ArticleProceedings of the National Academy of Sciences of the United States of America2020
Physics successfully implements Lagrange multiplier optimization.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 14 papers.
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14 citing papers in PubMed.
- Precision meets speed through an FPGA-based natively sparse Ising machine for combinatorial optimization.Nature communications · 2026Article
- Programmable optoelectronic Ising machine for optimization of real-world problems.Light, science & applications · 2026Article
- In-situ physical adjoint computing in multiple-scattering electromagnetic environments for wave control.Nature communications · 2025Article
- Femtojoule optical nonlinearity for deep learning with incoherent illumination.Science advances · 2025Article
- Programmable wave-based analog computing machine: a metastructure that designs metastructures.Nature communications · 2025Article
- Training neural networks using physical equations of motion.Proceedings of the National Academy of Sciences of the United States of America · 2024Article
- Machine learning without a processor: Emergent learning in a nonlinear analog network.Proceedings of the National Academy of Sciences of the United States of America · 2024Article
- Efficient optimization with higher-order ising machines.Nature communications · 2023Article
- Designing Ising machines with higher order spin interactions and their application in solving combinatorial optimization.Scientific reports · 2023Article
- Bifurcation behaviors shape how continuous physical dynamics solves discrete Ising optimization.Nature communications · 2023Article
- Multidimensional hyperspin machine.Nature communications · 2022Article
- Large-scale coherent Ising machine based on optoelectronic parametric oscillator.Light, science & applications · 2022Article
- Noise-injected analog Ising machines enable ultrafast statistical sampling and machine learning.Nature communications · 2022Article
- Global minimization via classical tunneling assisted by collective force field formation.Science advances · 2021Article
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3 authors.
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Abstract
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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