Description Usage Arguments Details Value Note Author(s) References Examples
Generates a separable bilinear problem of the form
\min_x \frac{1}{2} x^T G x + x^T g
Ax ≥q b
1 | QPgen.internal.bilinear(m, alphas)
|
m |
Integer parameter controlling the number of variables (2m) and constraints (3m) for the generated problem. |
alphas |
m positive parameters. |
The problem is an indefinite problem with 2^m local minima of which 2^n are global. Here, n is equal to the number of alphas exactly equal to 0.5. The constraints are guaranteed independent only at each solution, but not generally everywhere in the feasible region.
G |
The quadratic component of the objective function. |
g |
The linear component of the objective function |
A |
The constraints coefficient matrix. This matrix has 3m rows and 2m columns. |
b |
The vector with the lower bounds on the constraints. |
opt |
An approximate expected value at the optimum solutions. |
globals |
A list containing all of the global solutions to the problem. |
The function 'randomQP' uses 'QPgen.internal.bilinear' to construct non-separable indefinite problems. The technique used to conceal the separability of the problem also eliminates bi-linearity.
Andrea Giusto
“A new technique for generating quadratic programming test problems,” Calamai P.H., L.N. Vicente, and J.J. Judice, Mathematical Programming 61 (1993), pp. 215-231.
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