 0.2*
sqr(x103) + 0.2*sqr(x104) + 0.2*sqr(x105) + 0.2*sqr(x106) + 0.2*sqr(x107)
+ 0.2*sqr(x108) + 0.2*sqr(x109) + 0.2*sqr(x110) + 1000*(x61*x41 + x51*x31
+ x62*x42 + x52*x32 + x63*x43 + x53*x33 + x64*x44 + x54*x34 + x65*x45 +
x55*x35 + x66*x46 + x56*x36 + x67*x47 + x57*x37 + x68*x48 + x58*x38 + x69*
x49 + x59*x39 + x70*x50 + x60*x40)) + objvar =E= 0;
e2.. - x81 + x91 =E= 0.2;
e3.. - x82 + x92 =E= 0.2;
e4.. - x83 + x93 =E= 0.2;
e5.. - x84 + x94 =E= 0.2;
e6.. - x85 + x95 =E= 0.2;
e7.. - x86 + x96 =E= 0.2;
e8.. - x87 + x97 =E= 0.2;
e9.. - x88 + x98 =E= 0.2;
e10.. - x89 + x99 =E= 0.2;
e11.. - x90 + x100 =E= 0.2;
e12.. - x71 + x101 - 0.2*x111 =E= 0;
e13.. - x72 + x102 - 0.2*x112 =E= 0;
e14.. - x73 + x103 - 0.2*x113 =E= 0;
e15.. - x74 + x104 - 0.2*x114 =E= 0;
e16.. - x75 + x105 - 0.2*x115 =E= 0;
e17.. - x76 + x106 - 0.2*x116 =E= 0;
e18.. - x77 + x107 - 0.2*x117 =E= 0;
e19.. - x78 + x108 - 0.2*x118 =E= 0;
e20.. - x79 + x109 - 0.2*x119 =E= 0;
e21.. - x80 + x110 - 0.2*x120 =E= 0;
e22.. - x81 + x82 =E= 0.2;
e23.. - x82 + x83 =E= 0.2;
e24.. - x83 + x84 =E= 0.2;
e25.. - x84 + x85 =E= 0.2;
e26.. - x85 + x86 =E= 0.2;
e27.. - x86 + x87 =E= 0.2;
e28.. - x87 + x88 =E= 0.2;
e29.. - x88 + x89 =E= 0.2;
e30.. - x89 + x90 =E= 0.2;
e31.. - x71 + x72 - 0.2*x111 =E= 0;
e32.. - x72 + x73 - 0.2*x112 =E= 0;
e33.. - x73 + x74 - 0.2*x113 =E= 0;
e34.. - x74 + x75 - 0.2*x114 =E= 0;
e35.. - x75 + x76 - 0.2*x115 =E= 0;
e36.. - x76 + x77 - 0.2*x116 =E= 0;
e37.. - x77 + x78 - 0.2*x117 =E= 0;
e38.. - x78 + x79 - 0.2*x118 =E= 0;
e39.. - x79 + x80 - 0.2*x119 =E= 0;
e40.. - x80 - 0.2*x120 + x121 =E= 0;
e41.. x1 + x111 =E= 2;
e42.. x2 + x112 =E= 2;
e43.. x3 + x113 =E= 2;
e44.. x4 + x114 =E= 2;
e45.. x5 + x115 =E= 2;
e46.. x6 + x116 =E= 2;
e47.. x7 + x117 =E= 2;
e48.. x8 + x118 =E= 2;
e49.. x9 + x119 =E= 2;
e50.. x10 + x120 =E= 2;
e51.. - x11 + x21 + x101 =E= 0;
e52.. - x12 + x22 + x102 =E= 0;
e53.. - x13 + x23 + x103 =E= 0;
e54.. - x14 + x24 + x104 =E= 0;
e55.. - x15 + x25 + x105 =E= 0;
e56.. - x16 + x26 + x106 =E= 0;
e57.. - x17 + x27 + x107 =E= 0;
e58.. - x18 + x28 + x108 =E= 0;
e59.. - x19 + x29 + x109 =E= 0;
e60.. - x20 + x30 + x110 =E= 0;
e61.. - x11 + x31 =E= 0;
e62.. - x12 + x32 =E= 0;
e63.. - x13 + x33 =E= 0;
e64.. - x14 + x34 =E= 0;
e65.. - x15 + x35 =E= 0;
e66.. - x16 + x36 =E= 0;
e67.. - x17 + x37 =E= 0;
e68.. - x18 + x38 =E= 0;
e69.. - x19 + x39 =E= 0;
e70.. - x20 + x40 =E= 0;
e71.. - x21 + x41 =E= 0;
e72.. - x22 + x42 =E= 0;
e73.. - x23 + x43 =E= 0;
e74.. - x24 + x44 =E= 0;
e75.. - x25 + x45 =E= 0;
e76.. - x26 + x46 =E= 0;
e77.. - x27 + x47 =E= 0;
e78.. - x28 + x48 =E= 0;
e79.. - x29 + x49 =E= 0;
e80.. - x30 + x50 =E= 0;
e81.. x1 + x51 =E= 1;
e82.. x2 + x52 =E= 1;
e83.. x3 + x53 =E= 1;
e84.. x4 + x54 =E= 1;
e85.. x5 + x55 =E= 1;
e86.. x6 + x56 =E= 1;
e87.. x7 + x57 =E= 1;
e88.. x8 + x58 =E= 1;
e89.. x9 + x59 =E= 1;
e90.. x10 + x60 =E= 1;
e91.. - x1 + x61 =E= 1;
e92.. - x2 + x62 =E= 1;
e93.. - x3 + x63 =E= 1;
e94.. - x4 + x64 =E= 1;
e95.. - x5 + x65 =E= 1;
e96.. - x6 + x66 =E= 1;
e97.. - x7 + x67 =E= 1;
e98.. - x8 + x68 =E= 1;
e99.. - x9 + x69 =E= 1;
e100.. - x10 + x70 =E= 1;
* 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;
x71.fx = -2;
x81.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;
x72.l = -2;
x73.l = -2;
x74.l = -2;
x75.l = -2;
x76.l = -2;
x77.l = -2;
x78.l = -2;
x79.l = -2;
x80.l = -2;
x82.l = 1;
x83.l = 1;
x84.l = 1;
x85.l = 1;
x86.l = 1;
x87.l = 1;
x88.l = 1;
x89.l = 1;
x90.l = 1;
x91.l = 1;
x92.l = 1;
x93.l = 1;
x94.l = 1;
x95.l = 1;
x96.l = 1;
x97.l = 1;
x98.l = 1;
x99.l = 1;
x100.l = 1;
x101.l = -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;
x121.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