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Instance hadamard_9
Maximize determinant of 9 times 9 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ⓘ | 116413.00000000 (BARON) 161274.69180000 (SCIP) |
| Sourceⓘ | POLIP instance hadamard/hadamard_9 |
| Applicationⓘ | Linear Algebra |
| Added to libraryⓘ | 08 Dec 2018 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 82 |
| #Binary Variablesⓘ | 81 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 81 |
| #Nonlinear Binary Variablesⓘ | 81 |
| #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ⓘ | 82 |
| #Nonlinear Nonzeros in Jacobianⓘ | 81 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 5184 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 0 |
| #Blocks in Hessian of Lagrangianⓘ | 1 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 81 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 81 |
| Average blocksize in Hessian of Lagrangianⓘ | 81.0 |
| #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ⓘ |  |