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Foil 29 Physical Optimization Formulation of Navigation Problems

From Physical Optimization and Physical Computation CPSP713 Case studies in Computational Science -- Spring Semester 1996. by Geoffrey C. Fox
New effect: >1 (2 in fact) Lagrange multipliers
exp[-b1 E1 -b2 E2] bi = bi(T)
In this problem, goal (E1) easy to satisfy but constraints (E2) hard
At high temperatures make E2 go away
  • b2/b1 ® 0 as T ® ¥ implies that E1 = 0
(elastic string of zero length) is global minimum
Decrease temperature and gradually "switch on" constraint such that as T-> 0, constraint is rigorously enforced
    • Choose b2/b1 ® ¥ as T ® 0
e.g. b1 = 1/T b2 = 1/T2

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