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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)ⓘ | |
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;
Last updated: 2024-11-25 Git hash: de62f3e5