文章基本信息

标题：Physics successfully implements Lagrange multiplier optimization
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作者：Sri Krishna Vadlamani ; Tianyao Patrick Xiao ; Eli Yablonovitch 等
期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：2020
卷号：117
期号：43
页码：26639-26650
DOI：10.1073/pnas.2015192117
出版社：The National Academy of Sciences of the United States of America
摘要：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.
关键词：hardware accelerators ; physical optimization ; Ising solvers