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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance ex8_6_2
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | -45.00000000 (ANTIGONE) -45.00000000 (BARON) -45.00000003 (COUENNE) -45.00000000 (GUROBI) -45.00000000 (LINDO) -45.00000000 (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. |
| Sourceⓘ | Test Problem ex8.6.2 of Chapter 8 of Floudas e.a. handbook |
| Added to libraryⓘ | 31 Jul 2001 |
| Problem typeⓘ | NLP |
| #Variablesⓘ | 30 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 30 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | nonlinear |
| Objective curvatureⓘ | nonconvex |
| #Nonzeros in Objectiveⓘ | 30 |
| #Nonlinear Nonzeros in Objectiveⓘ | 30 |
| #Constraintsⓘ | 0 |
| #Linear Constraintsⓘ | 0 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | exp sqr vcpower |
| Constraints curvatureⓘ | linear |
| #Nonzeros in Jacobianⓘ | 0 |
| #Nonlinear Nonzeros in Jacobianⓘ | 0 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 900 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 30 |
| #Blocks in Hessian of Lagrangianⓘ | 1 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 30 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 30 |
| Average blocksize in Hessian of Lagrangianⓘ | 30.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 5.0000e-01 |
| Maximal coefficientⓘ | 3.0000e+00 |
| Infeasibility of initial pointⓘ | 0 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 1 1 0 0 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 31 31 0 0 0 0 0 0
* FX 6
*
* Nonzero counts
* Total const NL DLL
* 31 1 30 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,objvar;
Equations e1;
e1.. -(sqr(1 - exp(3 - 3*(sqr(x1 - x2) + sqr(x11 - x12) + sqr(x21 - x22))**0.5)
) + sqr(1 - exp(3 - 3*(sqr(x1 - x3) + sqr(x11 - x13) + sqr(x21 - x23))**
0.5)) + sqr(1 - exp(3 - 3*(sqr(x1 - x4) + sqr(x11 - x14) + sqr(x21 - x24))
**0.5)) + sqr(1 - exp(3 - 3*(sqr(x1 - x5) + sqr(x11 - x15) + sqr(x21 - x25
))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x1 - x6) + sqr(x11 - x16) + sqr(x21 -
x26))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x1 - x7) + sqr(x11 - x17) + sqr(x21
- x27))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x1 - x8) + sqr(x11 - x18) + sqr(
x21 - x28))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x1 - x9) + sqr(x11 - x19) +
sqr(x21 - x29))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x1 - x10) + sqr(x11 - x20)
+ sqr(x21 - x30))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x2 - x3) + sqr(x12 -
x13) + sqr(x22 - x23))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x2 - x4) + sqr(x12
- x14) + sqr(x22 - x24))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x2 - x5) + sqr(
x12 - x15) + sqr(x22 - x25))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x2 - x6) +
sqr(x12 - x16) + sqr(x22 - x26))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x2 - x7)
+ sqr(x12 - x17) + sqr(x22 - x27))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x2 -
x8) + sqr(x12 - x18) + sqr(x22 - x28))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x2
- x9) + sqr(x12 - x19) + sqr(x22 - x29))**0.5)) + sqr(1 - exp(3 - 3*(sqr(
x2 - x10) + sqr(x12 - x20) + sqr(x22 - x30))**0.5)) + sqr(1 - exp(3 - 3*(
sqr(x3 - x4) + sqr(x13 - x14) + sqr(x23 - x24))**0.5)) + sqr(1 - exp(3 - 3
*(sqr(x3 - x5) + sqr(x13 - x15) + sqr(x23 - x25))**0.5)) + sqr(1 - exp(3
- 3*(sqr(x3 - x6) + sqr(x13 - x16) + sqr(x23 - x26))**0.5)) + sqr(1 -
exp(3 - 3*(sqr(x3 - x7) + sqr(x13 - x17) + sqr(x23 - x27))**0.5)) + sqr(1
- exp(3 - 3*(sqr(x3 - x8) + sqr(x13 - x18) + sqr(x23 - x28))**0.5)) +
sqr(1 - exp(3 - 3*(sqr(x3 - x9) + sqr(x13 - x19) + sqr(x23 - x29))**0.5))
+ sqr(1 - exp(3 - 3*(sqr(x3 - x10) + sqr(x13 - x20) + sqr(x23 - x30))**
0.5)) + sqr(1 - exp(3 - 3*(sqr(x4 - x5) + sqr(x14 - x15) + sqr(x24 - x25))
**0.5)) + sqr(1 - exp(3 - 3*(sqr(x4 - x6) + sqr(x14 - x16) + sqr(x24 - x26
))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x4 - x7) + sqr(x14 - x17) + sqr(x24 -
x27))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x4 - x8) + sqr(x14 - x18) + sqr(x24
- x28))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x4 - x9) + sqr(x14 - x19) + sqr(
x24 - x29))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x4 - x10) + sqr(x14 - x20) +
sqr(x24 - x30))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x5 - x6) + sqr(x15 - x16)
+ sqr(x25 - x26))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x5 - x7) + sqr(x15 -
x17) + sqr(x25 - x27))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x5 - x8) + sqr(x15
- x18) + sqr(x25 - x28))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x5 - x9) + sqr(
x15 - x19) + sqr(x25 - x29))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x5 - x10) +
sqr(x15 - x20) + sqr(x25 - x30))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x6 - x7)
+ sqr(x16 - x17) + sqr(x26 - x27))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x6 -
x8) + sqr(x16 - x18) + sqr(x26 - x28))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x6
- x9) + sqr(x16 - x19) + sqr(x26 - x29))**0.5)) + sqr(1 - exp(3 - 3*(sqr(
x6 - x10) + sqr(x16 - x20) + sqr(x26 - x30))**0.5)) + sqr(1 - exp(3 - 3*(
sqr(x7 - x8) + sqr(x17 - x18) + sqr(x27 - x28))**0.5)) + sqr(1 - exp(3 - 3
*(sqr(x7 - x9) + sqr(x17 - x19) + sqr(x27 - x29))**0.5)) + sqr(1 - exp(3
- 3*(sqr(x7 - x10) + sqr(x17 - x20) + sqr(x27 - x30))**0.5)) + sqr(1 -
exp(3 - 3*(sqr(x8 - x9) + sqr(x18 - x19) + sqr(x28 - x29))**0.5)) + sqr(1
- exp(3 - 3*(sqr(x8 - x10) + sqr(x18 - x20) + sqr(x28 - x30))**0.5)) +
sqr(1 - exp(3 - 3*(sqr(x9 - x10) + sqr(x19 - x20) + sqr(x29 - x30))**0.5))
) + objvar =E= -45;
* set non-default bounds
x1.fx = 0;
x2.lo = -5; x2.up = 5;
x3.lo = -5; x3.up = 5;
x4.lo = -5; x4.up = 5;
x5.lo = -5; x5.up = 5;
x6.lo = -5; x6.up = 5;
x7.lo = -5; x7.up = 5;
x8.lo = -5; x8.up = 5;
x9.lo = -5; x9.up = 5;
x10.lo = -5; x10.up = 5;
x11.fx = 0;
x12.fx = 0;
x13.lo = -5; x13.up = 5;
x14.lo = -5; x14.up = 5;
x15.lo = -5; x15.up = 5;
x16.lo = -5; x16.up = 5;
x17.lo = -5; x17.up = 5;
x18.lo = -5; x18.up = 5;
x19.lo = -5; x19.up = 5;
x20.lo = -5; x20.up = 5;
x21.fx = 0;
x22.fx = 0;
x23.fx = 0;
x24.lo = -5; x24.up = 5;
x25.lo = -5; x25.up = 5;
x26.lo = -5; x26.up = 5;
x27.lo = -5; x27.up = 5;
x28.lo = -5; x28.up = 5;
x29.lo = -5; x29.up = 5;
x30.lo = -5; x30.up = 5;
* set non-default levels
x2.l = 3.43266708;
x3.l = 0.50375356;
x4.l = -1.98862096;
x5.l = -2.07787883;
x6.l = -2.75947133;
x7.l = -1.50169496;
x8.l = 3.56270347;
x9.l = -4.32886277;
x10.l = 0.00210668999999974;
x13.l = 4.91133039;
x14.l = 2.62250467;
x15.l = -3.69307517;
x16.l = 1.39718759;
x17.l = -3.40482136;
x18.l = -2.49919467;
x19.l = 1.68928609;
x20.l = -0.64643619;
x24.l = -3.49898212;
x25.l = 0.8911365;
x26.l = 3.30892812;
x27.l = -2.69184262;
x28.l = 1.6573446;
x29.l = 2.75857606;
x30.l = -1.96341523;
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