We present a new complexity result on solving the Markov decision problem (MDP) with $n$ states and a number of actions for each state, a special class of real-number linear programs with the Leontief matrix structure. We prove that, when the discount factor $\theta$ is strictly less than $1$, the problem can be solved in … Read more
We present a general aggregation method applicable to all finite-horizon Markov decision problems. States of the MDP are aggregated into macro-states based on a pre-selected collection of “distinguished” states which serve as entry points into macro-states. The resulting macro-problem is also an MDP, whose solution approximates an optimal solution to the original problem. The aggregation … Read more
We introduce an axiomatic definition of a conditional convex risk mapping and we derive its properties. In particular, we prove a representation theorem for conditional risk mappings in terms of conditional expectations. We also develop dynamic programming relations for multistage optimization problems involving conditional risk mappings. CitationPreprintArticleDownload View PDF
Scheduling a sequence of tasks – in the acceptation of finding the execution times – is not a trivial problem when the optimization criterion is irregular as for instance in earliness-tardiness problems. This paper presents an efficient Dynamic Programming algorithm to solve the problem with general cost functions depending on the end time of the … Read more
A dynamic optimization continuous problem poses the question of what is the optimal magnitude of a choice variable, at each point of time, in a given interval. To tackle such problems, three major approaches are available: dynamic programming; the calculus of variations; and the powerful optimal control approach. At the core of optimal control theory … Read more
In chemical engineering complex dynamic optimization problems formulated on moving horizons have to be solved on-line. In this work, we present a multiscale approach based on wavelets where a hierarchy of successively, adaptively refined problems are constructed.They are solved in the framework of nested iteration as long as the real-time restrictions are fulfilled. To avoid … Read more