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)
0.03221766 p1 ( gdx sol )
(infeas: 0)
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 of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangian Sparsity of 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: 2022-08-11 Git hash: f176bd52
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