New computer methods for global optimization
New computer methods for global optimization
Inclusion functions and global optimization 11
Mathematical Programming: Series A and B
Subdivision Direction Selection in Interval Methods for Global Optimization
SIAM Journal on Numerical Analysis
Testing Unconstrained Optimization Software
ACM Transactions on Mathematical Software (TOMS)
An Algorithm for Global Optimization using the Taylor–Bernstein Form as Inclusion Function
Journal of Global Optimization
Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)
An efficient algorithm for range computation of polynomials using the Bernstein form
Journal of Global Optimization
Journal of Global Optimization
Global optimization for the generalized polynomial sum of ratios problem
Journal of Global Optimization
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We propose an improved algorithm for unconstrained global optimization in the framework of the Moore--Skelboe algorithm of interval analysis (H. Ratschek and J. Rokne, New computer methods for global optimization, Wiley, New York, 1988). The proposed algorithm is an improvement over the one recently proposed in P.S.V. Nataraj and K. Kotecha, (J. Global Optimization, 24 (2002) 417). A novel and powerful feature of the proposed algorithm is that it uses a variety of inclusion function forms for the objective function -- the simple natural inclusion, the Taylor model (M. Berz and G. Hoffstatter, Reliable Computing, 4 (1998) 83), and the combined Taylor--Bernstein form (P.S.V. Nataraj and K. Kotecha, Reliable Computing, in press). Several improvements are also proposed for the combined Taylor--Bernstein form. The performance of the proposed algorithm is numerically tested and compared with those of existing algorithms on 11 benchmark examples. The results of the tests show the proposed algorithm to be overall considerably superior to the rest, in terms of the various performance metrics chosen for comparison.