Abstract
The Douglas–Rachford reflection method is a general-purpose algorithm useful for solving the feasibility problem of finding a point in the intersection of finitely many sets. In this chapter, we demonstrate that applied to a specific problem, the method can benefit from heuristics specific to said problem which exploit its special structure. In particular, we focus on the problem of protein conformation determination formulated within the framework of matrix completion, as was considered in a recent paper of the present authors.
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Notes
- 1.
When two amino acids form a peptide bond, a water molecule is formed. An amino acid residue is what remains of each amino acid after this reaction.
- 2.
RCSB Protein Data Bank: www.rcsb.org/pdb.
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Acknowledgements
The authors wish to thank Dr. Alister Page for introducing us to the bulk structure determination problem and for kindly sharing the PAN data set. The work of JMB is supported in part by the Australian Research Council. This work was performed during MKT’s candidature at the University of Newcastle where he was supported in part by an Australian Postgraduate Award.
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Borwein, J.M., Tam, M.K. (2017). Reflection Methods for Inverse Problems with Applications to Protein Conformation Determination. In: Aussel, D., Lalitha, C. (eds) Generalized Nash Equilibrium Problems, Bilevel Programming and MPEC. Forum for Interdisciplinary Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-10-4774-9_5
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