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

Authors: Iwona Skalna, Andrzej Pownuk

Addresses: Department of Applied Computer Science, AGH University of Science and Technology, Krakow, Poland. ' Department of Mathematical Sciences, University of Texas at El Paso, Texas, El Paso, TX 79968 USA

Abstract: 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.

Keywords: global optimisation; monotonicity test; parametric linear systems; interval hull solution; structural mechanics.

DOI: 10.1504/IJRS.2009.026843

International Journal of Reliability and Safety, 2009 Vol.3 No.1/2/3, pp.235 - 245

Published online: 27 Jun 2009 *

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