Invited Session Wed.1.MA 141

Wednesday, 10:30 - 12:00 h, Room: MA 141

Cluster 22: Stochastic optimization [...]

Algorithms for stochastic optimization and approximation

 

Chair: Marc C. Steinbach

 

 

Wednesday, 10:30 - 10:55 h, Room: MA 141, Talk 1

Vaclav Kozmik
Risk-averse stochastic dual dynamic programming

Coauthor: David P. Morton

 

Abstract:
We formulate a risk-averse multistage stochastic program using CVaR as the risk measure. The underlying random process is assumed to be stage-wise independent, and the stochastic dual dynamic programming (SDDP) algorithm is applied. We discuss the poor performance of the standard upper bound estimator in the risk-averse setting and provide a modified procedure, which improves the upper bound estimator. Only mild conditions and modest additional computational effort are required to apply the new upper bound estimator. The procedure allows for significant improvement in the terms of applying desirable stopping rules for the SDDP algorithm in the risk-averse setting. We give a numerical example with a simple multistage asset allocation problem using a log-normal distribution for the asset returns.

 

 

Wednesday, 11:00 - 11:25 h, Room: MA 141, Talk 2

Jens Hübner
Structure-exploiting parallel interior point method for multistage stochastic programs

Coauthor: Marc Christian Steinbach

 

Abstract:
Highly specialized and structure-exploiting solvers for the primal-dual system are essential to make interior point methods competitively applicable to multistage stochastic programs. In the underlying sequential direct approach, depth-first based recursions over the scenario tree and usage of hierarchical problem structures are the key ingredients to achieve memory-efficiency and reduce computational costs. Our parallel approach is based upon a node-distributing pre-process that applies a depth-first based splitting of the scenario tree. The node-related problem data are statically distributed among participating processes. Proper computation orders lead to little idle times and communication overhead. This way only few communication routines are
required to parallelize the sequential algorithm for distributed memory
systems without loosing its benefiting features. We use generic implementation techniques to adapt conforming data distributions to the entire IPM data. Thus, distributed memory systems can be used to solve even huge problems exceeding shared-memory capacities. Theoretical concepts and numerical results will be presented.

 

 

Wednesday, 11:30 - 11:55 h, Room: MA 141, Talk 3

Anthony Man-Cho So
Chance-constrained linear matrix inequalities with dependent perturbations: A safe tractable approximation approach

Coauthors: Sin-Shuen Cheung, Kuncheng Wang

 

Abstract:
In the formulation of optimization models, the data definining the objective functions and/or constraints are often collected via estimation or sampling, and hence are only approximations of the nominal values. One approach to incorporate data uncertainty in optimization models is through chance constrained programming. Although such an approach often leads to computationally difficult optimization problems, one of the successes is the development of so-called safe tractable approximations (STAs) of chance constrained programs. Currently, the STA approach mainly applies to problems where the data perturbations are independent. However, in some applications (e.g., portfolio optimization), the data perturbations are not independent, and so existing results cannot be applied. In this talk, we will demonstrate how tools from probability theory can be used to develop STAs of chance constrained programs with dependent data perturbations. An advantage of our approach is that the resulting STAs can be formulated as SDPs or even SOCPs, thus allowing them to be solved easily by off-the-shelf solvers. If time permits, we will also discuss some other applications of our approach.

 

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