QPgen.internal.convex: QPgen.internal.convex

In QPmin: Linearly Constrained Indefinite Quadratic Program Solver

Description

Generates a separable convex quadratic problem of the form

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

Ax ≥q b

Usage

QPgen.internal.convex(m, alphas, rhos, omegas)

Arguments

m	Integer parameter controlling the number of variables (2m) and constraints (3m) for the generated problem.
alphas	m parameters taking values between 5 and 7.5.
rhos	m parameters taking values in {0, 1}.
omegas	m parameters taking values in {0, 1}.

Details

The problem has a unique global minimum and the constraints are linearly independent at all of the solutions.

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.convex' to construct non-separable convex problems.

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
alphas <-  runif(m, min = 5, max = 7.4999)
rhos <- round(runif(m))
omegas <- round(runif(m))
QPgen.internal.convex(m, alphas, rhos, omegas)

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