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arXiv · 2302.09992

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

Tom M. Ragonneau·Zaikun Zhang
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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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Tom M. Ragonneau, Zaikun Zhang. 2023-02-20. An Optimal Interpolation Set for Model-Based Derivative-Free Optimization Methods. https://arxiv.org/abs/2302.09992

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