Max-plus algebra and mathematical fear in dynamic optimization
The reviewed paper is devoted to the max-plus algebra, a special case of Maslov's idempotent algebras, consisting of the set \(\overline R = R \cup \{ -\infty \}\) endowed with the operations \(\max\) and \(+\). Basic notions of the max-plus algebra and the corresponding linear algebra are presented. Its applications for solving a production scheduling problem as well as for discrete dynamic programming are illustrated. Interrelations between cost and probability measures are shown and the notion of Mathematical Fear -- an analogue of expectation -- are introduced and analyzed. Some applications for design and control in the imperfect information case are outlined.
scientific article; zbMATH DE number 1523576