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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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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 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;