Contractility of continuous optimization

09/03/2019 ∙ by Xiaopeng Luo, et al. ∙ 0

By introducing the concept of contractility, all the possible continuous optimization problems are divided into three categories: logarithmic time contractile, polynomial time contractile, or noncontractile. For the first two, we propose an efficient contraction algorithm to find the set of all global minimizers with a theoretical guarantee of linear convergence; for the last one, we discuss possible troubles caused by using the proposed algorithm.

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