MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
Home // Instances // Documentation // Download // Statistics
Instance nvs23
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | -1125.20000000 (ANTIGONE) -1125.20000000 (BARON) -1125.20000000 (COUENNE) -1125.20000000 (GUROBI) -1474.66511600 (LINDO) -1125.20000000 (SCIP) -1125.20000200 (SHOT) |
| Referencesⓘ | Gupta, Omprakash K and Ravindran, A, Branch and Bound Experiments in Convex Nonlinear Integer Programming, Management Science, 13:12, 1985, 1533-1546. Tawarmalani, M and Sahinidis, N V, Exact Algorithms for Global Optimization of Mixed-Integer Nonlinear Programs. In Pardalos, Panos M and Romeijn, H Edwin, Eds, Handbook of Global Optimization - Volume 2: Heuristic Approaches, Kluwer Academic Publishers, 65-85. Tawarmalani, M and Sahinidis, N V, Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications, Kluwer, 2002. |
| Sourceⓘ | BARON book instance gupta/gupta23 |
| Added to libraryⓘ | 25 Jul 2002 |
| Problem typeⓘ | IQCQP |
| #Variablesⓘ | 9 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 9 |
| #Nonlinear Variablesⓘ | 9 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 9 |
| Objective Senseⓘ | min |
| Objective typeⓘ | quadratic |
| Objective curvatureⓘ | convex |
| #Nonzeros in Objectiveⓘ | 9 |
| #Nonlinear Nonzeros in Objectiveⓘ | 9 |
| #Constraintsⓘ | 9 |
| #Linear Constraintsⓘ | 0 |
| #Quadratic Constraintsⓘ | 9 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 81 |
| #Nonlinear Nonzeros in Jacobianⓘ | 81 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 81 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 9 |
| #Blocks in Hessian of Lagrangianⓘ | 1 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 9 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 9 |
| Average blocksize in Hessian of Lagrangianⓘ | 9.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 2.0000e-01 |
| Maximal coefficientⓘ | 1.1840e+02 |
| Infeasibility of initial pointⓘ | 1.068e+06 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 10 1 9 0 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 10 1 0 9 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 91 1 90 0
*
* Solve m using MINLP minimizing objvar;
Variables i1,i2,i3,i4,i5,i6,i7,i8,i9,objvar;
Integer Variables i1,i2,i3,i4,i5,i6,i7,i8,i9;
Equations e1,e2,e3,e4,e5,e6,e7,e8,e9,e10;
e1.. (-9*sqr(i1)) - 10*i1*i2 - 8*sqr(i2) - 5*sqr(i3) - 6*i3*i1 - 10*i3*i2 - 7*
sqr(i4) - 10*i4*i1 - 6*i4*i2 - 2*i4*i3 - 2*i5*i2 - 7*sqr(i5) - 6*i6*i1 - 2
*i6*i2 - 2*i6*i4 - 5*sqr(i6) + 6*i7*i1 + 2*i7*i2 + 4*i7*i3 + 2*i7*i4 - 4*
i7*i5 + 4*i7*i6 - 8*sqr(i7) - 2*i8*i1 - 8*i8*i2 - 2*i8*i3 + 6*i8*i5 - 2*i8
*i7 - 6*sqr(i8) + 2*i9*i3 - 4*i9*i4 + 8*i9*i5 + 4*i9*i6 - 6*i9*i8 - 6*sqr(
i9) =G= -1850;
e2.. (-6*sqr(i1)) - 8*i1*i2 - 6*sqr(i2) - 4*sqr(i3) - 2*i3*i1 - 2*i3*i2 - 8*
sqr(i4) + 2*i4*i1 + 10*i4*i2 - 2*i5*i1 - 6*i5*i2 + 6*i5*i4 + 7*sqr(i5) - 2
*i6*i2 + 8*i6*i3 + 2*i6*i4 - 4*i6*i5 - 8*sqr(i6) - 6*i7*i1 - 10*i7*i2 - 2*
i7*i3 + 10*i7*i4 - 10*i7*i5 - 8*sqr(i7) - 2*i8*i1 - 4*i8*i2 - 2*i8*i3 - 8*
i8*i5 - 8*i8*i7 - 5*sqr(i8) - 2*i9*i1 - 2*i9*i2 + 4*i9*i6 + 2*i9*i7 - 6*
sqr(i9) =G= -3170;
e3.. (-9*sqr(i1)) - 6*sqr(i2) - 8*sqr(i3) + 2*i2*i1 + 2*i3*i2 - 6*sqr(i4) + 4*
i4*i1 + 4*i4*i2 - 2*i4*i3 - 6*i5*i1 - 2*i5*i2 + 4*i5*i4 + 6*sqr(i5) + 2*i6
*i1 + 4*i6*i2 - 6*i6*i4 - 2*i6*i5 - 5*sqr(i6) + 2*i7*i2 - 4*i7*i3 - 6*i7*
i5 - 4*i7*i6 - 7*sqr(i7) - 2*i8*i1 + 4*i8*i3 + 2*i8*i4 - 4*sqr(i8) + 10*i9
*i1 + 6*i9*i2 - 4*i9*i3 - 10*i9*i4 + 8*i9*i5 - 6*i9*i6 - 2*i9*i7 - 8*sqr(
i9) =G= -1770;
e4.. (-8*sqr(i1)) - 4*sqr(i2) - 9*sqr(i3) - 7*sqr(i4) - 2*i2*i1 - 2*i3*i1 - 4*
i3*i2 + 6*i4*i1 + 2*i4*i2 - 2*i4*i3 - 6*i5*i1 - 4*i5*i2 - 2*i5*i3 + 6*i5*
i4 + 6*sqr(i5) - 10*i6*i1 - 10*i6*i3 + 4*i6*i4 - 2*i6*i5 - 7*sqr(i6) + 6*
i7*i1 - 2*i7*i2 - 2*i7*i3 + 6*i7*i5 + 2*i7*i6 - 6*sqr(i7) + 4*i8*i1 - 4*i8
*i2 + 2*i8*i3 - 4*i8*i4 - 4*i8*i5 + 8*i8*i6 + 6*i8*i6 - 8*sqr(i8) - 4*i9*
i1 + 4*i9*i2 + 6*i9*i3 - 2*i9*i4 + 2*i9*i6 + 8*i9*i7 - 4*i9*i8 - 10*sqr(i9
) =G= -1460;
e5.. 2*i2*i1 - 4*sqr(i1) - 5*sqr(i2) - 6*i3*i1 - 8*sqr(i3) - 2*i4*i1 + 6*i4*i2
- 2*i4*i3 - 6*sqr(i4) - 4*i5*i1 + 2*i5*i2 - 6*i5*i3 - 8*i5*i4 - 7*sqr(i5)
+ 4*i6*i1 - 4*i6*i2 + 6*i6*i3 + 4*i6*i5 - 7*sqr(i6) + 4*i7*i1 - 4*i7*i2
- 4*i7*i3 + 4*i7*i4 + 4*i7*i5 + 4*i7*i6 - 8*sqr(i7) - 2*i8*i1 + 4*i8*i4
+ 2*i8*i6 + 2*i8*i7 - 4*sqr(i8) - 2*i9*i2 + 4*i9*i3 + 4*i9*i4 - 2*i9*i5
+ 2*i9*i6 + 6*i9*i7 - 6*i9*i8 - 7*sqr(i9) =G= -1140;
e6.. 2*i2*i1 - 7*sqr(i1) - 7*sqr(i2) - 6*i3*i1 - 2*i3*i2 - 6*sqr(i3) - 2*i4*i1
+ 2*i4*i2 - 2*i4*i3 - 5*sqr(i4) - 2*i5*i1 - 4*i5*i3 + 2*i5*i4 - 5*sqr(i5)
+ 2*i6*i1 - 4*i6*i2 + 4*i6*i3 + 2*i6*i4 + 6*i6*i5 - 9*sqr(i6) + 4*i7*i2
- 4*i7*i3 + 4*i7*i4 - 4*i7*i5 + 8*i7*i6 - 5*sqr(i7) + 4*i8*i1 + 8*i8*i2
+ 2*i8*i3 - 4*i8*i4 - 2*i8*i5 + 4*i8*i6 - 9*sqr(i8) - 4*i9*i1 + 2*i9*i4
+ 6*i9*i5 - 4*i9*i6 - 2*i9*i7 + 2*i9*i8 - 6*sqr(i9) =G= -940;
e7.. (-9*sqr(i1)) - 4*i2*i1 - 8*sqr(i2) + 4*i3*i1 + 2*i3*i2 - 7*sqr(i3) + 4*i4*
i1 + 4*i4*i3 - 7*sqr(i4) - 2*i5*i1 - 12*i5*i2 - 4*i5*i3 - 8*sqr(i5) - 8*i6
*i1 + 2*i6*i2 - 2*i6*i5 - 6*sqr(i6) - 4*i7*i1 - 6*i7*i2 - 2*i7*i3 + 10*i7*
i4 - 2*i7*i5 + 2*i7*i6 - 7*sqr(i7) - 2*i8*i1 + 2*i8*i2 + 2*i8*i3 + 2*i8*i4
- 6*i8*i6 - 2*i8*i7 - 6*sqr(i8) + 4*i9*i1 + 2*i9*i2 + 4*i9*i3 + 4*i9*i4
+ 2*i9*i5 - 2*i9*i6 - 8*sqr(i9) =G= -2720;
e8.. 4*i2*i1 - 7*sqr(i1) - 8*sqr(i2) + 4*i3*i1 - 8*sqr(i3) + 4*i4*i1 + 8*i4*i2
- 6*i4*i3 - 7*sqr(i4) - 2*i5*i2 + 2*i5*i4 - 5*sqr(i5) - 2*i6*i1 - 2*i6*i2
+ 4*i6*i4 - 4*i6*i5 - 7*sqr(i6) - 2*i7*i1 + 8*i7*i2 - 2*i7*i3 - 2*i7*i4
+ 6*i7*i5 + 2*i7*i6 - 7*sqr(i7) + 2*i8*i1 - 6*i8*i2 + 6*i8*i3 + 4*i8*i4
+ 2*i8*i5 - 4*i8*i6 - 6*sqr(i8) + 4*i9*i1 - 6*i9*i2 + 2*i9*i3 - 2*i9*i4
+ 2*i9*i5 + 6*i9*i6 + 2*i9*i7 - 4*i9*i8 - 6*sqr(i9) =G= -870;
e9.. 2*i2*i1 - 4*sqr(i1) - 7*sqr(i2) + 8*i3*i1 - 4*i3*i2 - 9*sqr(i3) - 2*i4*i1
- 4*i4*i2 - 2*i4*i3 - 6*sqr(i4) + 4*i5*i1 + 2*i5*i2 + 4*i5*i3 + 6*i5*i4
- 6*sqr(i5) + 4*i6*i3 - 6*i6*i4 - 7*sqr(i6) - 2*i7*i2 - 4*i7*i3 + 4*i7*i5
+ 8*i7*i6 - 7*sqr(i7) + 2*i8*i2 - 4*i8*i3 + 2*i8*i4 + 2*i8*i5 + 6*i8*i7
- 7*sqr(i8) + 4*i9*i1 + 2*i9*i2 - 10*i9*i3 + 2*i9*i5 + 2*i9*i6 - 8*i9*i8
- 6*sqr(i9) =G= -670;
e10.. -(7*sqr(i1) + 6*sqr(i2) + 24.4*i1 - 0.2*i2 + 8*sqr(i3) - 6*i3*i1 + 4*i3*
i2 + i3 + 6*sqr(i4) + 2*i4*i1 + 2*i4*i3 - 39.2*i4 + 7*sqr(i5) - 4*i5*i1
- 2*i5*i2 - 6*i5*i3 - 118.4*i5 + 4*sqr(i6) + 2*i6*i1 - 4*i6*i2 - 4*i6*i3
- 2*i6*i4 + 6*i6*i5 - 73*i6 + 6*sqr(i7) - 2*i7*i1 - 6*i7*i2 - 2*i7*i3 +
4*i7*i5 + 4*i7*i6 - 110.8*i7 + 7*sqr(i8) - 4*i8*i1 - 2*i8*i2 + 6*i8*i3 +
4*i8*i4 - 4*i8*i5 - 2*i8*i6 + 4*i8*i7 - 17.8*i8 + 8*sqr(i9) - 2*i9*i1 - 4
*i9*i2 + 4*i9*i3 + 4*i9*i4 - 4*i9*i5 - 4*i9*i6 + 8*i9*i7 + 4*i9*i8 - 29.4
*i9) + objvar =E= 0;
* set non-default bounds
i1.up = 200;
i2.up = 200;
i3.up = 200;
i4.up = 200;
i5.up = 200;
i6.up = 200;
i7.up = 200;
i8.up = 200;
i9.up = 200;
* set non-default levels
i1.l = 100;
i2.l = 100;
i3.l = 100;
i4.l = 100;
i5.l = 100;
i6.l = 100;
i7.l = 100;
i8.l = 100;
i9.l = 100;
Model m / all /;
m.limrow=0; m.limcol=0;
m.tolproj=0.0;
$if NOT '%gams.u1%' == '' $include '%gams.u1%'
$if not set MINLP $set MINLP MINLP
Solve m using %MINLP% minimizing objvar;
Last updated: 2025-08-07 Git hash: e62cedfc