Interval Methods for Global Optimization<br/>

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Interval Methods for Global Optimization

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 40936 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Mahdavi Amiri, Nezameddin
Abstract:
We explain new interval methods, recently introduced in the literature, for solving unconstrained and constrained global optimization problems. The strategy is characterized by a subdivision of the argument intervals of the expression and a recomputation of the expression with these new intervals. By varying the selection and termination criteria, we explain new variants. These methods are used to solve problems with an objective function that has possibly a large number of local minima and constraints that may be nonlinear or nonconvex. We describe algorithms that return global minima and points at which the objective function is within a defined distance from the global minima. Numerical experiments based on our developed software show the efficiency and stability of the algorithms.
Keywords:
Unconstrainted Optimization ; Constrained Optimization ; Interval Method ; Moore Skelboe Algorithm

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