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Instance hadamard_4

Maximize determinant of 4 times 4 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)ⓘ	3.00000000 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	3.00000000 (ANTIGONE) 3.00000001 (BARON) 3.00000000 (COUENNE) 3.00000000 (LINDO) 3.00000000 (SCIP) 3.00000000 (SHOT)
Sourceⓘ	POLIP instance hadamard/hadamard_4
Applicationⓘ	Linear Algebra
Added to libraryⓘ	08 Dec 2018
Problem typeⓘ	MBNLP
#Variablesⓘ	17
#Binary Variablesⓘ	16
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	16
#Nonlinear Binary Variablesⓘ	16
#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ⓘ	17
#Nonlinear Nonzeros in Jacobianⓘ	16
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	144
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	0
#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ⓘ	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
*         17        1       16        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         17        1       16        0
*
*  Solve m using MINLP maximizing objvar;


Variables  b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,objvar;

Binary Variables  b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16;

Equations  e1;


e1.. b1*b6*b11*b16 - b1*b6*b12*b15 + b1*b8*b10*b15 - b4*b5*b10*b15 + b4*b5*b11*
     b14 - b1*b8*b11*b14 + b1*b7*b12*b14 - b1*b7*b10*b16 + b3*b5*b10*b16 - b3*
     b5*b12*b14 + b3*b8*b9*b14 - b4*b7*b9*b14 + b4*b7*b10*b13 - b3*b8*b10*b13
      + b3*b6*b12*b13 - b3*b6*b9*b16 + b2*b7*b9*b16 - b2*b7*b12*b13 + b2*b8*b11
     *b13 - b4*b6*b11*b13 + b4*b6*b9*b15 - b2*b8*b9*b15 + b2*b5*b12*b15 - b2*b5
     *b11*b16 - 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;