2021
DOI: 10.48550/arxiv.2109.01865
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Nonmonotone local minimax methods for finding multiple saddle points

Abstract: In this paper, combining normalized nonmonotone search strategies with the Barzilai-Borwein-type step-size, a novel local minimax method (LMM), which is globally convergent, is proposed to find multiple (unstable) saddle points of nonconvex functionals in Hilbert spaces. Compared to traditional LMMs, this approach does not require the strict decrease of the objective functional value at each iterative step. Firstly, by introducing two kinds of normalized nonmonotone step-size search strategies to replace norma… Show more

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