MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance windfac
Formatsⓘ | ams gms mod nl osil py |
Primal Bounds (infeas ≤ 1e-08)ⓘ | |
Other points (infeas > 1e-08)ⓘ | |
Dual Boundsⓘ | 0.25448730 (COUENNE) 0.25448730 (LINDO) 0.25448730 (SCIP) 0.00000000 (SHOT) |
Referencesⓘ | Michna, Michael and Gdanska, Polytechnika, Winding Factor of Electrical Machines. |
Sourceⓘ | MacMINLP model wind-fac.mod, GAMS Model Library model windfac |
Applicationⓘ | Winding Factor of Electrical Machines |
Added to libraryⓘ | 01 May 2001 |
Problem typeⓘ | MINLP |
#Variablesⓘ | 14 |
#Binary Variablesⓘ | 0 |
#Integer Variablesⓘ | 3 |
#Nonlinear Variablesⓘ | 13 |
#Nonlinear Binary Variablesⓘ | 0 |
#Nonlinear Integer Variablesⓘ | 3 |
Objective Senseⓘ | min |
Objective typeⓘ | quadratic |
Objective curvatureⓘ | convex |
#Nonzeros in Objectiveⓘ | 2 |
#Nonlinear Nonzeros in Objectiveⓘ | 2 |
#Constraintsⓘ | 13 |
#Linear Constraintsⓘ | 3 |
#Quadratic Constraintsⓘ | 3 |
#Polynomial Constraintsⓘ | 0 |
#Signomial Constraintsⓘ | 1 |
#General Nonlinear Constraintsⓘ | 6 |
Operands in Gen. Nonlin. Functionsⓘ | div mul sin |
Constraints curvatureⓘ | indefinite |
#Nonzeros in Jacobianⓘ | 35 |
#Nonlinear Nonzeros in Jacobianⓘ | 22 |
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 29 |
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 7 |
#Blocks in Hessian of Lagrangianⓘ | 5 |
Minimal blocksize in Hessian of Lagrangianⓘ | 1 |
Maximal blocksize in Hessian of Lagrangianⓘ | 8 |
Average blocksize in Hessian of Lagrangianⓘ | 2.6 |
#Semicontinuitiesⓘ | 0 |
#Nonlinear Semicontinuitiesⓘ | 0 |
#SOS type 1ⓘ | 0 |
#SOS type 2ⓘ | 0 |
Minimal coefficientⓘ | 2.5000e-01 |
Maximal coefficientⓘ | 1.2566e+01 |
Infeasibility of initial pointⓘ | 2.85 |
Sparsity Jacobianⓘ | |
Sparsity Hessian of Lagrangianⓘ |
$offlisting * * Equation counts * Total E G L N X C B * 14 14 0 0 0 0 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 15 12 0 3 0 0 0 0 * FX 0 * * Nonzero counts * Total const NL DLL * 38 14 24 0 * * Solve m using MINLP minimizing objvar; Variables i1,i2,x3,x4,i5,x6,x7,x8,x9,x10,x11,objvar,x13,x14,x15; Integer Variables i1,i2,i5; Equations e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14; e1.. - 12*i1 + i2 =E= 0; e2.. -12.566370616/i2 + x3 =E= 0; e3.. - 0.25*i2 + x4 =E= 0; e4.. - x4 + i5 =E= -1; e5.. sin(0.5*x3)*i1*x6 - sin(0.5*i1*x3) =E= 0; e6.. -sin(1.570796327*i5/x4) + x9 =E= 0; e7.. -x9*x6 + x15 =E= 0; e8.. sin(1.5*x3)*i1*x7 - sin(1.5*i1*x3) =E= 0; e9.. -sin(4.712388981*i5/x4) + x10 =E= 0; e10.. -x10*x7 + x13 =E= 0; e11.. sin(2.5*x3)*i1*x8 - sin(2.5*i1*x3) =E= 0; e12.. -sin(7.853981635*i5/x4) + x11 =E= 0; e13.. -x11*x8 + x14 =E= 0; e14.. -(x13*x13 + x14*x14) + objvar =E= 0; * set non-default bounds i1.lo = 1; i1.up = 10; i2.lo = 1; i2.up = 100; i5.lo = 1; i5.up = 100; x15.lo = 0.8; * set non-default levels i1.l = 1.3; i2.l = 15.4; x3.l = 1.5; x4.l = 1; i5.l = 2.8; 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: 2024-08-26 Git hash: 6cc1607f