MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

Home // Instances // Documentation // Download // Statistics

Instance ramsey

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-2.48746864 p1 ( gdx sol ) (infeas: 1e-15)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-2.48747025 (ANTIGONE) -2.48746864 (BARON) -2.48746864 (COUENNE) -2.48746864 (LINDO) -2.48746876 (SCIP)
Referencesⓘ	Ramsey, F P, A Mathematical Theory of Saving, The Economic Journal, 38:152, 1928, 543-559. Murtagh, B A and Saunders, M A, A Projected Lagrangian Algorithm and its Implementation for Sparse Nonlinear Constraints, Mathematical Programming Study, 16, 1982, 84-117.
Sourceⓘ	GAMS Model Library model ramsey
Applicationⓘ	Portfolio Optimization
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	NLP
#Variablesⓘ	33
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	22
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	nonlinear
Objective curvatureⓘ	convex
#Nonzeros in Objectiveⓘ	11
#Nonlinear Nonzeros in Objectiveⓘ	11
#Constraintsⓘ	22
#Linear Constraintsⓘ	11
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	11
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ	log
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	65
#Nonlinear Nonzeros in Jacobianⓘ	11
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	22
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	22
#Blocks in Hessian of Lagrangianⓘ	22
Minimal blocksize in Hessian of Lagrangianⓘ	1
Maximal blocksize in Hessian of Lagrangianⓘ	1
Average blocksize in Hessian of Lagrangianⓘ	1.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	3.0000e-02
Maximal coefficientⓘ	1.1376e+01
Infeasibility of initial pointⓘ	0.2482
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         23       22        0        1        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         34       34        0        0        0        0        0        0
*  FX      2
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         77       55       22        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,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,objvar;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18,e19
          ,e20,e21,e22,e23;


e1.. 0.759835685651593*x1**0.25 - x12 - x23 =E= 0;

e2.. 0.77686866556676*x2**0.25 - x13 - x24 =E= 0;

e3.. 0.794283468039448*x3**0.25 - x14 - x25 =E= 0;

e4.. 0.812088652256959*x4**0.25 - x15 - x26 =E= 0;

e5.. 0.830292969275008*x5**0.25 - x16 - x27 =E= 0;

e6.. 0.848905366318769*x6**0.25 - x17 - x28 =E= 0;

e7.. 0.867934991180342*x7**0.25 - x18 - x29 =E= 0;

e8.. 0.88739119671479*x8**0.25 - x19 - x30 =E= 0;

e9.. 0.907283545436972*x9**0.25 - x20 - x31 =E= 0;

e10.. 0.92762181422141*x10**0.25 - x21 - x32 =E= 0;

e11.. 0.948415999107521*x11**0.25 - x22 - x33 =E= 0;

e12..  - x1 + x2 - x23 =E= 0;

e13..  - x2 + x3 - x24 =E= 0;

e14..  - x3 + x4 - x25 =E= 0;

e15..  - x4 + x5 - x26 =E= 0;

e16..  - x5 + x6 - x27 =E= 0;

e17..  - x6 + x7 - x28 =E= 0;

e18..  - x7 + x8 - x29 =E= 0;

e19..  - x8 + x9 - x30 =E= 0;

e20..  - x9 + x10 - x31 =E= 0;

e21..  - x10 + x11 - x32 =E= 0;

e22..    0.03*x11 - x33 =L= 0;

e23.. -(0.95*log(x12) + 0.9025*log(x13) + 0.857375*log(x14) + 0.81450625*log(
      x15) + 0.7737809375*log(x16) + 0.735091890625*log(x17) + 0.69833729609375
      *log(x18) + 0.663420431289062*log(x19) + 0.630249409724609*log(x20) + 
      0.598736939238379*log(x21) + 11.3760018455292*log(x22)) - objvar =E= 0;

* set non-default bounds
x1.fx = 3;
x2.lo = 3;
x3.lo = 3;
x4.lo = 3;
x5.lo = 3;
x6.lo = 3;
x7.lo = 3;
x8.lo = 3;
x9.lo = 3;
x10.lo = 3;
x11.lo = 3;
x12.lo = 0.95;
x13.lo = 0.95;
x14.lo = 0.95;
x15.lo = 0.95;
x16.lo = 0.95;
x17.lo = 0.95;
x18.lo = 0.95;
x19.lo = 0.95;
x20.lo = 0.95;
x21.lo = 0.95;
x22.lo = 0.95;
x23.fx = 0.05;
x24.lo = 0.05; x24.up = 0.0575;
x25.lo = 0.05; x25.up = 0.066125;
x26.lo = 0.05; x26.up = 0.07604375;
x27.lo = 0.05; x27.up = 0.0874503125;
x28.lo = 0.05; x28.up = 0.100567859375;
x29.lo = 0.05; x29.up = 0.11565303828125;
x30.lo = 0.05; x30.up = 0.133000994023437;
x31.lo = 0.05; x31.up = 0.152951143126953;
x32.lo = 0.05; x32.up = 0.175893814595996;
x33.lo = 0.05; x33.up = 0.202277886785395;

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;