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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance ex8_4_8_bnd
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 3.32184731 (ANTIGONE) 3.29845289 (BARON) 3.32184731 (COUENNE) 3.32169577 (LINDO) 0.00388927 (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. 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. Kim, I, Liebman, M J, and Edgar, T F, Robust Error-in-Variables Estimation Using Nonlinear Programming Techniques, AIChE Journal, 36:7, 1990, 985-993. |
| Sourceⓘ | Test Problem ex8.4.8 of Chapter 8 of Floudas e.a. handbook with added bounds |
| Added to libraryⓘ | 31 Jul 2001 |
| Problem typeⓘ | NLP |
| #Variablesⓘ | 42 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 42 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | quadratic |
| Objective curvatureⓘ | convex |
| #Nonzeros in Objectiveⓘ | 20 |
| #Nonlinear Nonzeros in Objectiveⓘ | 20 |
| #Constraintsⓘ | 30 |
| #Linear Constraintsⓘ | 0 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 10 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 20 |
| Operands in Gen. Nonlin. Functionsⓘ | div exp log mul sqr |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 120 |
| #Nonlinear Nonzeros in Jacobianⓘ | 110 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 154 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 32 |
| #Blocks in Hessian of Lagrangianⓘ | 6 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 2 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 32 |
| Average blocksize in Hessian of Lagrangianⓘ | 7.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e+00 |
| Maximal coefficientⓘ | 3.6266e+03 |
| Infeasibility of initial pointⓘ | 422.3 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 31 31 0 0 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 43 43 0 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 141 11 130 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,x34,x35,x36
,x37,x38,x39,x40,x41,x42,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,e24,e25,e26,e27,e28,e29,e30,e31;
e1.. -(sqr((-60) + 200*x1) + sqr((-39.4) + 66.6666666666667*x2) + sqr((-3231.5)
+ 3231.5*x3) + sqr((-645.066666666667) + 1.33333333333333*x4) + sqr((-80)
+ 200*x5) + sqr((-40.1333333333333) + 66.6666666666667*x6) + sqr((-3231.5
) + 3231.5*x7) + sqr((-657.6) + 1.33333333333333*x8) + sqr((-100) + 200*x9
) + sqr((-40.8) + 66.6666666666667*x10) + sqr((-3231.5) + 3231.5*x11) +
sqr((-666.533333333333) + 1.33333333333333*x12) + sqr((-140) + 200*x13) +
sqr((-43.8) + 66.6666666666667*x14) + sqr((-3231.5) + 3231.5*x15) + sqr((-
668.533333333333) + 1.33333333333333*x16) + sqr((-180) + 200*x17) + sqr((-
54.2666666666667) + 66.6666666666667*x18) + sqr((-3231.5) + 3231.5*x19) +
sqr((-626.266666666667) + 1.33333333333333*x20)) + objvar =E= 0;
e2.. exp(18.5875 - 3626.55/(-34.29 + 323.15*x3)) - x33 =E= 0;
e3.. exp(16.1764 - 2927.17/(-50.22 + 323.15*x3)) - x34 =E= 0;
e4.. exp(18.5875 - 3626.55/(-34.29 + 323.15*x7)) - x35 =E= 0;
e5.. exp(16.1764 - 2927.17/(-50.22 + 323.15*x7)) - x36 =E= 0;
e6.. exp(18.5875 - 3626.55/(-34.29 + 323.15*x11)) - x37 =E= 0;
e7.. exp(16.1764 - 2927.17/(-50.22 + 323.15*x11)) - x38 =E= 0;
e8.. exp(18.5875 - 3626.55/(-34.29 + 323.15*x15)) - x39 =E= 0;
e9.. exp(16.1764 - 2927.17/(-50.22 + 323.15*x15)) - x40 =E= 0;
e10.. exp(18.5875 - 3626.55/(-34.29 + 323.15*x19)) - x41 =E= 0;
e11.. exp(16.1764 - 2927.17/(-50.22 + 323.15*x19)) - x42 =E= 0;
e12.. x23*x1*x33 - x2*x4 =E= 0;
e13.. x25*x5*x35 - x6*x8 =E= 0;
e14.. x27*x9*x37 - x10*x12 =E= 0;
e15.. x29*x13*x39 - x14*x16 =E= 0;
e16.. x31*x17*x41 - x18*x20 =E= 0;
e17.. x24*(1 - x1)*x34 - (1 - x2)*x4 =E= 0;
e18.. x26*(1 - x5)*x36 - (1 - x6)*x8 =E= 0;
e19.. x28*(1 - x9)*x38 - (1 - x10)*x12 =E= 0;
e20.. x30*(1 - x13)*x40 - (1 - x14)*x16 =E= 0;
e21.. x32*(1 - x17)*x42 - (1 - x18)*x20 =E= 0;
e22.. x21/x3/sqr(1 + x21/x22*x1/(1 - x1)) - log(x23) =E= 0;
e23.. x21/x7/sqr(1 + x21/x22*x5/(1 - x5)) - log(x25) =E= 0;
e24.. x21/x11/sqr(1 + x21/x22*x9/(1 - x9)) - log(x27) =E= 0;
e25.. x21/x15/sqr(1 + x21/x22*x13/(1 - x13)) - log(x29) =E= 0;
e26.. x21/x19/sqr(1 + x21/x22*x17/(1 - x17)) - log(x31) =E= 0;
e27.. x22/x3/sqr(1 + x22/x21*(1 - x1)/x1) - log(x24) =E= 0;
e28.. x22/x7/sqr(1 + x22/x21*(1 - x5)/x5) - log(x26) =E= 0;
e29.. x22/x11/sqr(1 + x22/x21*(1 - x9)/x9) - log(x28) =E= 0;
e30.. x22/x15/sqr(1 + x22/x21*(1 - x13)/x13) - log(x30) =E= 0;
e31.. x22/x19/sqr(1 + x22/x21*(1 - x17)/x17) - log(x32) =E= 0;
* set non-default bounds
x1.lo = 0.285; x1.up = 0.315;
x2.lo = 0.546; x2.up = 0.636;
x3.lo = 0.999071638557945; x3.up = 1.00092836144205;
x4.lo = 481.55; x4.up = 486.05;
x5.lo = 0.385; x5.up = 0.415;
x6.lo = 0.557; x6.up = 0.647;
x7.lo = 0.999071638557945; x7.up = 1.00092836144205;
x8.lo = 490.95; x8.up = 495.45;
x9.lo = 0.485; x9.up = 0.515;
x10.lo = 0.567; x10.up = 0.657;
x11.lo = 0.999071638557945; x11.up = 1.00092836144205;
x12.lo = 497.65; x12.up = 502.15;
x13.lo = 0.685; x13.up = 0.715;
x14.lo = 0.612; x14.up = 0.702;
x15.lo = 0.999071638557945; x15.up = 1.00092836144205;
x16.lo = 499.15; x16.up = 503.65;
x17.lo = 0.885; x17.up = 0.915;
x18.lo = 0.769; x18.up = 0.859;
x19.lo = 0.999071638557945; x19.up = 1.00092836144205;
x20.lo = 467.45; x20.up = 471.95;
x21.lo = 1; x21.up = 2;
x22.lo = 1; x22.up = 2;
x23.lo = 0.1;
x24.lo = 0.1;
x25.lo = 0.1;
x26.lo = 0.1;
x27.lo = 0.1;
x28.lo = 0.1;
x29.lo = 0.1;
x30.lo = 0.1;
x31.lo = 0.1;
x32.lo = 0.1;
* set non-default levels
x1.l = 0.29015241396;
x2.l = 0.62189400372;
x3.l = 1.00009353307628;
x4.l = 482.905120568;
x5.l = 0.39376636351;
x6.l = 0.57716475803;
x7.l = 0.999721176860282;
x8.l = 494.8032165615;
x9.l = 0.48701341169;
x10.l = 0.61201896021;
x11.l = 1.00092486639703;
x12.l = 500.254300201;
x13.l = 0.71473399117;
x14.l = 0.68060254203;
x15.l = 0.999314298281912;
x16.l = 502.0287344155;
x17.l = 0.88978553592;
x18.l = 0.79150724797;
x19.l = 1.00031365361411;
x20.l = 469.4091037145;
x21.l = 1.9;
x22.l = 1.6;
x23.l = 1;
x24.l = 1;
x25.l = 1;
x26.l = 1;
x27.l = 1;
x28.l = 1;
x29.l = 1;
x30.l = 1;
x31.l = 1;
x32.l = 1;
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: 2025-08-07 Git hash: e62cedfc