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

 

Abstract:
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

 

Abstract:
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

 

Abstract:
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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