A global optimisation method for computing interval hull solution for parametric linear systems

An algorithm for computing the interval solution for a parametric interval linear system is presented. The basic idea behind the research is to combine an interval global optimisation method with the Direct Method for Checking the Monotonicity (MCM) of the parametric solution. The MCM is used to perform the monotonicity test to speed up the convergence of the global optimisation. Other acceleration techniques such as subdivision direction selection rules, multisection and the midpoint test are involved as well and checked for usefulness. By using the proposed algorithm, several examples of parametric linear systems are solved. The research proves that the proposed monotonicity test is crucial for the convergence of the interval global optimisation used for computing the interval hull for parametric solution sets, whereas other accelerating techniques are not relevant. The presented algorithm can be useful for solving real-life problems concerning structure mechanics.