scholarly journals Mixed Spatial and Temporal Decompositions for Large-Scale Multistage Stochastic Optimization Problems

2020 ◽  
Vol 186 (3) ◽  
pp. 985-1005
Author(s):  
Pierre Carpentier ◽  
Jean-Philippe Chancelier ◽  
Michel De Lara ◽  
François Pacaud
Keyword(s):  
Stochastic Optimization ◽  
Large Scale ◽  
Optimization Problems ◽  
Multistage Stochastic Optimization

scholarly journals Data Pooling in Stochastic Optimization

2021 ◽  
Author(s):  
Vishal Gupta ◽  
Nathan Kallus
Keyword(s):  
Stochastic Optimization ◽  
Inventory Management ◽  
Large Scale ◽  
Optimization Problems ◽  
Lot Sizing ◽  
A Priori ◽  
Real Data ◽  
Data Pooling ◽  
Combining Data ◽  
A Chain

Managing large-scale systems often involves simultaneously solving thousands of unrelated stochastic optimization problems, each with limited data. Intuition suggests that one can decouple these unrelated problems and solve them separately without loss of generality. We propose a novel data-pooling algorithm called Shrunken-SAA that disproves this intuition. In particular, we prove that combining data across problems can outperform decoupling, even when there is no a priori structure linking the problems and data are drawn independently. Our approach does not require strong distributional assumptions and applies to constrained, possibly nonconvex, nonsmooth optimization problems such as vehicle-routing, economic lot-sizing, or facility location. We compare and contrast our results to a similar phenomenon in statistics (Stein’s phenomenon), highlighting unique features that arise in the optimization setting that are not present in estimation. We further prove that, as the number of problems grows large, Shrunken-SAA learns if pooling can improve upon decoupling and the optimal amount to pool, even if the average amount of data per problem is fixed and bounded. Importantly, we highlight a simple intuition based on stability that highlights when and why data pooling offers a benefit, elucidating this perhaps surprising phenomenon. This intuition further suggests that data pooling offers the most benefits when there are many problems, each of which has a small amount of relevant data. Finally, we demonstrate the practical benefits of data pooling using real data from a chain of retail drug stores in the context of inventory management. This paper was accepted by Chung Piaw Teo, Special Issue on Data-Driven Prescriptive Analytics.

scholarly journals Multiscale stochastic optimization: modeling aspects and scenario generation

2019 ◽  
Vol 75 (1) ◽  
pp. 1-34 ◽  
Author(s):  
Martin Glanzer ◽  
Georg Ch. Pflug
Keyword(s):  
Stochastic Optimization ◽  
Real World ◽  
Optimization Problems ◽  
Decision Problems ◽  
Scenario Generation ◽  
Stochastic Evolution ◽  
Modeling Framework ◽  
Uncertainty Factors ◽  
Multistage Stochastic Optimization ◽  
Computational Solution

Abstract Real-world multistage stochastic optimization problems are often characterized by the fact that the decision maker may take actions only at specific points in time, even if relevant data can be observed much more frequently. In such a case there are not only multiple decision stages present but also several observation periods between consecutive decisions, where profits/costs occur contingent on the stochastic evolution of some uncertainty factors. We refer to such multistage decision problems with encapsulated multiperiod random costs, as multiscale stochastic optimization problems. In this article, we present a tailor-made modeling framework for such problems, which allows for a computational solution. We first establish new results related to the generation of scenario lattices and then incorporate the multiscale feature by leveraging the theory of stochastic bridge processes. All necessary ingredients to our proposed modeling framework are elaborated explicitly for various popular examples, including both diffusion and jump models.

scholarly journals Distributed Stochastic Optimization with Large Delays

2021 ◽  
Author(s):  
Zhengyuan Zhou ◽  
Panayotis Mertikopoulos ◽  
Nicholas Bambos ◽  
Peter Glynn ◽  
Yinyu Ye
Keyword(s):  
Stochastic Optimization ◽  
Gradient Descent ◽  
Large Scale ◽  
Optimization Problems ◽  
Broad Class ◽  
Algorithm Design ◽  
Stochastic Gradient ◽  
Stochastic Gradient Descent ◽  
Step Size ◽  
Critical Set

The recent surge of breakthroughs in machine learning and artificial intelligence has sparked renewed interest in large-scale stochastic optimization problems that are universally considered hard. One of the most widely used methods for solving such problems is distributed asynchronous stochastic gradient descent (DASGD), a family of algorithms that result from parallelizing stochastic gradient descent on distributed computing architectures (possibly) asychronously. However, a key obstacle in the efficient implementation of DASGD is the issue of delays: when a computing node contributes a gradient update, the global model parameter may have already been updated by other nodes several times over, thereby rendering this gradient information stale. These delays can quickly add up if the computational throughput of a node is saturated, so the convergence of DASGD may be compromised in the presence of large delays. Our first contribution is that, by carefully tuning the algorithm’s step size, convergence to the critical set is still achieved in mean square, even if the delays grow unbounded at a polynomial rate. We also establish finer results in a broad class of structured optimization problems (called variationally coherent), where we show that DASGD converges to a global optimum with a probability of one under the same delay assumptions. Together, these results contribute to the broad landscape of large-scale nonconvex stochastic optimization by offering state-of-the-art theoretical guarantees and providing insights for algorithm design.

Large Scale Plant Optimization Problems

1988 ◽  
Author(s):  
Paul Cronin ◽  
Harry Woerde ◽  
Rob Vasbinder
Keyword(s):  
Large Scale ◽  
Optimization Problems ◽  
Plant Optimization

scholarly journals A Practical Algorithm for General Large Scale Nonlinear Optimization Problems

1999 ◽  
Vol 9 (3) ◽  
pp. 755-778 ◽  
Author(s):  
Paul T. Boggs ◽  
Anthony J. Kearsley ◽  
Jon W. Tolle
Keyword(s):  
Nonlinear Optimization ◽  
Large Scale ◽  
Optimization Problems ◽  
Practical Algorithm

On the stochastic optimization problems of plastic metal-working processes

1997 ◽  
Vol 84 (3) ◽  
pp. 1109-1112 ◽  
Author(s):  
M. B. Gitman ◽  
P. V. Trusov ◽  
S. A. Fedoseev
Keyword(s):  
Stochastic Optimization ◽  
Optimization Problems ◽  
Metal Working ◽  
Plastic Metal ◽  
Working Processes
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