Multidimensional Global Optimization Using Interval Slopes

Ronald Waweru MWANGI  Hideyuki IMAI  Yoshiharu SATO  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E86-A   No.11   pp.2836-2843
Publication Date: 2003/11/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Numerical Analysis and Optimization
convexity,  interval slopes,  monotonicity,  Newton method,  quadratic method,  

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The knowledge of a good enclosure of the range of a function over small interval regions allows us to avoid convergence of optimization algorithms to a non-global point(s). We used interval slopes f[X,x] to check for monotonicity and integrated their derivative forms g[X,x], x X by quadratic and Newton methods to obtain narrow enclosures. In order to include boundary points in the search for the optimum point(s), we expanded the initial box by a small width on each dimension. These procedures resulted in an improvement in the algorithm proposed by Hansen.