New computer methods for global optimization
New computer methods for global optimization
Numerical Optimization of Computer Models
Numerical Optimization of Computer Models
Encyclopedia of Optimization
Empirical convergence speed of inclusion functions for facility location problems
Journal of Computational and Applied Mathematics - Special issue: Scientific computing, computer arithmetic, and validated numerics (SCAN 2004)
Computers and Operations Research
Continuous location problems and Big Triangle Small Triangle: constructing better bounds
Journal of Global Optimization
The theoretical and empirical rate of convergence for geometric branch-and-bound methods
Journal of Global Optimization
Convergence analysis of Taylor models and McCormick-Taylor models
Journal of Global Optimization
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Geometric branch-and-bound methods are commonly used solution algorithms for non-convex global optimization problems in small dimensions, say for problems with up to six or ten variables, and the efficiency of these methods depends on some required lower bounds. For example, in interval branch-and-bound methods various well-known lower bounds are derived from interval inclusion functions. The aim of this work is to analyze the quality of interval inclusion functions from the theoretical point of view making use of a recently introduced and general definition of the rate of convergence in geometric branch-and-bound methods. In particular, we compare the natural interval extension, the centered form, and Baumann's inclusion function. Furthermore, our theoretical findings are justified by detailed numerical studies using the Weber problem on the plane with some negative weights as well as some standard global optimization benchmark problems.