MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance synthes2
Formatsⓘ | ams gms mod nl osil py |
Primal Bounds (infeas ≤ 1e-08)ⓘ | |
Other points (infeas > 1e-08)ⓘ | |
Dual Boundsⓘ | 73.03504110 (ALPHAECP) 73.03531245 (ANTIGONE) 73.03531245 (BARON) 73.03531252 (BONMIN) 73.03531253 (COUENNE) 73.03531253 (LINDO) 73.03530997 (SCIP) 73.03529225 (SHOT) |
Referencesⓘ | Duran, Marco A and Grossmann, I E, An Outer-Approximation Algorithm for a Class of Mixed-integer Nonlinear Programs, Mathematical Programming, 36:3, 1986, 307-339. |
Sourceⓘ | MacMINLP model synthes2.mod |
Applicationⓘ | Synthesis of processing system |
Added to libraryⓘ | 01 May 2001 |
Problem typeⓘ | MBNLP |
#Variablesⓘ | 11 |
#Binary Variablesⓘ | 5 |
#Integer Variablesⓘ | 0 |
#Nonlinear Variablesⓘ | 4 |
#Nonlinear Binary Variablesⓘ | 0 |
#Nonlinear Integer Variablesⓘ | 0 |
Objective Senseⓘ | min |
Objective typeⓘ | nonlinear |
Objective curvatureⓘ | convex |
#Nonzeros in Objectiveⓘ | 11 |
#Nonlinear Nonzeros in Objectiveⓘ | 4 |
#Constraintsⓘ | 14 |
#Linear Constraintsⓘ | 11 |
#Quadratic Constraintsⓘ | 0 |
#Polynomial Constraintsⓘ | 0 |
#Signomial Constraintsⓘ | 0 |
#General Nonlinear Constraintsⓘ | 3 |
Operands in Gen. Nonlin. Functionsⓘ | exp log |
Constraints curvatureⓘ | convex |
#Nonzeros in Jacobianⓘ | 37 |
#Nonlinear Nonzeros in Jacobianⓘ | 4 |
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 6 |
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 4 |
#Blocks in Hessian of Lagrangianⓘ | 3 |
Minimal blocksize in Hessian of Lagrangianⓘ | 1 |
Maximal blocksize in Hessian of Lagrangianⓘ | 2 |
Average blocksize in Hessian of Lagrangianⓘ | 1.333333 |
#Semicontinuitiesⓘ | 0 |
#Nonlinear Semicontinuitiesⓘ | 0 |
#SOS type 1ⓘ | 0 |
#SOS type 2ⓘ | 0 |
Minimal coefficientⓘ | 2.0000e-01 |
Maximal coefficientⓘ | 6.0000e+01 |
Infeasibility of initial pointⓘ | 1 |
Sparsity Jacobianⓘ | |
Sparsity Hessian of Lagrangianⓘ |
$offlisting * * Equation counts * Total E G L N X C B * 15 2 0 13 0 0 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 12 7 5 0 0 0 0 0 * FX 0 * * Nonzero counts * Total const NL DLL * 49 41 8 0 * * Solve m using MINLP minimizing objvar; Variables x1,x2,x3,x4,x5,x6,b7,b8,b9,b10,b11,objvar; Positive Variables x1,x2,x3,x4,x5,x6; Binary Variables b7,b8,b9,b10,b11; Equations e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15; e1.. -log(1 + x4 + x5) =L= 0; e2.. exp(x1) - 10*b7 =L= 1; e3.. exp(0.833333*x2) - 10*b8 =L= 1; e4.. 1.25*x3 - 10*b9 =L= 0; e5.. x4 + x5 - 10*b10 =L= 0; e6.. - 2*x3 + 2*x6 - 10*b11 =L= 0; e7.. - x1 - x2 - 2*x3 + x4 + 2*x6 =L= 0; e8.. - x1 - x2 - 0.75*x3 + x4 + 2*x6 =L= 0; e9.. x3 - x6 =L= 0; e10.. 2*x3 - x4 - 2*x6 =L= 0; e11.. - 0.5*x4 + x5 =L= 0; e12.. - 0.2*x4 - x5 =L= 0; e13.. b7 + b8 =E= 1; e14.. b10 + b11 =L= 1; e15.. -(exp(x1) - 10*x1 + exp(0.833333*x2) - 15*x2 - 60*log(1 + x4 + x5) + 15* x4 + 5*x5) + 15*x3 + 20*x6 - 5*b7 - 8*b8 - 6*b9 - 10*b10 - 6*b11 + objvar =E= 140; * set non-default bounds x1.up = 2; x2.up = 2; x3.up = 2; x6.up = 3; 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