Core Global Search Algorithm and Convergence Study

Abstract

The discrete global search algorithm derived in Sections 2.1–2.3 aims to produce the same solution for the problem (2.1.1) as the one juxtaposed to this problem by the uniform grid technique, but with lesser computational effort than in the item-by-item examination inherent to the grid technique. In fact, as already mentioned in Remark 2.6 at the end of Section 2.3, it may be purposeful to select substantially greater number n+1 of nodes for the grid (2.1.2) than is needed to ensure the required accuracy. Moreover, the requirements for the desired accuracy may happen to increase in the search process, and it may be quite reasonable to substantially increase the number of nodes in advance, aiming to cut the necessity for readjustment of the grid which otherwise may arise in the course of minimization. To completely resolve this problem, we develop the ‘limit algorithm’ for the problem (2.1.1) by transforming the above discrete algorithm with n → ∞. These transformations are convenient to carry out in the following way.