  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 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 Entropy
Generation 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 which drive those systems
actually play the role of the corresponding Lagrange Multipliers.
