# MINLPLib

### A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

```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) ≤
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
 Formatsⓘ ams gms mod nl osil pip 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) 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 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: 2021-03-11 Git hash: 66559cbc