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Double descent and intermittent color diffusion for landscape exploration

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Abstract

In this work, we present a method to explore the landscape of a smooth potential in the search of global minimizers, combining a double-descent technique and a basin-escaping technique based on intermittent colored diffusion. Numerical results illustrate the performance of the method.

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Notes

  1. As an example, consider the function g1(x, y) = (x2y − x − 1)2 + (x2 − 1)2: it has two local minima at (1,2) and (− 1, 0), and no other critical point.

  2. Recall \(g:{\mathbb {R}}^{n}\rightarrow {\mathbb {R}}\)is coercive if \(\lim _{\|x\|\rightarrow \infty } g(x)= +\infty \), that is, for any constant M, there is a constant RM such that ∥g(x)∥ > M whenever ∥x∥ > RM.

  3. The same point can thus appear multiple times in the table.

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Funding

Manuela Manetta and Haomin Zhou’s work was supported under NSF Awards DMS-1419027, DMS-1620345 and ONR Award N000141310408.

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Authors and Affiliations

  1. School of Mathematics, Georgia Institute of Technology, Atlanta, USA

    Luca Dieci & Haomin Zhou

  2. Department of Mathematics, Emory University, Atlanta, USA

    Manuela Manetta

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  1. Luca Dieci
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  2. Manuela Manetta
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  3. Haomin Zhou
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Correspondence to Manuela Manetta.

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Dieci, L., Manetta, M. & Zhou, H. Double descent and intermittent color diffusion for landscape exploration. Numer Algor 85, 145–169 (2020). https://doi.org/10.1007/s11075-019-00807-6

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