2018/04/05 by Pierre Carpentier, Jean‐Philippe Chancelier, Carpentier, Pierre +7
Computer Science · Decision Sciences · Economics, Econometrics and Finance · #Economic theories and models #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Risk and Portfolio Optimization
paper · pdf · doi:10.48550/arxiv.1804.01711
openalex publication_date 2018/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Multistage stochastic optimization problems are, by essence, complex as their solutions are indexed both by stages and by uncertainties. Their large scale nature makes decomposition methods appealing, like dynamic programming which is a sequential decomposition using a state variable defined at all stages. In this paper, we introduce the notion of state reduction by time blocks, that is, at stages that are not necessarily all the original stages. Then, we prove a reduced dynamic programming equation. We position our result with respect to the most well-known mathematical frameworks for dynamic programming. We illustrate our contribution by showing its potential for applied problems with two time scales.