New computer methods for global optimization
New computer methods for global optimization
One dimensional global optimization using linear lower bounds
Recent advances in global optimization
Cord-slope form of Taylor's expansion in univariate global optimization
Journal of Optimization Theory and Applications
Expansion and estimation of the range of nonlinear functions
Mathematics of Computation
C++ Toolbox for Verified Computing I: Basic Numerical Problems Theory, Algorithms, and Programs
C++ Toolbox for Verified Computing I: Basic Numerical Problems Theory, Algorithms, and Programs
On Fibonacci search method with k-Lucas numbers
Applied Mathematics and Computation
A New Inclusion Function for Optimization: Kite&mdashlThe One Dimensional Case
Journal of Global Optimization
A second-order pruning step for verified global optimization
Journal of Global Optimization
A filled function method applied to nonsmooth constrained global optimization
Journal of Computational and Applied Mathematics
A one-parameter filled function method applied to nonsmooth constrained global optimization
Computers & Mathematics with Applications
On lower bounds using additively separable terms in interval b&b
ICCSA'12 Proceedings of the 12th international conference on Computational Science and Its Applications - Volume Part III
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In this paper we introduce a pruning technique based on slopes in the context of interval branch-and-bound methods for nonsmooth global optimization. We develop the theory for a slope pruning step which can be utilized as an accelerating device similar to the monotonicity test frequently used in interval methods for smooth problems. This pruning step offers the possibility to cut away a large part of the box currently investigated by the optimization algorithm. We underline the new technique‘s efficiency by comparing two variants of a global optimization model algorithm: one equipped with the monotonicity test and one equipped with the pruning step. For this reason, we compared the required CPU time, the number of function and derivative or slope evaluations, and the necessary storage space when solving several smooth global optimization problems with the two variants. The paper concludes on the test results for several nonsmooth examples.