MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance eq6_1
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 117.71712150 (ANTIGONE) 138.18320100 (BARON) 194.58290990 (COUENNE) 670.69402930 (GUROBI) -134.11040970 (LINDO) 282.51945160 (SCIP) |
| Sourceⓘ | AIMMS clients |
| Added to libraryⓘ | 06 Feb 2017 |
| Problem typeⓘ | NLP |
| #Variablesⓘ | 16 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 16 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | quadratic |
| Objective curvatureⓘ | convex |
| #Nonzeros in Objectiveⓘ | 16 |
| #Nonlinear Nonzeros in Objectiveⓘ | 16 |
| #Constraintsⓘ | 60 |
| #Linear Constraintsⓘ | 32 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 28 |
| Operands in Gen. Nonlin. Functionsⓘ | sqr sqrt |
| Constraints curvatureⓘ | nonconvex |
| #Nonzeros in Jacobianⓘ | 144 |
| #Nonlinear Nonzeros in Jacobianⓘ | 112 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 256 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 16 |
| #Blocks in Hessian of Lagrangianⓘ | 1 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 16 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 16 |
| Average blocksize in Hessian of Lagrangianⓘ | 16.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e+00 |
| Maximal coefficientⓘ | 3.2000e+01 |
| Infeasibility of initial pointⓘ | 2.995 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 61 1 0 60 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 17 17 0 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 161 33 128 0
*
* Solve m using NLP minimizing objvar;
Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,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,e32,e33,e34,e35,e36
,e37,e38,e39,e40,e41,e42,e43,e44,e45,e46,e47,e48,e49,e50,e51,e52,e53
,e54,e55,e56,e57,e58,e59,e60,e61;
e1.. -sqrt(sqr(x1 - x2) + sqr(x9 - x10)) =L= -2.995353;
e2.. -sqrt(sqr(x1 - x3) + sqr(x9 - x11)) =L= -2.532248;
e3.. -sqrt(sqr(x1 - x4) + sqr(x9 - x12)) =L= -2.638959;
e4.. -sqrt(sqr(x1 - x5) + sqr(x9 - x13)) =L= -2.638959;
e5.. -sqrt(sqr(x1 - x6) + sqr(x9 - x14)) =L= -2.121321;
e6.. -sqrt(sqr(x1 - x7) + sqr(x9 - x15)) =L= -1.914214;
e7.. -sqrt(sqr(x1 - x8) + sqr(x9 - x16)) =L= -2.828428;
e8.. -sqrt(sqr(x2 - x3) + sqr(x10 - x11)) =L= -2.699173;
e9.. -sqrt(sqr(x2 - x4) + sqr(x10 - x12)) =L= -2.805884;
e10.. -sqrt(sqr(x2 - x5) + sqr(x10 - x13)) =L= -2.805884;
e11.. -sqrt(sqr(x2 - x6) + sqr(x10 - x14)) =L= -2.288246;
e12.. -sqrt(sqr(x2 - x7) + sqr(x10 - x15)) =L= -2.081139;
e13.. -sqrt(sqr(x2 - x8) + sqr(x10 - x16)) =L= -2.995353;
e14.. -sqrt(sqr(x3 - x4) + sqr(x11 - x12)) =L= -2.342779;
e15.. -sqrt(sqr(x3 - x5) + sqr(x11 - x13)) =L= -2.342779;
e16.. -sqrt(sqr(x3 - x6) + sqr(x11 - x14)) =L= -1.825141;
e17.. -sqrt(sqr(x3 - x7) + sqr(x11 - x15)) =L= -1.618034;
e18.. -sqrt(sqr(x3 - x8) + sqr(x11 - x16)) =L= -2.532248;
e19.. -sqrt(sqr(x4 - x5) + sqr(x12 - x13)) =L= -2.44949;
e20.. -sqrt(sqr(x4 - x6) + sqr(x12 - x14)) =L= -1.931852;
e21.. -sqrt(sqr(x4 - x7) + sqr(x12 - x15)) =L= -1.724745;
e22.. -sqrt(sqr(x4 - x8) + sqr(x12 - x16)) =L= -2.638959;
e23.. -sqrt(sqr(x5 - x6) + sqr(x13 - x14)) =L= -1.931852;
e24.. -sqrt(sqr(x5 - x7) + sqr(x13 - x15)) =L= -1.724745;
e25.. -sqrt(sqr(x5 - x8) + sqr(x13 - x16)) =L= -2.638959;
e26.. -sqrt(sqr(x6 - x7) + sqr(x14 - x15)) =L= -1.207107;
e27.. -sqrt(sqr(x6 - x8) + sqr(x14 - x16)) =L= -2.121321;
e28.. -sqrt(sqr(x7 - x8) + sqr(x15 - x16)) =L= -1.914214;
e29.. - x1 =L= 1.210786;
e30.. - x2 =L= 1.043861;
e31.. - x3 =L= 1.506966;
e32.. - x4 =L= 1.400255;
e33.. - x5 =L= 1.400255;
e34.. - x6 =L= 1.917893;
e35.. - x7 =L= 2.125;
e36.. - x8 =L= 1.210786;
e37.. x1 =L= 1.210786;
e38.. x2 =L= 1.043861;
e39.. x3 =L= 1.506966;
e40.. x4 =L= 1.400255;
e41.. x5 =L= 1.400255;
e42.. x6 =L= 1.917893;
e43.. x7 =L= 2.125;
e44.. x8 =L= 1.210786;
e45.. - x9 =L= 3.710786;
e46.. - x10 =L= 3.543861;
e47.. - x11 =L= 4.006966;
e48.. - x12 =L= 3.900255;
e49.. - x13 =L= 3.900255;
e50.. - x14 =L= 4.417893;
e51.. - x15 =L= 4.625;
e52.. - x16 =L= 3.710786;
e53.. x9 =L= 3.710786;
e54.. x10 =L= 3.543861;
e55.. x11 =L= 4.006966;
e56.. x12 =L= 3.900255;
e57.. x13 =L= 3.900255;
e58.. x14 =L= 4.417893;
e59.. x15 =L= 4.625;
e60.. x16 =L= 3.710786;
e61.. 10*x2*x1 - 18*sqr(x1) - 14*sqr(x2) - 18*sqr(x9) + 10*x10*x9 - 14*sqr(x10)
+ 4*x3*x1 + 6*x3*x2 - 10*sqr(x3) + 4*x11*x9 + 6*x11*x10 - 10*sqr(x11) +
8*x4*x1 - 23*sqr(x4) + 8*x12*x9 - 23*sqr(x12) + 2*x5*x1 + 4*x5*x2 + 10*x5
*x4 - 18*sqr(x5) + 2*x13*x9 + 4*x13*x10 + 10*x13*x12 - 18*sqr(x13) + 4*x6
*x2 + 4*x6*x4 + 20*x6*x5 - 20*sqr(x6) + 4*x14*x10 + 4*x14*x12 + 20*x14*
x13 - 20*sqr(x14) + 12*x8*x1 + 10*x8*x3 + 20*x8*x4 + 2*x8*x6 - 32*sqr(x8)
+ 12*x16*x9 + 10*x16*x11 + 20*x16*x12 + 2*x16*x14 - 32*sqr(x16) + 4*x7*
x2 + 4*x7*x4 + 10*x7*x6 + 20*x7*x8 - 19*sqr(x7) + 4*x15*x10 + 4*x15*x12
+ 10*x15*x14 + 20*x15*x16 - 19*sqr(x15) + objvar =E= 0;
* set non-default bounds
x1.lo = -18.999999; x1.up = 18.999999;
x2.lo = -18.999999; x2.up = 18.999999;
x3.lo = -18.999999; x3.up = 18.999999;
x4.lo = -18.999999; x4.up = 18.999999;
x5.lo = -18.999999; x5.up = 18.999999;
x6.lo = -18.999999; x6.up = 18.999999;
x7.lo = -18.999999; x7.up = 18.999999;
x8.lo = -18.999999; x8.up = 18.999999;
x9.lo = -18.999999; x9.up = 18.999999;
x10.lo = -18.999999; x10.up = 18.999999;
x11.lo = -18.999999; x11.up = 18.999999;
x12.lo = -18.999999; x12.up = 18.999999;
x13.lo = -18.999999; x13.up = 18.999999;
x14.lo = -18.999999; x14.up = 18.999999;
x15.lo = -18.999999; x15.up = 18.999999;
x16.lo = -18.999999; x16.up = 18.999999;
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