QPgen.internal.bilinear: QPgen.internal.bilinear

In QPmin: Linearly Constrained Indefinite Quadratic Program Solver

Description

Generates a separable bilinear problem of the form

\min_x \frac{1}{2} x^T G x + x^T g

Ax ≥q b

Usage

QPgen.internal.bilinear(m, alphas)

Arguments

m	Integer parameter controlling the number of variables (2m) and constraints (3m) for the generated problem.
alphas	m positive parameters.

Details

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.

Value

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.

Note

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.

Author(s)

Andrea Giusto

References

“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.

Examples

m <- 3
nhalves <- ceiling(log(m))
nmiss <- m - nhalves
alphas <- c(runif(nmiss), rep(0.5, nhalves))
QPgen.internal.bilinear(m, alphas)

QPmin documentation built on April 15, 2021, 5:06 p.m.