MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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


Instance: ex8_4_5

Formats ams gms mod nl osil
Primal Bounds
0.00122530 p1 ( gdx sol )
(infeas: 1e-16)
0.00030749 p2 ( gdx sol )
(infeas: 3e-17)
Dual Bounds
0.00030748 (ANTIGONE)
0.00030745 (BARON)
0.00030749 (COUENNE)
0.00030740 (LINDO)
0.00030654 (SCIP)
References Floudas, C A, Pardalos, Panos M, Adjiman, C S, Esposito, W R, Gumus, Zeynep H, Harding, S T, Klepeis, John L, Meyer, Clifford A, and Schweiger, C A, Handbook of Test Problems in Local and Global Optimization, Kluwer Academic Publishers, 1999.
Moore, R E, Hansen, E, and Leclerc, A, Rigorous Methods for Global Optimization. In Floudas, C A and M, Pardalos P, Eds, Recent Advances in Global Optimization, Princeton University Press, 1992, 321-342.
Esposito, W R and Floudas, C A, Global Optimization in Parameter Estimation of Nonlinear Algebraic Models via the Error-in-Variables Approach, Industrial and Engineering Chemistry Research, 37:5, 1998, 1841-1858.
Source Test Problem ex8.4.5 of Chapter 8 of Floudas e.a. handbook
Added to library 31 Jul 2001
Problem type NLP
#Variables 15
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 15
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type quadratic
Objective curvature convex
#Nonzeros in Objective 11
#Nonlinear Nonzeros in Objective 11
#Constraints 11
#Linear Constraints 0
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 11
Operands in Gen. Nonlin. Functions mul div
Constraints curvature indefinite
#Nonzeros in Jacobian 55
#Nonlinear Nonzeros in Jacobian 44
#Nonzeros in (Upper-Left) Hessian of Lagrangian 25
#Nonzeros in Diagonal of Hessian of Lagrangian 13
#Blocks in Hessian of Lagrangian 12
Minimal blocksize in Hessian of Lagrangian 1
Maximal blocksize in Hessian of Lagrangian 4
Average blocksize in Hessian of Lagrangian 1.25
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Infeasibility of initial point 0.1575
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
*         12       12        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         16       16        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         67       12       55        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,objvar;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12;


e1.. -(sqr((-0.1957) + x1) + sqr((-0.1947) + x2) + sqr((-0.1735) + x3) + sqr((-
     0.16) + x4) + sqr((-0.0844) + x5) + sqr((-0.0627) + x6) + sqr((-0.0456) + 
     x7) + sqr((-0.0342) + x8) + sqr((-0.0323) + x9) + sqr((-0.0235) + x10) + 
     sqr((-0.0246) + x11)) + objvar =E= 0;

e2.. x12*(16 + 4*x13)/(16 + 4*x14 + x15) - x1 =E= 0;

e3.. x12*(4 + 2*x13)/(4 + 2*x14 + x15) - x2 =E= 0;

e4.. x12*(1 + x13)/(1 + x14 + x15) - x3 =E= 0;

e5.. x12*(0.25 + 0.5*x13)/(0.25 + 0.5*x14 + x15) - x4 =E= 0;

e6.. x12*(0.0625 + 0.25*x13)/(0.0625 + 0.25*x14 + x15) - x5 =E= 0;

e7.. x12*(0.0277777777777778 + 0.166666666666667*x13)/(0.0277777777777778 + 
     0.166666666666667*x14 + x15) - x6 =E= 0;

e8.. x12*(0.015625 + 0.125*x13)/(0.015625 + 0.125*x14 + x15) - x7 =E= 0;

e9.. x12*(0.01 + 0.1*x13)/(0.01 + 0.1*x14 + x15) - x8 =E= 0;

e10.. x12*(0.00694444444444444 + 0.0833333333333333*x13)/(0.00694444444444444
       + 0.0833333333333333*x14 + x15) - x9 =E= 0;

e11.. x12*(0.00510204081632653 + 0.0714285714285714*x13)/(0.00510204081632653
       + 0.0714285714285714*x14 + x15) - x10 =E= 0;

e12.. x12*(0.00390625 + 0.0625*x13)/(0.00390625 + 0.0625*x14 + x15) - x11 =E= 0
      ;

* set non-default bounds
x1.lo = 0.1757; x1.up = 0.2157;
x2.lo = 0.1747; x2.up = 0.2147;
x3.lo = 0.1535; x3.up = 0.1935;
x4.lo = 0.14; x4.up = 0.18;
x5.lo = 0.0644; x5.up = 0.1044;
x6.lo = 0.0427; x6.up = 0.0827;
x7.lo = 0.0256; x7.up = 0.0656;
x8.lo = 0.0142; x8.up = 0.0542;
x9.lo = 0.0123; x9.up = 0.0523;
x10.lo = 0.0035; x10.up = 0.0435;
x11.lo = 0.0046; x11.up = 0.0446;
x12.lo = -0.2892; x12.up = 0.2893;
x13.lo = -0.2892; x13.up = 0.2893;
x14.lo = -0.2892; x14.up = 0.2893;
x15.lo = -0.2892; x15.up = 0.2893;

* set non-default levels
x1.l = 0.18256988528;
x2.l = 0.20843066832;
x3.l = 0.17551501424;
x4.l = 0.15204551616;
x5.l = 0.07608848468;
x6.l = 0.05166211468;
x7.l = 0.03959322016;
x8.l = 0.04845081388;
x9.l = 0.01498454892;
x10.l = 0.02350842676;
x11.l = 0.04452470508;
x12.l = 0.045597259173;
x13.l = 0.2841704630615;
x14.l = 0.1517618951595;
x15.l = -0.2135943985845;

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: 2018-09-14 Git hash: ac5a5314
Imprint / Privacy Policy