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Instance worst

Formats ams gms osil
Primal Bounds (infeas ≤ 1e-08)
20762609.21000000 p1 ( gdx sol )
(infeas: 3e-13)
Other points (infeas > 1e-08)  
Dual Bounds
20762609.21000000 (LINDO)
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 worst
Application Portfolio Optimization
Added to library 31 Jul 2001
Problem type NLP
#Variables 34
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 23
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 13
#Nonlinear Nonzeros in Objective 0
#Constraints 29
#Linear Constraints 8
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 21
Operands in Gen. Nonlin. Functions div errorf exp log mul sqr
Constraints curvature indefinite
#Nonzeros in Jacobian 98
#Nonlinear Nonzeros in Jacobian 53
#Nonzeros in (Upper-Left) Hessian of Lagrangian 79
#Nonzeros in Diagonal of Hessian of Lagrangian 23
#Blocks in Hessian of Lagrangian 3
Minimal blocksize in Hessian of Lagrangian 1
Maximal blocksize in Hessian of Lagrangian 11
Average blocksize in Hessian of Lagrangian 7.666667
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 1.0101e-02
Maximal coefficient 5.0000e+04
Infeasibility of initial point 1.766
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
*         30       30        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         35       35        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        112       59       53        0
*
*  Solve m using NLP 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,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35;

Positive Variables  x23,x24,x25,x26,x27,x28,x29,x30;

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;


e1..    objvar - x18 - x19 - x20 - x21 - x22 + 30000*x23 - 25000*x24
      + 30000*x25 + 50000*x26 - 25000*x27 - 5000*x28 - 15000*x29 - 50000*x30
      =E= 20682900;

e2.. -95.54*exp(0.09167*x31) + x18 =E= 0;

e3.. -93.27*exp(0.33889*x32) + x19 =E= 0;

e4.. -95.54*exp(0.09167*x31) + x20 =E= 0;

e5.. -93.27*exp(0.33889*x32) + x21 =E= 0;

e6.. -91.03*exp(0.58889*x33) + x22 =E= 0;

e7.. -exp(-0.33889*x32)*(errorf(x2)*x21 - 95*errorf(x10)) + x23 =E= 0;

e8.. -exp(-0.33889*x32)*(errorf(x3)*x21 - 97*errorf(x11)) + x25 =E= 0;

e9.. -exp(-0.58889*x33)*(errorf(x6)*x22 - 95*errorf(x14)) + x24 =E= 0;

e10.. -exp(-0.58889*x33)*(errorf(x7)*x22 - 97*errorf(x15)) + x26 =E= 0;

e11.. -exp(-0.58889*x33)*(errorf(x8)*x22 - 99*errorf(x16)) + x27 =E= 0;

e12.. -exp(-0.33889*x32)*(95*errorf(-x12) - errorf(-x4)*x21) + x28 =E= 0;

e13.. -exp(-0.33889*x32)*(97*errorf(-x13) - errorf(-x5)*x21) + x29 =E= 0;

e14.. -exp(-0.58889*x33)*(99*errorf(-x17) - errorf(-x9)*x22) + x30 =E= 0;

e15.. -1.71779218689115*(log(0.0105263157894737*x21) + 0.169445*sqr(x34))/x34
       + x2 =E= 0;

e16.. -1.71779218689115*(log(0.0103092783505155*x21) + 0.169445*sqr(x34))/x34
       + x3 =E= 0;

e17.. -1.71779218689115*(log(0.0105263157894737*x21) + 0.169445*sqr(x34))/x34
       + x4 =E= 0;

e18.. -1.71779218689115*(log(0.0103092783505155*x21) + 0.169445*sqr(x34))/x34
       + x5 =E= 0;

e19.. -1.30311549893554*(log(0.0105263157894737*x22) + 0.294445*sqr(x35))/x35
       + x6 =E= 0;

e20.. -1.30311549893554*(log(0.0103092783505155*x22) + 0.294445*sqr(x35))/x35
       + x7 =E= 0;

e21.. -1.30311549893554*(log(0.0101010101010101*x22) + 0.294445*sqr(x35))/x35
       + x8 =E= 0;

e22.. -1.30311549893554*(log(0.0101010101010101*x22) + 0.294445*sqr(x35))/x35
       + x9 =E= 0;

e23..  - x2 + x10 + 0.582142594215541*x34 =E= 0;

e24..  - x3 + x11 + 0.582142594215541*x34 =E= 0;

e25..  - x4 + x12 + 0.582142594215541*x34 =E= 0;

e26..  - x5 + x13 + 0.582142594215541*x34 =E= 0;

e27..  - x6 + x14 + 0.767391686168152*x35 =E= 0;

e28..  - x7 + x15 + 0.767391686168152*x35 =E= 0;

e29..  - x8 + x16 + 0.767391686168152*x35 =E= 0;

e30..  - x9 + x17 + 0.767391686168152*x35 =E= 0;

* set non-default bounds
x18.lo = 0.001;
x19.lo = 0.001;
x20.lo = 0.001;
x21.lo = 0.001;
x22.lo = 0.001;
x31.lo = 0.05245; x31.up = 0.0857;
x32.lo = 0.06175; x32.up = 0.095;
x33.lo = 0.0619; x33.up = 0.0939;
x34.lo = 0.0368; x34.up = 0.0768;
x35.lo = 0.0368; x35.up = 0.0768;

* set non-default levels
x18.l = 96.1523975231246;
x19.l = 95.8007796007676;
x20.l = 96.1523975231246;
x21.l = 95.8007796007676;
x22.l = 95.303225278852;
x31.l = 0.069075;
x32.l = 0.078375;
x33.l = 0.0779;
x34.l = 0.0568;
x35.l = 0.0568;

Model m / all /;

m.limrow=0; m.limcol=0;
m.tolproj=0.0;

$if NOT '%gams.u1%' == '' $include '%gams.u1%'

$if not set NLP $set NLP NLP
Solve m using %NLP% minimizing objvar;


Last updated: 2022-04-26 Git hash: de668763
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