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Instance portfol_buyin

Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
0.02942380 p1 ( gdx sol )
(infeas: 0)
Other points (infeas > 1e-08)  
Dual Bounds
0.02933190 (ALPHAECP)
0.02942291 (ANTIGONE)
0.02942380 (BARON)
0.02942380 (BONMIN)
0.02942205 (COUENNE)
0.02942380 (LINDO)
0.02942380 (SCIP)
0.00000000 (SHOT)
References Bonami, Pierre and Lejeune, M A, An Exact Solution Approach for Portfolio Optimization Problems Under Stochastic and Integer Constraints, Operations Research, 57:3, 2009, 650-670.
Source BuyInThreshold
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 19
#Linear Constraints 17
#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 57
#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 1
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
*         20        2        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
*         59       43       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;


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 + 0.1*b10 =L= 0;

e14..  - x2 + 0.1*b11 =L= 0;

e15..  - x3 + 0.1*b12 =L= 0;

e16..  - x4 + 0.1*b13 =L= 0;

e17..  - x5 + 0.1*b14 =L= 0;

e18..  - x6 + 0.1*b15 =L= 0;

e19..  - x7 + 0.1*b16 =L= 0;

e20..  - x8 + 0.1*b17 =L= 0;

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: 2022-10-14 Git hash: 2be6d7c0
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