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A NEW INTERPRETATION OF THE progressive hedging algorithm FOR MULTISTAGE STOCHASTIC MINIMIZATION PROBLEMS

JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 2020年第4期16卷 1655-1662页

作者： Sun, Tie Xu, Honglei Zhang, Min Curtin Univ Sch Elect Engn Comp & Math Sci Perth WA Australia Natl Univ Singapore Sch Business Singapore Singapore

The progressive hedging algorithm of Rockafellar and Wets for multistage stochastic programming problems could be viewed as a two-block alternating direction method of multipliers. This correspondence brings in some useful results. In particular, it provides a new proof for the convergence of the progressive hedging algorithm with a flexibility in the selection of primal and dual step lengths and it helps to develop a new progressive hedging algorithm for solving risk averse stochastic optimization problems with cross constraints.

关键词： progressive hedging algorithm alternating direction method of multipliers multistage stochastic optimization problems stochastic variational inequalities

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A Localized progressive hedging algorithm for Solving Nonmonotone Stochastic Variational Inequalities

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MATHEMATICS OF OPERATIONS RESEARCH 2024年第3期49卷 1303-2047, C2页

作者： Cui, Xingbang Zhang, Liping Tsinghua Univ Dept Math Sci Beijing 100084 Peoples R China

The progressive hedging algorithm (PHA) is an effective solution method for solving monotone stochastic variational inequalities (SVIs). However, this validity is based on the assumption of global maximal monotonicity. In this paper, we propose a localized PHA for solving nonmonotone SVIs and show that its validity is based on the weaker assumption of locally elicitable maximal monotonicity. Furthermore, we prove that such assumption holds when the mapping involved in the SVI is locally elicitable monotone or locally monotone. The local convergence of the proposed algorithm is established, and it is shown that the localized PHA has the rate of linear convergence under some mild assumptions. Some numerical experiments, including a two-stage orange market problem and randomly generated two-stage piecewise stochastic linear complementarity problems, indicate that the proposed algorithm is efficient.

关键词： locally elicitable maximal monotonicity progressive hedging algorithm stochastic variational inequalities

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Risk-Averse Optimal Control Model Under Uncertainty and Its Modified progressive hedging algorithm

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2024年第1期203卷 960-984页

作者： Sun, Jie Wu, Di Yu, Changjun Curtin Univ Sch EECS Bentley Australia Shanghai Univ Engn Sci Sch Math Phys & Stat Shanghai Peoples R China Shanghai Univ Dept Math Shanghai Peoples R China

It is of practical importance to incorporate a risk-averse objective in an optimal control problem under uncertainty. By leveraging the dual relationship between risk and regret measures, the risk-averse optimal control problem can be equivalently transformed into an optimal control problem with nonanticipativity constraints and expectation objective function. A modified progressive hedging algorithm is then proposed to solve the transformed problem, in which the descent conditions are enforced to ensure global convergence of the algorithm. Numerical results of three different types of problems are presented to show the applicability and effectiveness of the modified progressive hedging algorithm.

关键词： Optimal control under uncertainty progressive hedging algorithm Risk and regret measures

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A RANDOMIZED progressive hedging algorithm FOR STOCHASTIC VARIATIONAL INEQUALITY

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JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 2024年第3期20卷 1142-1155页

作者： Mu, Zhenguo Nanjing Univ Posts & Telecommun Coll Sci Nanjing Peoples R China

Recently, stochastic variational inequality (SVI) has been extended from single stage to multistage by Rockafellar and Wets (Math. Program., 165:331-360, 2017) and progressive hedging algorithm (PHA) has also been extended from stochastic programming to multistage stochastic linear comple-mentarity and SVI by Rockafellar and Sun (Math. Program., 174:453-471, 2019). However, the per-iteration cost of PHA can be prohibitively high when the scenario set is large, despite the decomposition and parallelizable nature of the algorithm. To address this issue, we propose a randomized PHA that allows us to control the per-iteration cost by randomly selecting a small subset of scenarios and updating only the corresponding variable components while freezing the variables corresponding to the unselected scenarios at the current iteration. By measuring the quality of an approximate solution using a re-stricted merit function, we demonstrate that despite the significant reduction in per-iteration cost, the randomized PHA converges in expectation and in an ergodic sense at the same sublinear rate as the original PHA.

关键词： Stochastic variational inequality progressive hedging algorithm nonanticipativity stochastic programming

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Joint tank container demurrage policy and flow optimisation using a progressive hedging algorithm with expanded time-space network

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2023年第2期307卷 663-679页

作者： Xing, Xinjie Song, Dongping Qiu, Chengfeng Drake, Paul R. Zhan, Yuanzhu Univ Liverpool Management Sch Chatham St Liverpool L69 7ZH England NetEase Zhiqi Technol Co LTD Hangzhou Peoples R China Univ Birmingham Birmingham Business Sch Birmingham B15 2TT England

A key feature of the tank container (TC) operating industry is that customers overhold TCs to provide temporary storage equipment for their contents rather than provide their own storage facilities. TC operators charge a very profitable fee (demurrage charge) for this service making it an attractive business proposition, but it can be detrimental to holistic network flows and fleet sizing. This paper addresses the problem of jointly optimising TC demurrage policy and TC flow, in the face of uncertain TC maintenance times, to maximise profits. A progressive hedging algorithm with expanded time-space network (PHA-ETSN) is designed to tackle this tactical level optimisation problem as other established techniques struggle with this optimisation in terms of computational time and memory requirements. Experiments are performed to illustrate how the optimisation tool can be used to investigate how demurrage policy affects different operational costs and TC hire revenue and thereby profit. These experiments demonstrate how the optimisation tool can be used by managers not only to optimise demurrage policy but also to explore and to understand more deeply the costs and profits in their operations.& COPY;2022 Elsevier B.V. All rights reserved.

关键词： OR in maritime industry Time -space network modelling progressive hedging algorithm Detention and demurrage Pricing and fleet size optimisation

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Structural properties of the progressive hedging algorithm

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Annals of Operations Research 1991年第1期31卷 445-455页

作者： Wallace, Stein W. Helgason, Thorkell Haugesund Maritime College Haugesund N-5500 Skåregaten 103 Norway University of Iceland Reykjavík S-107 Dunhagi 3 Iceland

This short note discusses some structural properties of the progressive hedging algorithm. It is based on the finite case, but allows for event trees that are unbalanced and where the nodes can have a varying number of children. Generic procedures and a generic record definition for the algorithms are presented. © 1991 J.C. Baltzer A. G. Scientific Publishing Company.

关键词： data structures generic algorithms progressive hedging algorithm scenario aggregation Stochastic programming

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Energy Storage Cluster Planning Method Accelerated by progressive hedging algorithm Considering Uncertainty in Renewable Energy and Load 2

Energy Storage Cluster Planning Method Accelerated by Progre...

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IEEE 2nd International Conference on Power Science and Technology (ICPST)

作者： Wang, Weihua Zhao, Shuai Lin, Yingming Liu, Yang Xie, Pingping Li, Yiran Li, Gengfeng Guangdong Power Grid Co Ltd Elect Power Dispatching & Control Ctr Guangzhou Peoples R China Xi An Jiao Tong Univ Smart Grid Key Lab Shaanxi Prov Xian 710049 Peoples R China

ISBN: (纸本)9798350349047;9798350349030

The high proportion of renewable energy presents numerous new features in the power system, which poses new challenges for the planning and operation of the power system. The energy storage system is an important technology and basic equipment to support the construction of the new power system under the dual carbon goals. Rational configuration of energy storage cluster can effectively improve the operation of the power system. To solve the issue that the current requirements on the energy storage cluster scale of power systems with substantial renewable energy output are too general to provide a suitable energy storage cluster configuration scheme, this paper proposes an energy storage cluster planning method to describe the uncertainty of renewable energy output and load. Considering the characteristics of the system, the proposed method is formulated as a stochastic programming model to plan the energy storage cluster. The progressive hedging algorithm is employed to solve the proposed model. Finally, the modified IEEE RTS79 test system is used to verify the method, and the best RER range is obtained.

关键词： uncertainty stochastic programming progressive hedging algorithm energy storage cluster

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Stochastic Integer Waste Management Problem Solved by a Modified progressive hedging algorithm

Stochastic Integer Waste Management Problem Solved by a Modi...

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作者： Malek, Martin Brno University of Technology

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.

关键词： waste management decision making stochastic programming facility location problem progressive hedging algorithm

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A note on progressive hedging algorithm for multistage stochastic variational inequalities

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APPLIED MATHEMATICS LETTERS 2024年 152卷

作者： Yan, Xihong Wang, Chuanlong Yang, Junfeng Taiyuan Normal Univ Shanxi Prov Dept Educ Key Lab Engn & Comp Sci Jinzhong 030619 Shanxi Peoples R China Nanjing Univ Dept Math Nanjing Peoples R China

progressive hedging algorithm (PHA) is a long-standing algorithm originally designed for stochastic programming problems and has recently been extended to solving multistage stochastic variational inequalities (SVIs), both are important tools for processing mathematical programming problems with uncertainty. In this note, we first show that PHA for two-stage stochastic linear complementarity problems, a special case of multistage SVIs, is an application of the DouglasRachford operator splitting algorithm and then extend this result to multistage SVIs. To do this, we first reformulate the focused problems as zero-finding problems of the sum of two maximal monotone operators. This reformulation plays a key role in establishing the connections Since Douglas-Rachford operator splitting algorithm can be viewed as a proximal point algorithm, our result sharpens the understanding of PHA.

关键词： progressive hedging algorithm Stochastic variational inequality Douglas-Rachford operator splitting Stochastic linear complementarity problem

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An effective progressive hedging algorithm for the two-layers time window assignment vehicle routing problem in a stochastic environment

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EXPERT SYSTEMS WITH APPLICATIONS 2021年 165卷 113877-113877页

作者： Jalilvand, Mahdi Bashiri, Mahdi Nikzad, Erfaneh Shahed Univ Dept Ind Engn Fac Engn Tehran Iran Coventry Univ Sch Strategy & Leadership Fac Business & Law Coventry W Midlands England

This paper presents an effective progressive hedging algorithm for vehicle routing problem with two-layers time window assignment and stochastic service times (2L-TWAVRPSST). Based on a predefined exogenous time window determined by the customers, an endogenous time window is assigned to each customer. Endogenous time windows have flexible width and composed of two-layers. The outer layer is wider than inner layer and is determined by violation variable. This approach aims to giving more flexibility to career companies for serving more customers using less vehicles. Customers could be visited even after the end of their assigned time windows by paying proportional penalty, while extra violation from the outer layer is not permitted. This problem is formulated as a two-stage stochastic model with the first-stage decisions of assigning inner and outer layers time window. Then in the second stage, routes are planned for each scenario combination of stochastic demand and service time. The validity and effectiveness of the proposed model was examined by various numerical examples. The problem was solved by a progressive hedging (PH) algorithm for large-scale instances. The results confirm efficiency of the considered solution approach in different instances.

关键词： Vehicle routing Time window assignment Stochastic programming Stochastic service time progressive hedging algorithm Scenario decomposition

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