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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)
0.64951905 p1 ( gdx sol )
(infeas: 2e-11)
Other points (infeas > 1e-08)  
Dual Bounds
0.18232633 (ANTIGONE)
0.27892712 (BARON)
0.32005563 (COUENNE)
0.12279480 (LINDO)
0.32723792 (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 of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangian Sparsity of 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: 2022-05-24 Git hash: 1198c186
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