Contraction methods for continuous optimization
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We describe a class of algorithms that establishes a contracting sequence of closed sets for solving continuous optimization. From the perspective of ensuring effective contractions to achieve a certain accuracy, all the possible continuous optimization problems could be divided into three categories: logarithmic time contractile, polynomial time contractile, or noncontractile. For any problem from the first two categories, the constructed contracting sequence converges to the set of all global minimizers with a theoretical guarantee of linear convergence; for any problem from the last category, we also discuss possible troubles caused by using the proposed algorithms.
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