random_problem: Random squared (n x n) linear programming problems are...

In intpoint: linear programming solver by the interior point method and graphically (two dimensions)

Description

A random linear programming problem, with the form Max Z=CX subject to AX≤q b, X ≥q 0 is generated, using U(0,1) values for both the matrix A and the vectors C and b. Next, the interior point is used to solve the problem. If the number of equations (variables) is least than or equal to 5, the input problem is shown.

Usage

random_problem(n)

Arguments

n	The size of the problem (number of equations and variables)

Value

A	The coefficient matrix A
c	The coefficients of the objective function
b	The right hand side constants
z	Optimum value for the objective function
xf	Solution vector
n	Number of iterations

Author(s)

Alejandro Quintela del Rio [e-mail]

References

Gill, P.E., Murray, W. and Wright, M.H. (1991) Numerical Linear Algebra and Optimization vol. 1, Addison-Wesley.

Karmarkar, N. (1984) A new polynomial-time algorithm for linear programming. Combinatorica 4, pp. 373-395.

Vanderbei, R.J., Meketon, M.S. and Freedman, B.A. (1986) A modification of Karmarkar's linear programming algorithm. Algorithmica 1, pp. 395-407.

Examples

## generating and solving a linear programming problem with uniform (0,1)
## random values
random_problem(10)

Example output

$`The optimum value of Z is`
[1] 3.966858

$`The optimal solution X`
              [,1]
 [1,] 2.602136e-06
 [2,] 1.245861e-05
 [3,] 7.511170e-07
 [4,] 6.967498e-06
 [5,] 2.351661e+00
 [6,] 1.587935e-06
 [7,] 1.918489e+00
 [8,] 7.431164e-06
 [9,] 1.090491e+00
[10,] 1.914368e-06

$`Number of iterations`
[1] 13

intpoint documentation built on May 29, 2017, 8:59 p.m.