A Global Optimization Method for Solving Parametric Linear Systems Whose Input Data Are Rational Functions of Interval Parameters

An interval global optimization method combined with the Direct Method for solving parametric linear systems is used for computing a tight enclosure for the solution set of parametric linear system whose input data are non-linear functions of interval parameters. Revised affine arithmetic is used to handle the nonlinear dependencies. The Direct Method performs the monotonicity test to speed up the convergence of the global optimization. It is shown that the monotonicity test significantly increases the convergence of the global optimization method. Some illustrative examples are solved by the discussed method; the results are compared to literature data produces by other methods.