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Instance hybriddynamic_var
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) 1.53641513 (COUENNE) 1.53641426 (LINDO) 1.53641432 (SCIP) 0.00000000 (SHOT) |
| Referencesⓘ | Baumrucker, Brian and Biegler, L T, MINLP & MPCC Strategies for Optimization of a Class of Hybrid Dynamic Systems, 2009. |
| Sourceⓘ | del_asl_minlp.gms from minlp.org model 27 |
| Applicationⓘ | Hybrid Dynamic Systems |
| Added to libraryⓘ | 24 Sep 2013 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 81 |
| #Binary Variablesⓘ | 10 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 31 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | polynomial |
| Objective curvatureⓘ | indefinite |
| #Nonzeros in Objectiveⓘ | 21 |
| #Nonlinear Nonzeros in Objectiveⓘ | 21 |
| #Constraintsⓘ | 100 |
| #Linear Constraintsⓘ | 80 |
| #Quadratic Constraintsⓘ | 20 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 265 |
| #Nonlinear Nonzeros in Jacobianⓘ | 40 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 51 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 11 |
| #Blocks in Hessian of Lagrangianⓘ | 11 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 1 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 3 |
| Average blocksize in Hessian of Lagrangianⓘ | 2.818182 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e+00 |
| Maximal coefficientⓘ | 2.0000e+00 |
| Infeasibility of initial pointⓘ | 3 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 101 61 20 20 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 82 72 10 0 0 0 0 0
* FX 2
*
* Nonzero counts
* Total const NL DLL
* 287 226 61 0
*
* Solve m using MINLP minimizing objvar;
Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,b11,b12,b13,b14,b15,b16,b17,b18,b19
,b20,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,objvar;
Binary Variables b11,b12,b13,b14,b15,b16,b17,b18,b19,b20;
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;
e1.. -(sqr((-1.66666666666667) + x81) + sqr(x61)*x21 + sqr(x62)*x22 + sqr(x63)*
x23 + sqr(x64)*x24 + sqr(x65)*x25 + sqr(x66)*x26 + sqr(x67)*x27 + sqr(x68)
*x28 + sqr(x69)*x29 + sqr(x70)*x30) + objvar =E= 0;
e2.. - x21 - x41 + x51 =E= 0;
e3.. - x22 - x42 + x52 =E= 0;
e4.. - x23 - x43 + x53 =E= 0;
e5.. - x24 - x44 + x54 =E= 0;
e6.. - x25 - x45 + x55 =E= 0;
e7.. - x26 - x46 + x56 =E= 0;
e8.. - x27 - x47 + x57 =E= 0;
e9.. - x28 - x48 + x58 =E= 0;
e10.. - x29 - x49 + x59 =E= 0;
e11.. - x30 - x50 + x60 =E= 0;
e12.. -x21*x71 - x31 + x61 =E= 0;
e13.. -x22*x72 - x32 + x62 =E= 0;
e14.. -x23*x73 - x33 + x63 =E= 0;
e15.. -x24*x74 - x34 + x64 =E= 0;
e16.. -x25*x75 - x35 + x65 =E= 0;
e17.. -x26*x76 - x36 + x66 =E= 0;
e18.. -x27*x77 - x37 + x67 =E= 0;
e19.. -x28*x78 - x38 + x68 =E= 0;
e20.. -x29*x79 - x39 + x69 =E= 0;
e21.. -x30*x80 - x40 + x70 =E= 0;
e22.. x1 - 2*b11 =E= -1;
e23.. x2 - 2*b12 =E= -1;
e24.. x3 - 2*b13 =E= -1;
e25.. x4 - 2*b14 =E= -1;
e26.. x5 - 2*b15 =E= -1;
e27.. x6 - 2*b16 =E= -1;
e28.. x7 - 2*b17 =E= -1;
e29.. x8 - 2*b18 =E= -1;
e30.. x9 - 2*b19 =E= -1;
e31.. x10 - 2*b20 =E= -1;
e32.. 2*b11 - x61 =L= 2;
e33.. 2*b12 - x62 =L= 2;
e34.. 2*b13 - x63 =L= 2;
e35.. 2*b14 - x64 =L= 2;
e36.. 2*b15 - x65 =L= 2;
e37.. 2*b16 - x66 =L= 2;
e38.. 2*b17 - x67 =L= 2;
e39.. 2*b18 - x68 =L= 2;
e40.. 2*b19 - x69 =L= 2;
e41.. 2*b20 - x70 =L= 2;
e42.. 2*b11 - x61 =G= 0;
e43.. 2*b12 - x62 =G= 0;
e44.. 2*b13 - x63 =G= 0;
e45.. 2*b14 - x64 =G= 0;
e46.. 2*b15 - x65 =G= 0;
e47.. 2*b16 - x66 =G= 0;
e48.. 2*b17 - x67 =G= 0;
e49.. 2*b18 - x68 =G= 0;
e50.. 2*b19 - x69 =G= 0;
e51.. 2*b20 - x70 =G= 0;
e52.. 2*b11 =L= 2;
e53.. 2*b12 - x61 =L= 2;
e54.. 2*b13 - x62 =L= 2;
e55.. 2*b14 - x63 =L= 2;
e56.. 2*b15 - x64 =L= 2;
e57.. 2*b16 - x65 =L= 2;
e58.. 2*b17 - x66 =L= 2;
e59.. 2*b18 - x67 =L= 2;
e60.. 2*b19 - x68 =L= 2;
e61.. 2*b20 - x69 =L= 2;
e62.. 2*b11 =G= 0;
e63.. 2*b12 - x61 =G= 0;
e64.. 2*b13 - x62 =G= 0;
e65.. 2*b14 - x63 =G= 0;
e66.. 2*b15 - x64 =G= 0;
e67.. 2*b16 - x65 =G= 0;
e68.. 2*b17 - x66 =G= 0;
e69.. 2*b18 - x67 =G= 0;
e70.. 2*b19 - x68 =G= 0;
e71.. 2*b20 - x69 =G= 0;
e72.. - x21 - x41 + x42 =E= 0;
e73.. - x22 - x42 + x43 =E= 0;
e74.. - x23 - x43 + x44 =E= 0;
e75.. - x24 - x44 + x45 =E= 0;
e76.. - x25 - x45 + x46 =E= 0;
e77.. - x26 - x46 + x47 =E= 0;
e78.. - x27 - x47 + x48 =E= 0;
e79.. - x28 - x48 + x49 =E= 0;
e80.. - x29 - x49 + x50 =E= 0;
e81.. -x21*x71 - x31 + x32 =E= 0;
e82.. -x22*x72 - x32 + x33 =E= 0;
e83.. -x23*x73 - x33 + x34 =E= 0;
e84.. -x24*x74 - x34 + x35 =E= 0;
e85.. -x25*x75 - x35 + x36 =E= 0;
e86.. -x26*x76 - x36 + x37 =E= 0;
e87.. -x27*x77 - x37 + x38 =E= 0;
e88.. -x28*x78 - x38 + x39 =E= 0;
e89.. -x29*x79 - x39 + x40 =E= 0;
e90.. -x30*x80 - x40 + x81 =E= 0;
e91.. x1 + x71 =E= 2;
e92.. x2 + x72 =E= 2;
e93.. x3 + x73 =E= 2;
e94.. x4 + x74 =E= 2;
e95.. x5 + x75 =E= 2;
e96.. x6 + x76 =E= 2;
e97.. x7 + x77 =E= 2;
e98.. x8 + x78 =E= 2;
e99.. x9 + x79 =E= 2;
e100.. x10 + x80 =E= 2;
e101.. x21 + x22 + x23 + x24 + x25 + x26 + x27 + x28 + x29 + x30 =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;
x21.lo = 0.16; x21.up = 0.24;
x22.lo = 0.16; x22.up = 0.24;
x23.lo = 0.16; x23.up = 0.24;
x24.lo = 0.16; x24.up = 0.24;
x25.lo = 0.16; x25.up = 0.24;
x26.lo = 0.16; x26.up = 0.24;
x27.lo = 0.16; x27.up = 0.24;
x28.lo = 0.16; x28.up = 0.24;
x29.lo = 0.16; x29.up = 0.24;
x30.lo = 0.16; x30.up = 0.24;
x31.fx = -2;
x41.fx = 0;
x61.lo = -2; x61.up = 2;
x62.lo = -2; x62.up = 2;
x63.lo = -2; x63.up = 2;
x64.lo = -2; x64.up = 2;
x65.lo = -2; x65.up = 2;
x66.lo = -2; x66.up = 2;
x67.lo = -2; x67.up = 2;
x68.lo = -2; x68.up = 2;
x69.lo = -2; x69.up = 2;
x70.lo = -2; x70.up = 2;
* 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;
x21.l = 0.2;
x22.l = 0.2;
x23.l = 0.2;
x24.l = 0.2;
x25.l = 0.2;
x26.l = 0.2;
x27.l = 0.2;
x28.l = 0.2;
x29.l = 0.2;
x30.l = 0.2;
x32.l = -2;
x33.l = -2;
x34.l = -2;
x35.l = -2;
x36.l = -2;
x37.l = -2;
x38.l = -2;
x39.l = -2;
x40.l = -2;
x42.l = 1;
x43.l = 1;
x44.l = 1;
x45.l = 1;
x46.l = 1;
x47.l = 1;
x48.l = 1;
x49.l = 1;
x50.l = 1;
x51.l = 1;
x52.l = 1;
x53.l = 1;
x54.l = 1;
x55.l = 1;
x56.l = 1;
x57.l = 1;
x58.l = 1;
x59.l = 1;
x60.l = 1;
x61.l = -2;
x62.l = -2;
x63.l = -2;
x64.l = -2;
x65.l = -2;
x66.l = -2;
x67.l = -2;
x68.l = -2;
x69.l = -2;
x70.l = -2;
x81.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 MINLP $set MINLP MINLP
Solve m using %MINLP% minimizing objvar;
Last updated: 2025-08-07 Git hash: e62cedfc