Idempotent superposition principle

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Maslov superposition principle

A method used in idempotent analysis and similar to the well-known superposition principle in quantum theory. Just as the basic equations of quantum mechanics are linear, the Hamilton–Jacobi equation (i.e. the basic equation in classical mechanics; cf. also Hamilton–Jacobi theory) and the Bellman equation (i.e. the basic equation for optimization problems) are linear over suitable idempotent semi-rings (cf. Idempotent semi-ring). Using this idea it is possible to generalize classical linear methods to these equations (which are non-linear in the traditional sense); it is useful, e.g., for the explicit construction of their solutions [a1], [a2].


[a1] V.P. Maslov, "New superposition principle for optimization problems" Russian Math. Surveys , 42 (1987) (In Russian)
[a2] V.N. Kolokoltsov, V.P. Maslov, "Idempotent analysis and applications" , Kluwer Acad. Publ. (1996) (In Russian)
How to Cite This Entry:
Idempotent superposition principle. G.L. Litvinov (originator), Encyclopedia of Mathematics. URL:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098