Function: [x, y] = verlinineqnn (A, b)

Verified nonnegative solution of a system of linear inequalities.

For a rectangular real matrix A and a matching real vector b, this function either computes a verified solution of the system of linear inequalities

A * x ≤ b, 

          x ≥ 0,

or verifies nonexistence of a solution, or yields no verified result.

Possible outputs:

• Either x is a real vector verified to satisfy both inequalities and y is a vector of NaN’s,
• or y is a real vector verified to satisfy

  A’ * y ≥ 0, 
  
             y ≥ 0, 
  
  b’ * y ≤ -1
  

  (which by Farka’s lemma implies nonexistence of a solution to the original inequalities), and x is a vector of NaN’s,

• or both x and y are NaN’s. In this case no verified result could be found.

This work was supported by the Czech Republic National Research Program “Information Society”, project 1ET400300415.

See also: linprog.

Package: interval