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Instance hadamard_5

Maximize determinant of 5 times 5 binary matrix
Let a(n) be the maximal determinant of a 0/1-matrix of size
n by n. Hadamard proved that a(n) ≤
2(-n) (n+1)((n+1)/2). A Hadamard matrix
attains this bound. The Hadamard conjecture states that this is the
case if and only if n+1 is 1 or 2 or a multiple of 4. The
values of a(n) for small n are known. See the on-line encyclopedia of integer
sequences for more information.

Formatsⓘ	ams gms mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	5.00000000 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	5.00000001 (ANTIGONE) 5.00000001 (BARON) 5.00000000 (COUENNE) 5.00000000 (LINDO) 5.00000000 (SCIP) 5.00000000 (SHOT)
Sourceⓘ	POLIP instance hadamard/hadamard_5
Applicationⓘ	Linear Algebra
Added to libraryⓘ	08 Dec 2018
Problem typeⓘ	MBNLP
#Variablesⓘ	26
#Binary Variablesⓘ	25
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	25
#Nonlinear Binary Variablesⓘ	25
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	max
Objective typeⓘ	linear
Objective curvatureⓘ	linear
#Nonzeros in Objectiveⓘ	1
#Nonlinear Nonzeros in Objectiveⓘ	0
#Constraintsⓘ	1
#Linear Constraintsⓘ	0
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	1
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	26
#Nonlinear Nonzeros in Jacobianⓘ	25
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	400
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	0
#Blocks in Hessian of Lagrangianⓘ	1
Minimal blocksize in Hessian of Lagrangianⓘ	25
Maximal blocksize in Hessian of Lagrangianⓘ	25
Average blocksize in Hessian of Lagrangianⓘ	25.0
#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ⓘ	0
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          1        0        1        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         26        1       25        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         26        1       25        0
*
*  Solve m using MINLP maximizing objvar;


Variables  b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17,b18,b19
          ,b20,b21,b22,b23,b24,b25,objvar;

Binary Variables  b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17
          ,b18,b19,b20,b21,b22,b23,b24,b25;

Equations  e1;


e1.. b1*b7*b13*b19*b25 - b1*b7*b13*b20*b24 + b1*b7*b15*b18*b24 - b1*b10*b12*b18
     *b24 + b5*b6*b12*b18*b24 - b5*b6*b12*b19*b23 + b1*b10*b12*b19*b23 - b1*b7*
     b15*b19*b23 + b1*b7*b14*b20*b23 - b1*b7*b14*b18*b25 + b1*b9*b12*b18*b25 - 
     b1*b9*b12*b20*b23 + b1*b9*b15*b17*b23 - b1*b10*b14*b17*b23 + b5*b6*b14*b17
     *b23 - b5*b9*b11*b17*b23 + b4*b10*b11*b17*b23 - b4*b6*b15*b17*b23 + b4*b6*
     b12*b20*b23 - b4*b6*b12*b18*b25 + b4*b6*b13*b17*b25 - b4*b6*b13*b20*b22 + 
     b4*b6*b15*b18*b22 - b4*b10*b11*b18*b22 + b5*b9*b11*b18*b22 - b5*b6*b14*b18
     *b22 + b1*b10*b14*b18*b22 - b1*b9*b15*b18*b22 + b1*b9*b13*b20*b22 - b1*b9*
     b13*b17*b25 + b1*b8*b14*b17*b25 - b1*b8*b14*b20*b22 + b1*b8*b15*b19*b22 - 
     b1*b10*b13*b19*b22 + b5*b6*b13*b19*b22 - b5*b6*b13*b17*b24 + b1*b10*b13*
     b17*b24 - b1*b8*b15*b17*b24 + b1*b8*b12*b20*b24 - b1*b8*b12*b19*b25 + b3*
     b6*b12*b19*b25 - b3*b6*b12*b20*b24 + b3*b6*b15*b17*b24 - b3*b10*b11*b17*
     b24 + b5*b8*b11*b17*b24 - b5*b8*b11*b19*b22 + b3*b10*b11*b19*b22 - b3*b6*
     b15*b19*b22 + b3*b6*b14*b20*b22 - b3*b6*b14*b17*b25 + b3*b9*b11*b17*b25 - 
     b3*b9*b11*b20*b22 + b3*b9*b15*b16*b22 - b3*b10*b14*b16*b22 + b5*b8*b14*b16
     *b22 - b5*b9*b13*b16*b22 + b4*b10*b13*b16*b22 - b4*b8*b15*b16*b22 + b4*b8*
     b11*b20*b22 - b4*b8*b11*b17*b25 + b4*b8*b12*b16*b25 - b4*b8*b12*b20*b21 + 
     b4*b8*b15*b17*b21 - b4*b10*b13*b17*b21 + b5*b9*b13*b17*b21 - b5*b8*b14*b17
     *b21 + b3*b10*b14*b17*b21 - b3*b9*b15*b17*b21 + b3*b9*b12*b20*b21 - b3*b9*
     b12*b16*b25 + b3*b7*b14*b16*b25 - b3*b7*b14*b20*b21 + b3*b7*b15*b19*b21 - 
     b3*b10*b12*b19*b21 + b5*b8*b12*b19*b21 - b5*b8*b12*b16*b24 + b3*b10*b12*
     b16*b24 - b3*b7*b15*b16*b24 + b3*b7*b11*b20*b24 - b3*b7*b11*b19*b25 + b2*
     b8*b11*b19*b25 - b2*b8*b11*b20*b24 + b2*b8*b15*b16*b24 - b2*b10*b13*b16*
     b24 + b5*b7*b13*b16*b24 - b5*b7*b13*b19*b21 + b2*b10*b13*b19*b21 - b2*b8*
     b15*b19*b21 + b2*b8*b14*b20*b21 - b2*b8*b14*b16*b25 + b2*b9*b13*b16*b25 - 
     b2*b9*b13*b20*b21 + b2*b9*b15*b18*b21 - b2*b10*b14*b18*b21 + b5*b7*b14*b18
     *b21 - b5*b9*b12*b18*b21 + b4*b10*b12*b18*b21 - b4*b7*b15*b18*b21 + b4*b7*
     b13*b20*b21 - b4*b7*b13*b16*b25 + b4*b7*b11*b18*b25 - b4*b7*b11*b20*b23 + 
     b4*b7*b15*b16*b23 - b4*b10*b12*b16*b23 + b5*b9*b12*b16*b23 - b5*b7*b14*b16
     *b23 + b2*b10*b14*b16*b23 - b2*b9*b15*b16*b23 + b2*b9*b11*b20*b23 - b2*b9*
     b11*b18*b25 + b2*b6*b14*b18*b25 - b2*b6*b14*b20*b23 + b2*b6*b15*b19*b23 - 
     b2*b10*b11*b19*b23 + b5*b7*b11*b19*b23 - b5*b7*b11*b18*b24 + b2*b10*b11*
     b18*b24 - b2*b6*b15*b18*b24 + b2*b6*b13*b20*b24 - b2*b6*b13*b19*b25
      - objvar =G= 0;

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% maximizing objvar;