MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance portfol_card
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 0.03219287 (ALPHAECP) 0.03221624 (ANTIGONE) 0.03221766 (BARON) 0.03221766 (BONMIN) 0.03221766 (COUENNE) 0.03221766 (LINDO) 0.03221765 (SCIP) 0.00000000 (SHOT) |
| Referencesⓘ | Ehrgott, Matthias, Waters, Chris, Gasimov, Rafail N, and Ustun, Ozden, Multiobjective Programming and Multiattribute Utility Functions in Portfolio Optimization, Information Systems and Operational Research, 47:1, 2009, 31-42. |
| Sourceⓘ | NumberAssets |
| Applicationⓘ | Portfolio Optimization |
| Added to libraryⓘ | 31 May 2014 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 17 |
| #Binary Variablesⓘ | 8 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 8 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 1 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 20 |
| #Linear Constraintsⓘ | 18 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 2 |
| Operands in Gen. Nonlin. Functionsⓘ | sqr sqrt |
| Constraints curvatureⓘ | convex |
| #Nonzeros in Jacobianⓘ | 65 |
| #Nonlinear Nonzeros in Jacobianⓘ | 16 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 64 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 8 |
| #Blocks in Hessian of Lagrangianⓘ | 1 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 8 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 8 |
| Average blocksize in Hessian of Lagrangianⓘ | 8.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.1364e-03 |
| Maximal coefficientⓘ | 1.1412e+00 |
| Infeasibility of initial pointⓘ | 5 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 21 3 2 16 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 18 10 8 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 67 51 16 0
*
* Solve m using MINLP minimizing objvar;
Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,b10,b11,b12,b13,b14,b15,b16,b17,objvar;
Positive Variables x1,x2,x3,x4,x5,x6,x7,x8,x9;
Binary Variables b10,b11,b12,b13,b14,b15,b16,b17;
Equations e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18,e19
,e20,e21;
e1.. x9 - objvar =E= 0;
e2.. 1.07813636363636*x1 - sqrt(0.0476190476190476*sqr((-0.00313636363636371*x1
) - 0.150909090909091*x2 - 0.267772727272727*x3 - 0.308636363636363*x4 -
0.423318181818182*x5 - 0.0687727272727274*x6 - 0.290227272727273*x7 +
0.548045454545455*x8) + 0.0476190476190476*sqr(0.0058636363636364*x1 -
0.0729090909090906*x2 - 0.384772727272727*x3 - 0.407636363636363*x4 -
0.459318181818182*x5 - 0.0897727272727273*x6 - 0.373227272727273*x7 +
0.593045454545455*x8) + 0.0476190476190476*sqr((-0.0171363636363637*x1) -
0.0369090909090906*x2 + 0.251227272727273*x3 + 0.261363636363637*x4 +
0.196681818181818*x5 + 0.0312272727272727*x6 + 0.212772727272727*x7 -
0.368954545454545*x8) + 0.0476190476190476*sqr(0.0820909090909094*x2 -
0.0261363636363636*x1 + 0.116227272727273*x3 + 0.142363636363637*x4 +
0.158681818181818*x5 + 0.0642272727272726*x6 - 0.116227272727273*x7 -
0.168954545454545*x8) + 0.0476190476190476*sqr((-0.0231363636363637*x1) -
0.0909090909090906*x2 - 0.193772727272727*x3 - 0.149636363636363*x4 -
0.0283181818181817*x5 - 0.0617727272727273*x6 + 0.0397727272727273*x7 +
0.0710454545454546*x8) + 0.0476190476190476*sqr((-0.00113636363636371*x1)
- 0.110909090909091*x2 - 0.0557727272727273*x3 - 0.0306363636363634*x4 +
0.0246818181818182*x5 - 0.0797727272727273*x6 + 0.184772727272727*x7 +
0.166045454545455*x8) + 0.0476190476190476*sqr(0.0308636363636363*x1 -
0.114909090909091*x2 + 0.0642272727272726*x3 + 0.132363636363637*x4 +
0.185681818181818*x5 - 0.0687727272727274*x6 - 0.0932272727272727*x7 +
1.08304545454545*x8) + 0.0476190476190476*sqr(0.0488636363636363*x1 -
0.145909090909091*x2 + 0.203227272727273*x3 + 0.213363636363637*x4 +
0.245681818181818*x5 - 0.0607727272727274*x6 + 0.0847727272727272*x7 +
0.167045454545455*x8) + 0.0476190476190476*sqr(0.0778636363636362*x1 -
0.0899090909090907*x2 - 0.170772727272727*x3 - 0.160636363636363*x4 -
0.131318181818182*x5 - 0.0187727272727274*x6 - 0.164227272727273*x7 -
0.440954545454545*x8) + 0.0476190476190476*sqr(0.0388636363636363*x1 +
0.372090909090909*x2 + 0.0952272727272727*x3 + 0.0633636363636367*x4 +
0.0916818181818184*x5 + 0.219227272727273*x6 - 0.160227272727273*x7 -
0.0449545454545452*x8) + 0.0476190476190476*sqr(0.0138636363636364*x1 -
0.107909090909091*x2 + 0.104227272727273*x3 + 0.111363636363637*x4 +
0.0956818181818184*x5 - 0.0117727272727273*x6 + 0.0957727272727273*x7 -
0.256954545454545*x8) + 0.0476190476190476*sqr(0.0248636363636363*x1 +
0.0660909090909094*x2 - 0.0587727272727274*x3 - 0.0936363636363633*x4 -
0.218318181818182*x5 + 0.0582272727272726*x6 - 0.0672272727272727*x7 -
0.303954545454545*x8) + 0.0476190476190476*sqr(0.0018636363636364*x1 +
0.273090909090909*x2 + 0.196227272727273*x3 + 0.202363636363637*x4 +
0.211681818181818*x5 + 0.121227272727273*x6 + 0.420772727272727*x7 -
0.122954545454545*x8) + 0.0476190476190476*sqr(0.216090909090909*x2 -
0.0151363636363637*x1 + 0.0662272727272726*x3 + 0.0373636363636367*x4 -
0.0353181818181816*x5 + 0.0642272727272726*x6 + 0.552772727272727*x7 +
0.0870454545454546*x8) + 0.0476190476190476*sqr((-0.0171363636363637*x1)
- 0.167909090909091*x2 - 0.0677727272727273*x3 - 0.100636363636363*x4 -
0.162318181818182*x5 - 0.0687727272727274*x6 + 0.104772727272727*x7 +
0.115045454545455*x8) + 0.0476190476190476*sqr((-0.00713636363636372*x1)
- 0.00690909090909053*x2 + 0.0452272727272727*x3 + 0.0553636363636367*x4
+ 0.0436818181818184*x5 - 0.0157727272727273*x6 + 0.141772727272727*x7 -
0.267954545454545*x8) + 0.0476190476190476*sqr(0.0088636363636363*x1 +
0.119090909090909*x2 + 0.196227272727273*x3 + 0.168363636363637*x4 +
0.0826818181818183*x5 + 0.0502272727272726*x6 - 0.0362272727272728*x7 -
0.151954545454545*x8) + 0.0476190476190476*sqr(0.0018636363636364*x1 -
0.0389090909090906*x2 - 0.151772727272727*x3 - 0.185636363636363*x4 -
0.291318181818182*x5 - 0.00877272727272738*x6 - 0.375227272727273*x7 -
0.206954545454545*x8) + 0.0476190476190476*sqr(0.100090909090909*x2 -
0.0211363636363637*x1 + 0.184227272727273*x3 + 0.218363636363637*x4 +
0.472681818181818*x5 + 0.0692272727272727*x6 - 0.0202272727272728*x7 -
0.170954545454545*x8) + 0.0476190476190476*sqr((-0.0421363636363636*x1) -
0.0139090909090906*x2 - 0.0437727272727273*x3 - 0.0336363636363632*x4 +
0.0526818181818183*x5 - 0.0157727272727273*x6 - 0.263227272727273*x7 -
0.202954545454545*x8) + 0.0476190476190476*sqr(0.124090909090909*x2 -
0.0471363636363638*x1 - 0.0197727272727273*x3 - 0.0106363636363633*x4 +
0.0406818181818183*x5 + 0.0182272727272728*x6 + 0.184772727272727*x7 +
0.0170454545454546*x8) + 0.0476190476190476*sqr((-0.0331363636363637*x1)
- 0.203909090909091*x2 - 0.107772727272727*x3 - 0.124636363636363*x4 -
0.153318181818182*x5 - 0.126772727272727*x6 - 0.0632272727272727*x7 -
0.138954545454545*x8)) + 1.09290909090909*x2 + 1.11977272727273*x3 +
1.12363636363636*x4 + 1.12131818181818*x5 + 1.09177272727273*x6 +
1.14122727272727*x7 + 1.12895454545455*x8 =G= 0.05;
e3.. -sqrt(0.0476190476190476*sqr((-0.00313636363636371*x1) - 0.150909090909091
*x2 - 0.267772727272727*x3 - 0.308636363636363*x4 - 0.423318181818182*x5
- 0.0687727272727274*x6 - 0.290227272727273*x7 + 0.548045454545455*x8) +
0.0476190476190476*sqr(0.0058636363636364*x1 - 0.0729090909090906*x2 -
0.384772727272727*x3 - 0.407636363636363*x4 - 0.459318181818182*x5 -
0.0897727272727273*x6 - 0.373227272727273*x7 + 0.593045454545455*x8) +
0.0476190476190476*sqr((-0.0171363636363637*x1) - 0.0369090909090906*x2 +
0.251227272727273*x3 + 0.261363636363637*x4 + 0.196681818181818*x5 +
0.0312272727272727*x6 + 0.212772727272727*x7 - 0.368954545454545*x8) +
0.0476190476190476*sqr(0.0820909090909094*x2 - 0.0261363636363636*x1 +
0.116227272727273*x3 + 0.142363636363637*x4 + 0.158681818181818*x5 +
0.0642272727272726*x6 - 0.116227272727273*x7 - 0.168954545454545*x8) +
0.0476190476190476*sqr((-0.0231363636363637*x1) - 0.0909090909090906*x2 -
0.193772727272727*x3 - 0.149636363636363*x4 - 0.0283181818181817*x5 -
0.0617727272727273*x6 + 0.0397727272727273*x7 + 0.0710454545454546*x8) +
0.0476190476190476*sqr((-0.00113636363636371*x1) - 0.110909090909091*x2 -
0.0557727272727273*x3 - 0.0306363636363634*x4 + 0.0246818181818182*x5 -
0.0797727272727273*x6 + 0.184772727272727*x7 + 0.166045454545455*x8) +
0.0476190476190476*sqr(0.0308636363636363*x1 - 0.114909090909091*x2 +
0.0642272727272726*x3 + 0.132363636363637*x4 + 0.185681818181818*x5 -
0.0687727272727274*x6 - 0.0932272727272727*x7 + 1.08304545454545*x8) +
0.0476190476190476*sqr(0.0488636363636363*x1 - 0.145909090909091*x2 +
0.203227272727273*x3 + 0.213363636363637*x4 + 0.245681818181818*x5 -
0.0607727272727274*x6 + 0.0847727272727272*x7 + 0.167045454545455*x8) +
0.0476190476190476*sqr(0.0778636363636362*x1 - 0.0899090909090907*x2 -
0.170772727272727*x3 - 0.160636363636363*x4 - 0.131318181818182*x5 -
0.0187727272727274*x6 - 0.164227272727273*x7 - 0.440954545454545*x8) +
0.0476190476190476*sqr(0.0388636363636363*x1 + 0.372090909090909*x2 +
0.0952272727272727*x3 + 0.0633636363636367*x4 + 0.0916818181818184*x5 +
0.219227272727273*x6 - 0.160227272727273*x7 - 0.0449545454545452*x8) +
0.0476190476190476*sqr(0.0138636363636364*x1 - 0.107909090909091*x2 +
0.104227272727273*x3 + 0.111363636363637*x4 + 0.0956818181818184*x5 -
0.0117727272727273*x6 + 0.0957727272727273*x7 - 0.256954545454545*x8) +
0.0476190476190476*sqr(0.0248636363636363*x1 + 0.0660909090909094*x2 -
0.0587727272727274*x3 - 0.0936363636363633*x4 - 0.218318181818182*x5 +
0.0582272727272726*x6 - 0.0672272727272727*x7 - 0.303954545454545*x8) +
0.0476190476190476*sqr(0.0018636363636364*x1 + 0.273090909090909*x2 +
0.196227272727273*x3 + 0.202363636363637*x4 + 0.211681818181818*x5 +
0.121227272727273*x6 + 0.420772727272727*x7 - 0.122954545454545*x8) +
0.0476190476190476*sqr(0.216090909090909*x2 - 0.0151363636363637*x1 +
0.0662272727272726*x3 + 0.0373636363636367*x4 - 0.0353181818181816*x5 +
0.0642272727272726*x6 + 0.552772727272727*x7 + 0.0870454545454546*x8) +
0.0476190476190476*sqr((-0.0171363636363637*x1) - 0.167909090909091*x2 -
0.0677727272727273*x3 - 0.100636363636363*x4 - 0.162318181818182*x5 -
0.0687727272727274*x6 + 0.104772727272727*x7 + 0.115045454545455*x8) +
0.0476190476190476*sqr((-0.00713636363636372*x1) - 0.00690909090909053*x2
+ 0.0452272727272727*x3 + 0.0553636363636367*x4 + 0.0436818181818184*x5
- 0.0157727272727273*x6 + 0.141772727272727*x7 - 0.267954545454545*x8) +
0.0476190476190476*sqr(0.0088636363636363*x1 + 0.119090909090909*x2 +
0.196227272727273*x3 + 0.168363636363637*x4 + 0.0826818181818183*x5 +
0.0502272727272726*x6 - 0.0362272727272728*x7 - 0.151954545454545*x8) +
0.0476190476190476*sqr(0.0018636363636364*x1 - 0.0389090909090906*x2 -
0.151772727272727*x3 - 0.185636363636363*x4 - 0.291318181818182*x5 -
0.00877272727272738*x6 - 0.375227272727273*x7 - 0.206954545454545*x8) +
0.0476190476190476*sqr(0.100090909090909*x2 - 0.0211363636363637*x1 +
0.184227272727273*x3 + 0.218363636363637*x4 + 0.472681818181818*x5 +
0.0692272727272727*x6 - 0.0202272727272728*x7 - 0.170954545454545*x8) +
0.0476190476190476*sqr((-0.0421363636363636*x1) - 0.0139090909090906*x2 -
0.0437727272727273*x3 - 0.0336363636363632*x4 + 0.0526818181818183*x5 -
0.0157727272727273*x6 - 0.263227272727273*x7 - 0.202954545454545*x8) +
0.0476190476190476*sqr(0.124090909090909*x2 - 0.0471363636363638*x1 -
0.0197727272727273*x3 - 0.0106363636363633*x4 + 0.0406818181818183*x5 +
0.0182272727272728*x6 + 0.184772727272727*x7 + 0.0170454545454546*x8) +
0.0476190476190476*sqr((-0.0331363636363637*x1) - 0.203909090909091*x2 -
0.107772727272727*x3 - 0.124636363636363*x4 - 0.153318181818182*x5 -
0.126772727272727*x6 - 0.0632272727272727*x7 - 0.138954545454545*x8)) + x9
=G= 0;
e4.. x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 =E= 1;
e5.. x1 - b10 =L= 0;
e6.. x2 - b11 =L= 0;
e7.. x3 - b12 =L= 0;
e8.. x4 - b13 =L= 0;
e9.. x5 - b14 =L= 0;
e10.. x6 - b15 =L= 0;
e11.. x7 - b16 =L= 0;
e12.. x8 - b17 =L= 0;
e13.. - x1 + 0.05*b10 =L= 0;
e14.. - x2 + 0.05*b11 =L= 0;
e15.. - x3 + 0.05*b12 =L= 0;
e16.. - x4 + 0.05*b13 =L= 0;
e17.. - x5 + 0.05*b14 =L= 0;
e18.. - x6 + 0.05*b15 =L= 0;
e19.. - x7 + 0.05*b16 =L= 0;
e20.. - x8 + 0.05*b17 =L= 0;
e21.. b10 + b11 + b12 + b13 + b14 + b15 + b16 + b17 =E= 5;
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