MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance orth_d4m6_pl
computation of the minimal orthogonality measure of a 4x6 matrix with orthonormal rows; formulation based on parametrization via Plücker coordinates
| Formatsⓘ | ams gms mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 0.18232633 (ANTIGONE) 0.27892712 (BARON) 0.32005563 (COUENNE) 0.64951803 (GUROBI) 0.12279480 (LINDO) 0.32775872 (SCIP) |
| Sourceⓘ | Matthias Schymura |
| Applicationⓘ | Geometry |
| Added to libraryⓘ | 11 Sep 2017 |
| Problem typeⓘ | NLP |
| #Variablesⓘ | 42 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 41 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 1 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 86 |
| #Linear Constraintsⓘ | 45 |
| #Quadratic Constraintsⓘ | 15 |
| #Polynomial Constraintsⓘ | 26 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 384 |
| #Nonlinear Nonzeros in Jacobianⓘ | 270 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 255 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 15 |
| #Blocks in Hessian of Lagrangianⓘ | 2 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 6 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 35 |
| Average blocksize in Hessian of Lagrangianⓘ | 20.5 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e+00 |
| Maximal coefficientⓘ | 1.0000e+00 |
| Infeasibility of initial pointⓘ | 4 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 86 42 0 44 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 42 42 0 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 384 114 270 0
*
* Solve m using NLP minimizing objvar;
Variables objvar,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;
Positive Variables 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,x29;
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,e62,e63,e64,e65,e66,e67,e68,e69,e70
,e71,e72,e73,e74,e75,e76,e77,e78,e79,e80,e81,e82,e83,e84,e85,e86;
e1.. -x2*x3*x4 + x5 =E= 0;
e2.. -x2*x3*x6 + x7 =E= 0;
e3.. -x2*x3*x8 + x9 =E= 0;
e4.. -x2*x3*x10 + x11 =E= 0;
e5.. -x2*x4*x6 + x12 =E= 0;
e6.. -x2*x4*x8 + x13 =E= 0;
e7.. -x2*x4*x10 + x14 =E= 0;
e8.. -x2*x6*x8 + x15 =E= 0;
e9.. -x2*x6*x10 + x16 =E= 0;
e10.. -x2*x8*x10 + x17 =E= 0;
e11.. -x3*x4*x6 + x18 =E= 0;
e12.. -x3*x4*x8 + x19 =E= 0;
e13.. -x3*x4*x10 + x20 =E= 0;
e14.. -x3*x6*x8 + x21 =E= 0;
e15.. -x3*x6*x10 + x22 =E= 0;
e16.. -x3*x8*x10 + x23 =E= 0;
e17.. -x4*x6*x8 + x24 =E= 0;
e18.. -x4*x6*x10 + x25 =E= 0;
e19.. -x4*x8*x10 + x26 =E= 0;
e20.. -x6*x8*x10 + x27 =E= 0;
e21.. x2 + x3 + x4 + x6 + x8 + x10 =E= 4;
e22.. x28 - x29 =L= 0;
e23.. - x29 + x30 =L= 0;
e24.. - x29 + x31 =L= 0;
e25.. - x29 + x32 =L= 0;
e26.. - x29 + x33 =L= 0;
e27.. - x29 + x34 =L= 0;
e28.. - x29 + x35 =L= 0;
e29.. - x29 + x36 =L= 0;
e30.. - x29 + x37 =L= 0;
e31.. - x29 + x38 =L= 0;
e32.. - x29 + x39 =L= 0;
e33.. - x29 + x40 =L= 0;
e34.. - x29 + x41 =L= 0;
e35.. - x29 + x42 =L= 0;
e36.. sqr(x28)*x18 + sqr(x30)*x19 + sqr(x31)*x20 + sqr(x32)*x21 + sqr(x33)*x22
+ sqr(x34)*x23 + sqr(x35)*x24 + sqr(x36)*x25 + sqr(x37)*x26 + sqr(x38)*
x27 =E= 1;
e37.. sqr(x28)*x12 + sqr(x30)*x13 + sqr(x31)*x14 + sqr(x32)*x15 + sqr(x33)*x16
+ sqr(x34)*x17 + sqr(x39)*x24 + sqr(x40)*x25 + sqr(x41)*x26 + sqr(x42)*
x27 =E= 1;
e38.. sqr(x28)*x7 + sqr(x30)*x9 + sqr(x31)*x11 + sqr(x35)*x15 + sqr(x36)*x16 +
sqr(x37)*x17 + sqr(x39)*x21 + sqr(x40)*x22 + sqr(x41)*x23 + sqr(x29)*x27
=E= 1;
e39.. sqr(x28)*x5 + sqr(x32)*x9 + sqr(x33)*x11 + sqr(x35)*x13 + sqr(x36)*x14 +
sqr(x38)*x17 + sqr(x39)*x19 + sqr(x40)*x20 + sqr(x42)*x23 + sqr(x29)*x26
=E= 1;
e40.. sqr(x30)*x5 + sqr(x32)*x7 + sqr(x34)*x11 + sqr(x35)*x12 + sqr(x37)*x14 +
sqr(x38)*x16 + sqr(x39)*x18 + sqr(x41)*x20 + sqr(x42)*x22 + sqr(x29)*x25
=E= 1;
e41.. sqr(x31)*x5 + sqr(x33)*x7 + sqr(x34)*x9 + sqr(x36)*x12 + sqr(x37)*x13 +
sqr(x38)*x15 + sqr(x40)*x18 + sqr(x41)*x19 + sqr(x42)*x21 + sqr(x29)*x24
=E= 1;
e42.. x28*x34 - x30*x33 + x31*x32 =E= 0;
e43.. x28*x37 - x30*x36 + x31*x35 =E= 0;
e44.. x28*x41 - x30*x40 + x31*x39 =E= 0;
e45.. x28*x38 - x32*x36 + x33*x35 =E= 0;
e46.. x28*x42 - x32*x40 + x33*x39 =E= 0;
e47.. x28*x29 - x35*x40 + x36*x39 =E= 0;
e48.. x30*x38 - x32*x37 + x34*x35 =E= 0;
e49.. x30*x42 - x32*x41 + x34*x39 =E= 0;
e50.. x29*x30 - x35*x41 + x37*x39 =E= 0;
e51.. x31*x38 - x33*x37 + x34*x36 =E= 0;
e52.. x31*x42 - x33*x41 + x34*x40 =E= 0;
e53.. x29*x31 - x36*x41 + x37*x40 =E= 0;
e54.. x29*x32 - x35*x42 + x38*x39 =E= 0;
e55.. x29*x33 - x36*x42 + x38*x40 =E= 0;
e56.. x29*x34 - x37*x42 + x38*x41 =E= 0;
e57.. - objvar - x28 =L= 0;
e58.. - objvar + x28 =L= 0;
e59.. - objvar - x30 =L= 0;
e60.. - objvar + x30 =L= 0;
e61.. - objvar - x31 =L= 0;
e62.. - objvar + x31 =L= 0;
e63.. - objvar - x32 =L= 0;
e64.. - objvar + x32 =L= 0;
e65.. - objvar - x33 =L= 0;
e66.. - objvar + x33 =L= 0;
e67.. - objvar - x34 =L= 0;
e68.. - objvar + x34 =L= 0;
e69.. - objvar - x35 =L= 0;
e70.. - objvar + x35 =L= 0;
e71.. - objvar - x36 =L= 0;
e72.. - objvar + x36 =L= 0;
e73.. - objvar - x37 =L= 0;
e74.. - objvar + x37 =L= 0;
e75.. - objvar - x38 =L= 0;
e76.. - objvar + x38 =L= 0;
e77.. - objvar - x39 =L= 0;
e78.. - objvar + x39 =L= 0;
e79.. - objvar - x40 =L= 0;
e80.. - objvar + x40 =L= 0;
e81.. - objvar - x41 =L= 0;
e82.. - objvar + x41 =L= 0;
e83.. - objvar - x42 =L= 0;
e84.. - objvar + x42 =L= 0;
e85.. - objvar - x29 =L= 0;
e86.. - objvar + x29 =L= 0;
* set non-default bounds
objvar.lo = 0; objvar.up = 1;
x2.up = 1;
x3.up = 1;
x4.up = 1;
x5.up = 1;
x6.up = 1;
x7.up = 1;
x8.up = 1;
x9.up = 1;
x10.up = 1;
x11.up = 1;
x12.up = 1;
x13.up = 1;
x14.up = 1;
x15.up = 1;
x16.up = 1;
x17.up = 1;
x18.up = 1;
x19.up = 1;
x20.up = 1;
x21.up = 1;
x22.up = 1;
x23.up = 1;
x24.up = 1;
x25.up = 1;
x26.up = 1;
x27.up = 1;
x28.lo = -1; x28.up = 1;
x29.up = 1;
x30.lo = -1; x30.up = 1;
x31.lo = -1; x31.up = 1;
x32.lo = -1; x32.up = 1;
x33.lo = -1; x33.up = 1;
x34.lo = -1; x34.up = 1;
x35.lo = -1; x35.up = 1;
x36.lo = -1; x36.up = 1;
x37.lo = -1; x37.up = 1;
x38.lo = -1; x38.up = 1;
x39.lo = -1; x39.up = 1;
x40.lo = -1; x40.up = 1;
x41.lo = -1; x41.up = 1;
x42.lo = -1; x42.up = 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