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Physics successfully implements Lagrange multiplier optimization

Optimization is a major part of human effort. While being mathematical, optimization is also built into physics. For example, physics has the Principle of Least Action; the Principle of Minimum Power Dissipation, also called Minimum Entropy Generation; and the Variational Principle. Physics also has...

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Autores principales: Vadlamani, Sri Krishna, Xiao, Tianyao Patrick, Yablonovitch, Eli
Formato: Online Artículo Texto
Lenguaje:English
Publicado: National Academy of Sciences 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7604416/
https://www.ncbi.nlm.nih.gov/pubmed/33046659
http://dx.doi.org/10.1073/pnas.2015192117
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author Vadlamani, Sri Krishna
Xiao, Tianyao Patrick
Yablonovitch, Eli
author_facet Vadlamani, Sri Krishna
Xiao, Tianyao Patrick
Yablonovitch, Eli
author_sort Vadlamani, Sri Krishna
collection PubMed
description Optimization is a major part of human effort. While being mathematical, optimization is also built into physics. For example, physics has the Principle of Least Action; the Principle of Minimum Power Dissipation, also called Minimum Entropy Generation; and the Variational Principle. Physics also has Physical Annealing, which, of course, preceded computational Simulated Annealing. Physics has the Adiabatic Principle, which, in its quantum form, is called Quantum Annealing. Thus, physical machines can solve the mathematical problem of optimization, including constraints. Binary constraints can be built into the physical optimization. In that case, the machines are digital in the same sense that a flip–flop is digital. A wide variety of machines have had recent success at optimizing the Ising magnetic energy. We demonstrate in this paper that almost all those machines perform optimization according to the Principle of Minimum Power Dissipation as put forth by Onsager. Further, we show that this optimization is in fact equivalent to Lagrange multiplier optimization for constrained problems. We find that the physical gain coefficients that drive those systems actually play the role of the corresponding Lagrange multipliers.
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spelling pubmed-76044162020-11-12 Physics successfully implements Lagrange multiplier optimization Vadlamani, Sri Krishna Xiao, Tianyao Patrick Yablonovitch, Eli Proc Natl Acad Sci U S A Physical Sciences Optimization is a major part of human effort. While being mathematical, optimization is also built into physics. For example, physics has the Principle of Least Action; the Principle of Minimum Power Dissipation, also called Minimum Entropy Generation; and the Variational Principle. Physics also has Physical Annealing, which, of course, preceded computational Simulated Annealing. Physics has the Adiabatic Principle, which, in its quantum form, is called Quantum Annealing. Thus, physical machines can solve the mathematical problem of optimization, including constraints. Binary constraints can be built into the physical optimization. In that case, the machines are digital in the same sense that a flip–flop is digital. A wide variety of machines have had recent success at optimizing the Ising magnetic energy. We demonstrate in this paper that almost all those machines perform optimization according to the Principle of Minimum Power Dissipation as put forth by Onsager. Further, we show that this optimization is in fact equivalent to Lagrange multiplier optimization for constrained problems. We find that the physical gain coefficients that drive those systems actually play the role of the corresponding Lagrange multipliers. National Academy of Sciences 2020-10-27 2020-10-12 /pmc/articles/PMC7604416/ /pubmed/33046659 http://dx.doi.org/10.1073/pnas.2015192117 Text en Copyright © 2020 the Author(s). Published by PNAS. https://creativecommons.org/licenses/by-nc-nd/4.0/ https://creativecommons.org/licenses/by-nc-nd/4.0/This open access article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND) (https://creativecommons.org/licenses/by-nc-nd/4.0/) .
spellingShingle Physical Sciences
Vadlamani, Sri Krishna
Xiao, Tianyao Patrick
Yablonovitch, Eli
Physics successfully implements Lagrange multiplier optimization
title Physics successfully implements Lagrange multiplier optimization
title_full Physics successfully implements Lagrange multiplier optimization
title_fullStr Physics successfully implements Lagrange multiplier optimization
title_full_unstemmed Physics successfully implements Lagrange multiplier optimization
title_short Physics successfully implements Lagrange multiplier optimization
title_sort physics successfully implements lagrange multiplier optimization
topic Physical Sciences
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7604416/
https://www.ncbi.nlm.nih.gov/pubmed/33046659
http://dx.doi.org/10.1073/pnas.2015192117
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