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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance orth_d3m6_pl

computation of the minimal orthogonality measure of a 3x6 matrix with orthonormal rows; formulation based on parametrization via Plücker coordinates

Formatsⓘ	ams gms mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	1.00000000 p1 ( gdx sol ) (infeas: 3e-16) 0.70710678 p2 ( gdx sol ) (infeas: 4e-10)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	0.19793135 (ANTIGONE) 0.19778752 (BARON) 0.04012082 (COUENNE) 0.10454148 (LINDO) 0.40000000 (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ⓘ	127
#Linear Constraintsⓘ	61
#Quadratic Constraintsⓘ	60
#Polynomial Constraintsⓘ	6
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	590
#Nonlinear Nonzeros in Jacobianⓘ	450
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	370
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	20
#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ⓘ	3
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*        127       67        1       59        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
*        590      140      450        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,x24;

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,e87
          ,e88,e89,e90,e91,e92,e93,e94,e95,e96,e97,e98,e99,e100,e101,e102,e103
          ,e104,e105,e106,e107,e108,e109,e110,e111,e112,e113,e114,e115,e116
          ,e117,e118,e119,e120,e121,e122,e123,e124,e125,e126,e127;


e1..    objvar =G= 0;

e2.. -x3*x4 + x2 =E= 0;

e3.. -x3*x6 + x5 =E= 0;

e4.. -x3*x8 + x7 =E= 0;

e5.. -x3*x10 + x9 =E= 0;

e6.. -x3*x12 + x11 =E= 0;

e7.. -x4*x6 + x13 =E= 0;

e8.. -x4*x8 + x14 =E= 0;

e9.. -x4*x10 + x15 =E= 0;

e10.. -x4*x12 + x16 =E= 0;

e11.. -x6*x8 + x17 =E= 0;

e12.. -x6*x10 + x18 =E= 0;

e13.. -x6*x12 + x19 =E= 0;

e14.. -x8*x10 + x20 =E= 0;

e15.. -x8*x12 + x21 =E= 0;

e16.. -x10*x12 + x22 =E= 0;

e17..    x3 + x4 + x6 + x8 + x10 + x12 =E= 3;

e18..    x23 - x24 =L= 0;

e19..  - x24 + x25 =L= 0;

e20..  - x24 + x26 =L= 0;

e21..  - x24 + x27 =L= 0;

e22..  - x24 + x28 =L= 0;

e23..  - x24 + x29 =L= 0;

e24..  - x24 + x30 =L= 0;

e25..  - x24 + x31 =L= 0;

e26..  - x24 + x32 =L= 0;

e27..  - x24 + x33 =L= 0;

e28..  - x24 + x34 =L= 0;

e29..  - x24 + x35 =L= 0;

e30..  - x24 + x36 =L= 0;

e31..  - x24 + x37 =L= 0;

e32..  - x24 + x38 =L= 0;

e33..  - x24 + x39 =L= 0;

e34..  - x24 + x40 =L= 0;

e35..  - x24 + x41 =L= 0;

e36..  - x24 + x42 =L= 0;

e37.. sqr(x23)*x13 + sqr(x25)*x14 + sqr(x26)*x15 + sqr(x27)*x16 + sqr(x28)*x17
       + sqr(x29)*x18 + sqr(x30)*x19 + sqr(x31)*x20 + sqr(x32)*x21 + sqr(x33)*
      x22 =E= 1;

e38.. sqr(x23)*x5 + sqr(x25)*x7 + sqr(x26)*x9 + sqr(x27)*x11 + sqr(x34)*x17 + 
      sqr(x35)*x18 + sqr(x36)*x19 + sqr(x37)*x20 + sqr(x38)*x21 + sqr(x39)*x22
       =E= 1;

e39.. sqr(x23)*x2 + sqr(x28)*x7 + sqr(x29)*x9 + sqr(x30)*x11 + sqr(x34)*x14 + 
      sqr(x35)*x15 + sqr(x36)*x16 + sqr(x40)*x20 + sqr(x41)*x21 + sqr(x42)*x22
       =E= 1;

e40.. sqr(x25)*x2 + sqr(x28)*x5 + sqr(x31)*x9 + sqr(x32)*x11 + sqr(x34)*x13 + 
      sqr(x37)*x15 + sqr(x38)*x16 + sqr(x40)*x18 + sqr(x41)*x19 + sqr(x24)*x22
       =E= 1;

e41.. sqr(x26)*x2 + sqr(x29)*x5 + sqr(x31)*x7 + sqr(x33)*x11 + sqr(x35)*x13 + 
      sqr(x37)*x14 + sqr(x39)*x16 + sqr(x40)*x17 + sqr(x42)*x19 + sqr(x24)*x21
       =E= 1;

e42.. sqr(x27)*x2 + sqr(x30)*x5 + sqr(x32)*x7 + sqr(x33)*x9 + sqr(x36)*x13 + 
      sqr(x38)*x14 + sqr(x39)*x15 + sqr(x41)*x17 + sqr(x42)*x18 + sqr(x24)*x20
       =E= 1;

e43.. x23*x31 - x25*x29 + x26*x28 =E= 0;

e44.. x23*x37 - x25*x35 + x26*x34 =E= 0;

e45.. x23*x32 - x25*x30 + x27*x28 =E= 0;

e46.. x23*x38 - x25*x36 + x27*x34 =E= 0;

e47.. x23*x33 - x26*x30 + x27*x29 =E= 0;

e48.. x23*x39 - x26*x36 + x27*x35 =E= 0;

e49.. x23*x40 - x28*x35 + x29*x34 =E= 0;

e50.. x23*x41 - x28*x36 + x30*x34 =E= 0;

e51.. x23*x42 - x29*x36 + x30*x35 =E= 0;

e52.. x25*x33 - x26*x32 + x27*x31 =E= 0;

e53.. x25*x39 - x26*x38 + x27*x37 =E= 0;

e54.. x25*x40 - x28*x37 + x31*x34 =E= 0;

e55.. x25*x41 - x28*x38 + x32*x34 =E= 0;

e56.. x24*x25 - x31*x38 + x32*x37 =E= 0;

e57.. x26*x40 - x29*x37 + x31*x35 =E= 0;

e58.. x26*x42 - x29*x39 + x33*x35 =E= 0;

e59.. x24*x26 - x31*x39 + x33*x37 =E= 0;

e60.. x27*x41 - x30*x38 + x32*x36 =E= 0;

e61.. x27*x42 - x30*x39 + x33*x36 =E= 0;

e62.. x24*x27 - x32*x39 + x33*x38 =E= 0;

e63.. x28*x33 - x29*x32 + x30*x31 =E= 0;

e64.. x28*x42 - x29*x41 + x30*x40 =E= 0;

e65.. x24*x28 - x31*x41 + x32*x40 =E= 0;

e66.. x24*x29 - x31*x42 + x33*x40 =E= 0;

e67.. x24*x30 - x32*x42 + x33*x41 =E= 0;

e68.. x34*x39 - x35*x38 + x36*x37 =E= 0;

e69.. x34*x42 - x35*x41 + x36*x40 =E= 0;

e70.. x24*x34 - x37*x41 + x38*x40 =E= 0;

e71.. x24*x35 - x37*x42 + x39*x40 =E= 0;

e72.. x24*x36 - x38*x42 + x39*x41 =E= 0;

e73.. x23*x24 - x25*x42 + x26*x41 - x27*x40 =E= 0;

e74.. x23*x24 - x25*x42 + x28*x39 - x33*x34 =E= 0;

e75.. x23*x24 + x26*x41 - x29*x38 + x32*x35 =E= 0;

e76.. x23*x24 - x27*x40 + x30*x37 - x31*x36 =E= 0;

e77.. x23*x24 + x28*x39 - x29*x38 + x30*x37 =E= 0;

e78.. x23*x24 - x31*x36 + x32*x35 - x33*x34 =E= 0;

e79.. x25*x42 - x26*x41 + x30*x37 - x31*x36 =E= 0;

e80.. x25*x42 + x27*x40 - x29*x38 + x32*x35 =E= 0;

e81.. x25*x42 - x28*x39 - x31*x36 + x32*x35 =E= 0;

e82.. x25*x42 - x29*x38 + x30*x37 + x33*x34 =E= 0;

e83.. x26*x41 - x27*x40 - x28*x39 + x33*x34 =E= 0;

e84.. x26*x41 - x28*x39 - x30*x37 + x32*x35 =E= 0;

e85.. x26*x41 - x29*x38 + x31*x36 + x33*x34 =E= 0;

e86.. x27*x40 + x28*x39 - x29*x38 + x31*x36 =E= 0;

e87.. x27*x40 - x30*x37 + x32*x35 - x33*x34 =E= 0;

e88..  - objvar + x23 =L= 0;

e89..  - objvar - x23 =L= 0;

e90..  - objvar + x25 =L= 0;

e91..  - objvar - x25 =L= 0;

e92..  - objvar + x26 =L= 0;

e93..  - objvar - x26 =L= 0;

e94..  - objvar + x27 =L= 0;

e95..  - objvar - x27 =L= 0;

e96..  - objvar + x28 =L= 0;

e97..  - objvar - x28 =L= 0;

e98..  - objvar + x29 =L= 0;

e99..  - objvar - x29 =L= 0;

e100..  - objvar + x30 =L= 0;

e101..  - objvar - x30 =L= 0;

e102..  - objvar + x31 =L= 0;

e103..  - objvar - x31 =L= 0;

e104..  - objvar + x32 =L= 0;

e105..  - objvar - x32 =L= 0;

e106..  - objvar + x33 =L= 0;

e107..  - objvar - x33 =L= 0;

e108..  - objvar + x34 =L= 0;

e109..  - objvar - x34 =L= 0;

e110..  - objvar + x35 =L= 0;

e111..  - objvar - x35 =L= 0;

e112..  - objvar + x36 =L= 0;

e113..  - objvar - x36 =L= 0;

e114..  - objvar + x37 =L= 0;

e115..  - objvar - x37 =L= 0;

e116..  - objvar + x38 =L= 0;

e117..  - objvar - x38 =L= 0;

e118..  - objvar + x39 =L= 0;

e119..  - objvar - x39 =L= 0;

e120..  - objvar + x40 =L= 0;

e121..  - objvar - x40 =L= 0;

e122..  - objvar + x41 =L= 0;

e123..  - objvar - x41 =L= 0;

e124..  - objvar + x42 =L= 0;

e125..  - objvar - x42 =L= 0;

e126..  - objvar + x24 =L= 0;

e127..  - objvar - x24 =L= 0;

* set non-default bounds
objvar.lo = 0;
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.lo = -1; x23.up = 1;
x24.up = 1;
x25.lo = -1; x25.up = 1;
x26.lo = -1; x26.up = 1;
x27.lo = -1; x27.up = 1;
x28.lo = -1; x28.up = 1;
x29.lo = -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;