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Complexity Analysis of the Regular Simplicial Search Method with Reflection and Shrinking Steps for Derivative-Free Optimization
Liyuan Cao, Wei Hu, Jinxin Wang
https://arxiv.org/abs/2508.16561

Complexity Analysis of the Regular Simplicial Search Method with Reflection and Shrinking Steps for Derivative-Free Optimization
Simplex-type methods, such as the well-known Nelder-Mead algorithm, are widely used in derivative-free optimization (DFO), particularly in practice. Despite their popularity, the theoretical understanding of their convergence properties has been limited, and until very recently essentially no worst-case complexity bounds were available. Recently, Cao et al. provided a sharp error bound for linear interpolation and extrapolation and derived a worst-case complexity result for a basic simplex-type…