Invited Session Thu.1.MA 144

Thursday, 10:30 - 12:00 h, Room: MA 144

Cluster 22: Stochastic optimization [...]

Decomposition methods for multistage stochastic programs


Chair: Vincent Guigues



Thursday, 10:30 - 10:55 h, Room: MA 144, Talk 1

Vincent Guigues
Sampling-based decomposition methods for multistage stochastic programs based on extended polyhedral risk measures

Coauthor: Werner Römisch


We define a risk-averse nonanticipative feasible policy for multistage stochastic programs and propose a methodology to implement it. The approach is based on dynamic programming equations written for a risk-averse formulation of the problem.
This formulation relies on a new class of multiperiod risk functionals called extended polyhedral risk measures. Dual representations of such risk functionals are given and used to derive conditions of coherence. In the one-period case,
conditions for convexity and consistency with second order stochastic dominance are also provided. The risk-averse dynamic programming equations are specialized considering convex combinations of one-period extended polyhedral risk measures such as spectral risk measures.
To implement the proposed policy, the approximation of the risk-averse recourse functions for stochastic linear programs is discussed. In this context, we detail a stochastic dual dynamic programming algorithm which converges to the optimal value of the risk-averse problem.



Thursday, 11:00 - 11:25 h, Room: MA 144, Talk 2

Wajdi Tekaya
Risk neutral and risk averse stochastic dual dynamic programming method

Coauthors: Joari P. Da Costa, Alexander Shapiro, Murilo P. Soares


In this talk, we discuss risk neutral and risk averse approaches to multistage linear stochastic programming problems based on the Stochastic Dual Dynamic Programming (SDDP) method. We give a general description of the algorithm and present computational studies related to planning of the Brazilian interconnected power system.



Thursday, 11:30 - 11:55 h, Room: MA 144, Talk 3

Suvrajeet Sen
Multi-stage stochastic decomposition

Coauthor: Zhihong Zhou


In this paper, we propose a statistically motivated sequential
sampling method that is applicable to multi-stage stochastic linear programs, and we refer to it as the Multi-stage Stochastic Decomposition (MSD) algorithm. As with earlier SD methods for two-stage stochastic linear programs, this approach preserves one of the most attractive features of
SD: asymptotic convergence of the solutions can be proven (with probability one) without any iteration requiring more than a small sample-size. Our asymptotic analysis shows the power of regularization in overcoming some of the assumptions (e.g., independence between stages) associated with other sample-based algorithms for multi-stage stochastic programming.


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