Basic HTML version of Foils prepared 15 March 1996

Foil 9 Typical Formalism for Physical Optimization

From Physical Optimization and Physical Computation CPSP713 Case studies in Computational Science -- Spring Semester 1996. by Geoffrey C. Fox
1 Minimize E = E(parameters y)
2 y can be continuous or discrete, or a mix
3 Introduce a fake temperature T and set b = 1/T
  • Often T ~ distance scale at which you look at problem
4 Probability of state y = exp(-bE)/Z where
5 As b ® ¥, minimum E (ground state) dominates
6 Find y(T) by minimizing Free Energy
7 F = E - TS = -1/b log Z
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