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Instance: meanvarx

Formats ams gms lp mod nl osil pip
Primal Bounds (infeas ≤ 1e-08)
14.36923211 p1 ( gdx sol )
(infeas: 6e-17)
Other points (infeas > 1e-08)  
Dual Bounds
14.36874739 (ALPHAECP)
14.36923063 (ANTIGONE)
14.36923210 (BARON)
14.36923210 (BONMIN)
14.36923000 (COUENNE)
14.36923211 (LINDO)
14.36923180 (SCIP)
References Dahl, H, Meeraus, Alexander, and Zenios, Stavros A, Some Financial Optimization Models: Risk Management. In Zenios, Stavros A, Ed, Financial Optimization, Cambridge University Press, New York, NY, 1993.
Source GAMS Model Library model meanvarx
Application Financial Optimization
Added to library 01 May 2001
Problem type MBQP
#Variables 35
#Binary Variables 14
#Integer Variables 0
#Nonlinear Variables 7
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type quadratic
Objective curvature convex
#Nonzeros in Objective 7
#Nonlinear Nonzeros in Objective 7
#Constraints 44
#Linear Constraints 44
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature linear
#Nonzeros in Jacobian 103
#Nonlinear Nonzeros in Jacobian 0
#Nonzeros in (Upper-Left) Hessian of Lagrangian 49
#Nonzeros in Diagonal of Hessian of Lagrangian 7
#Blocks in Hessian of Lagrangian 1
Minimal blocksize in Hessian of Lagrangian 7
Maximal blocksize in Hessian of Lagrangian 7
Average blocksize in Hessian of Lagrangian 7.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
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
*         45        9       14       22        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         36       22       14        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        111      104        7        0
*
*  Solve m using MINLP minimizing objvar;


Variables  objvar,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18
          ,x19,x20,x21,x22,b23,b24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34,b35
          ,b36;

Positive Variables  x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17
          ,x18,x19,x20,x21,x22;

Binary Variables  b23,b24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34,b35,b36;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18,e19
          ,e20,e21,e22,e23,e24,e25,e26,e27,e28,e29,e30,e31,e32,e33,e34,e35,e36
          ,e37,e38,e39,e40,e41,e42,e43,e44,e45;


e1..    x2 + x3 + x4 + x5 + x6 + x7 + x8 =E= 1;

e2..    x2 - x9 + x16 =E= 0.2;

e3..    x3 - x10 + x17 =E= 0.2;

e4..    x4 - x11 + x18 =E= 0;

e5..    x5 - x12 + x19 =E= 0;

e6..    x6 - x13 + x20 =E= 0.2;

e7..    x7 - x14 + x21 =E= 0.2;

e8..    x8 - x15 + x22 =E= 0.2;

e9..    x9 + x10 + x11 + x12 + x13 + x14 + x15 =L= 0.3;

e10..    x9 - 0.11*b23 =L= 0;

e11..    x10 - 0.1*b24 =L= 0;

e12..    x11 - 0.07*b25 =L= 0;

e13..    x12 - 0.11*b26 =L= 0;

e14..    x13 - 0.2*b27 =L= 0;

e15..    x14 - 0.1*b28 =L= 0;

e16..    x15 - 0.1*b29 =L= 0;

e17..    x9 - 0.03*b23 =G= 0;

e18..    x10 - 0.04*b24 =G= 0;

e19..    x11 - 0.04*b25 =G= 0;

e20..    x12 - 0.03*b26 =G= 0;

e21..    x13 - 0.03*b27 =G= 0;

e22..    x14 - 0.03*b28 =G= 0;

e23..    x15 - 0.03*b29 =G= 0;

e24..    x16 - 0.2*b30 =L= 0;

e25..    x17 - 0.15*b31 =L= 0;

e26..    x18 =L= 0;

e27..    x19 =L= 0;

e28..    x20 - 0.1*b34 =L= 0;

e29..    x21 - 0.15*b35 =L= 0;

e30..    x22 - 0.2*b36 =L= 0;

e31..    x16 - 0.02*b30 =G= 0;

e32..    x17 - 0.02*b31 =G= 0;

e33..    x18 - 0.04*b32 =G= 0;

e34..    x19 - 0.04*b33 =G= 0;

e35..    x20 - 0.04*b34 =G= 0;

e36..    x21 - 0.04*b35 =G= 0;

e37..    x22 - 0.04*b36 =G= 0;

e38..    b23 + b30 =L= 1;

e39..    b24 + b31 =L= 1;

e40..    b25 + b32 =L= 1;

e41..    b26 + b33 =L= 1;

e42..    b27 + b34 =L= 1;

e43..    b28 + b35 =L= 1;

e44..    b29 + b36 =L= 1;

e45.. -(42.18*x2*x2 + 40.36*x2*x3 + 21.76*x2*x4 + 10.6*x2*x5 + 24.64*x2*x6 + 
      47.68*x2*x7 + 34.82*x2*x8 + 70.89*x3*x3 + 43.16*x3*x4 + 30.82*x3*x5 + 
      46.48*x3*x6 + 47.6*x3*x7 + 25.24*x3*x8 + 25.51*x4*x4 + 19.2*x4*x5 + 45.26
      *x4*x6 + 26.44*x4*x7 + 9.4*x4*x8 + 22.33*x5*x5 + 20.64*x5*x6 + 20.92*x5*
      x7 + 2*x5*x8 + 30.01*x6*x6 + 32.72*x6*x7 + 14.4*x6*x8 + 42.23*x7*x7 + 
      19.8*x7*x8 + 16.42*x8*x8 - 0.06435*x2 - 0.0548*x3 - 0.02505*x4 - 0.0762*
      x5 - 0.03815*x6 - 0.0927*x7 - 0.031*x8) + objvar =E= 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: 2019-09-25 Git hash: 3ba36264
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