QPmin (version 0.5-1)

QPgen.internal.bilinear: QPgen.internal.bilinear

Description

Generates a separable bilinear problem of the form $$ \min_x \frac{1}{2} x^T G x + x^T g $$ $$ Ax \geq b $$

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.

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.

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.

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

# NOT RUN {
m <- 3
nhalves <- ceiling(log(m))
nmiss <- m - nhalves
alphas <- c(runif(nmiss), rep(0.5, nhalves))
QPgen.internal.bilinear(m, alphas)
# }