Structural properties of the progressive hedging algorithm

1991 ◽  
Vol 31 (1) ◽  
pp. 445-455 ◽  
Author(s):  
Stein W. Wallace ◽  
Thorkell Helgason
Keyword(s):  
Structural Properties ◽  
Progressive Hedging ◽  
Progressive Hedging Algorithm

A Model of Multistage Risk-Averse Stochastic Optimization and its Solution by Scenario-Based Decomposition Algorithms

2020 ◽  
Vol 37 (04) ◽  
pp. 2040004
Author(s):  
Min Zhang ◽  
Liangshao Hou ◽  
Jie Sun ◽  
Ailing Yan
Keyword(s):  
Stochastic Optimization ◽  
Financial Management ◽  
Mean Deviation ◽  
Decomposition Algorithms ◽  
Risk Averse ◽  
Stochastic Variational Inequalities ◽  
Business Operations ◽  
Convergence Results ◽  
Progressive Hedging ◽  
Progressive Hedging Algorithm

Stochastic optimization models based on risk-averse measures are of essential importance in financial management and business operations. This paper studies new algorithms for a popular class of these models, namely, the mean-deviation models in multistage decision making under uncertainty. It is argued that these types of problems enjoy a scenario-decomposable structure, which could be utilized in an efficient progressive hedging procedure. In case that linkage constraints arise in reformulations of the original problem, a Lagrange progressive hedging algorithm could be utilized to solve the reformulated problem. Convergence results of the algorithms are obtained based on the recent development of the Lagrangian form of stochastic variational inequalities. Numerical results are provided to show the effectiveness of the proposed algorithms.

scholarly journals A Novel Pre-Dispatching Strategy of Power System under Extreme Weather

Processes ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 2112
Author(s):  
Tianen Huang ◽  
Zhenjie Wu ◽  
Yuantao Wang ◽  
Jian Tang ◽  
Xiang Li ◽  
...  
Keyword(s):  
Distribution Network ◽  
Distribution Networks ◽  
Test System ◽  
Power Grids ◽  
Economic Losses ◽  
Power Outage ◽  
Progressive Hedging ◽  
Progressive Hedging Algorithm ◽  
On Line ◽  
The Cost

Pre-dispatch is an important way for distribution networks to cope with typhoon weather, enhance resilience and reduce economic losses. In order to accurately describe the faults and consequences of components’ failure in the distribution network, this paper establishes a pre-dispatch model to cope with typhoon weather based on line failures consequence analysis. First, Monte Carlo simulation is used to sample the typical fault scenarios of vulnerable lines. According to the location of switchgear, the distribution network is partitioned and a block breaker correlation matrix is established. Combined with the line fault status, a fault consequence model of distribution lines related to the pre-dispatching strategy is established. Then, the objective function is given to minimize the sum of the cost of the pre-dispatch operation and the power outage, and then establish a pre-dispatch model for the distribution network. In order to reduce the computational complexity, PH (Progressive Hedging) algorithm is used to solve the model. Finally, the IEEE-69 test system is used to analyze the effectiveness of the method. The results show that the proposed dispatching model can effectively avoid potential risks, reduce system economic losses and improve the resilience of power grids.

scholarly journals Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs

2016 ◽  
Vol 157 (1) ◽  
pp. 47-67 ◽  
Author(s):  
Dinakar Gade ◽  
Gabriel Hackebeil ◽  
Sarah M. Ryan ◽  
Jean-Paul Watson ◽  
Roger J.-B. Wets ◽  
...  
Keyword(s):  
Lower Bounds ◽  
Mixed Integer ◽  
Integer Programs ◽  
Mixed Integer Programs ◽  
Progressive Hedging ◽  
Progressive Hedging Algorithm

scholarly journals Approximate scenario solutions in the progressive hedging algorithm

1991 ◽  
Vol 31 (1) ◽  
pp. 425-444 ◽  
Author(s):  
Thorkell Helgason ◽  
Stein W. Wallace
Keyword(s):  
Progressive Hedging ◽  
Progressive Hedging Algorithm

scholarly journals Stochastic Integer Waste Management Problem Solved by a Modified Progressive Hedging Algorithm

MENDEL ◽  
2018 ◽  
Vol 24 (2) ◽  
Author(s):  
Martin Malek ◽  
Radovan Somplak ◽  
Pavel Popela ◽  
Jakub Kudela
Keyword(s):  
Waste Management ◽  
Real World ◽  
Large Scale ◽  
Management Decision ◽  
Management Problem ◽  
Real World Data ◽  
Progressive Hedging ◽  
Progressive Hedging Algorithm ◽  
Decision Making Problem ◽  
Management Decision Making

In this paper we describe a real-world large-scale stochastic integer waste-management decision making problem. The problem consists of choosing the optimal locations and capacities of new incineration plants, that will be used for the disposal of waste. To solve this problem, we implement a modied version of the progressive hedging algorithm. The presented case study with real-world data concerns the situation in the Czech Republic.

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