# 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

 1 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.

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

 1 2 3 4 5 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.