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Stability and characterisation conditions in negative programming
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- Journal:
- Journal of Applied Probability / Volume 17 / Issue 3 / September 1980
- Published online by Cambridge University Press:
- 14 July 2016, pp. 635-645
- Print publication:
- September 1980
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- Article
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Let F be the infinite-horizon minimal cost function, and FKS the minimal cost function for horizon s and terminal cost function K. In Section 2 we define the ‘stable domain' (the set of K for which
), determine some of its properties, and relate these to the questions of stability of the process (whether 
) and whether a given solution of the dynamic programming equation can be identified with F These ideas are developed in Sections 3 and 5 for various strengthenings and weakenings of the hypothesis of non-negative costs. In Section 5 we derive a new sufficient condition for stability and for characterisation of F.
), determine some of its properties, and relate these to the questions of stability of the process (whether 
) and whether a given solution of the dynamic programming equation can be identified with 