An Optimal Interpolation Set for Model-Based Derivative-Free Optimization Methods

2023/02/20 by Ragonneau, Tom M., Zhang, Zaikun · 1 citation
#41A10 #65K05 #90C30 #90C56 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2302.09992

Abstract

This paper demonstrates the optimality of an interpolation set employed in derivative-free trust-region methods. This set is optimal in the sense that it minimizes the constant of well-poisedness in a ball centred at the starting point. It is chosen as the default initial interpolation set by many derivative-free trust-region methods based on underdetermined quadratic interpolation, including NEWUOA, BOBYQA, LINCOA, and COBYQA. Our analysis provides a theoretical justification for this choice.

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