  Tropical and idempotent analysis with their relations to the Hamilton-Jacobi
and matrix Bellman equations are discussed. Some dequantization procedures are
important in tropical and idempotent mathematics. In particular, the
Hamilton-Jacobi-Bellman equation is treated as a result of the Maslov
dequantization applied to the Schr\"{o}dinger equation. This leads to a
linearity of the Hamilton-Jacobi-Bellman equation over tropical algebras. The
correspondence principle and the superposition principle of idempotent
mathematics are formulated and examined. The matrix Bellman equation and its
applications to optimization problems on graphs are discussed. Universal
algorithms for numerical algorithms in idempotent mathematics are investigated.
In particular, an idempotent version of interval analysis is briefly discussed.
