On Distributionally Robust Multistage Convex Optimization: New Algorithms and Complexity Analysis

Abstract

This paper presents an algorithmic study and complexity analysis for solving distributionally robust multistage convex optimization (DR-MCO) problems. Our main contribution is a novel nonconsecutive dual dynamic programming (NDDP) algorithm which explores different stages in an adaptive fashion. In contrast with the usual consecutive dual dynamic programming (CDDP) algorithm, we show that NDDP reduces the subproblem complexity from quadratic to linear dependency on the number of stages. Two different DR-MCO examples are also presented to show the efficiency and effectiveness of the proposed NDDP algorithm.

This version contains newly added comparisons with recent complexity results and an appendix on specializations of the proposed DR-MCO framework, besides some typographical fixes and minor clarifications. To be published in SIAM Journal on Optimization