Table of Content

30 June 2022, Volume 10 Issue 2

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Preface: Special Issue on New Developments in Mathematical Programming and Operations Research

Yu-Hong Dai, De-Ren Han, Ling-Yun Wu, Yan Xu

2022, 10(2):  193-195.  doi:10.1007/s40305-022-00392-x

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The Developments of Proximal Point Algorithms

Xing-Ju Cai, Ke Guo, Fan Jiang, Kai Wang, Zhong-Ming Wu, De-Ren Han

2022, 10(2):  197-239.  doi:10.1007/s40305-021-00352-x

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The problem of finding a zero point of a maximal monotone operator plays a central role in modeling many application problems arising from various fields, and the proximal point algorithm (PPA) is among the fundamental algorithms for solving the zero-finding problem. PPA not only provides a very general framework of analyzing convergence and rate of convergence of many algorithms, but also can be very efficient in solving some structured problems. In this paper, we give a survey on the developments of PPA and its variants, including the recent results with linear proximal term, with the nonlinear proximal term, as well as the inexact forms with various approximate criteria.

Certifying the Global Optimality of Quartic Minimization over the Sphere

Sheng-Long Hu

2022, 10(2):  241-287.  doi:10.1007/s40305-021-00347-8

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The quartic minimization over the sphere is an NP-hard problem in the general case. There exist various methods for computing an approximate solution for any given instance. In practice, it is quite often that a global optimal solution was found but without a certification. We will present in this article two classes of methods which are able to certify the global optimality, i.e., algebraic methods and semidefinite program (SDP) relaxation methods. Several advances on these topics are summarized, accompanied with some emerged new results. We want to emphasize that for mediumor large-scaled instances, the problem is still a challenging one, due to an apparent limitation on the current force for solving SDP problems and the intrinsic one on the approximation techniques for the problem.

Optimization and Operations Research in Mitigation of a Pandemic

Cai-Hua Chen, Yu-Hang Du, Dong-Dong Ge, Lin Lei, Yin-Yu Ye

2022, 10(2):  289-304.  doi:10.1007/s40305-022-00391-y

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The pandemic of COVID-19 initiated in 2019 and spread all over the world in 2020 has caused significant damages to the human society, making troubles to all aspects of our daily life. Facing the serious outbreak of the virus, we consider possible solutions from the perspectives of both governments and enterprises. Particularly, this paper discusses several applications of supply chain management, public resource allocation, and pandemic prevention using optimization and machine learning methods. Some useful insights in mitigating the pandemic and economy reopening are provided at the end of this paper. These insights might help governments to reduce the severity of the current pandemic and prevent the next round of outbreak. They may also improve companies' reactions to the increasing uncertainties appearing in the business operations. Although the coronavirus imposes challenges to the entire society at the moment, we are confident to develop new techniques to prevent and eradicate the disease.

Augmented Lagrangian Methods for Convex Matrix Optimization Problems

Ying Cui, Chao Ding, Xu-Dong Li, Xin-Yuan Zhao

2022, 10(2):  305-342.  doi:10.1007/s40305-021-00346-9

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In this paper, we provide some gentle introductions to the recent advance in augmented Lagrangian methods for solving large-scale convex matrix optimization problems (cMOP). Specifically, we reviewed two types of sufficient conditions for ensuring the quadratic growth conditions of a class of constrained convex matrix optimization problems regularized by nonsmooth spectral functions. Under a mild quadratic growth condition on the dual of cMOP, we further discussed the R-superlinear convergence of the Karush-Kuhn-Tucker (KKT) residuals of the sequence generated by the augmented Lagrangian methods (ALM) for solving convex matrix optimization problems. Implementation details of the ALM for solving core convex matrix optimization problems are also provided.

A Survey of Truck–Drone Routing Problem: Literature Review and Research Prospects

Yi-Jing Liang, Zhi-Xing Luo

2022, 10(2):  343-377.  doi:10.1007/s40305-021-00383-4

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The vehicle routing problem (VRP) has been an important research topic in operations research for decades. The major applications of the VRP arise in transportation, especially the last-mile delivery. In recent years, a growing number of logistic companies introduce drones or unmanned aerial vehicles in the delivery operations. Therefore, the truck-drone routing problem (TDRP), where trucks and drones are scheduled and coordinated to serve customers, vitalizes a new research stream in the literature. In this paper, we provide a comprehensive review on the TDRP. First, two basic models for the traveling salesman problem with drones and vehicle routing problem with drones are presented. Second, researches devoted to the TDRP are classified according to their addressed constraints and features. Third, prevalent algorithms that have been widely used in the existing literature are reviewed and described. Last, potential research opportunities are identified for future study.

Game Theory and the Evolution of Cooperation

Bo-Yu Zhang, Shan Pei

2022, 10(2):  379-399.  doi:10.1007/s40305-021-00350-z

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Evolution is based on the competition between individuals and therefore rewards only selfish behavior. How cooperation or altruism behavior could prevail in social dilemma then becomes a problematic issue. Game theory offers a powerful mathematical approach for studying social behavior. It has been widely used to explain the evolution of cooperation. In this paper, we first introduce related static and dynamic game methods. Then we review two types of mechanisms that can promote cooperation in groups of genetically unrelated individuals, (i) direct reciprocity in repeated games, and (ii) incentive mechanisms such as reward and punishment.

Operations Research in the Blockchain Technology

Xu Wang, Ling-Yun Wu

2022, 10(2):  401-422.  doi:10.1007/s40305-021-00348-7

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In the past decade, as a decentralized distributed database technology blockchain has developed rapidly at an unprecedented speed and been applied to a wide range of scenarios far beyond cryptocurrencies, for example, insurance, energy, risk management, and Internet of things (IoT). The blockchain technology combines the achievements from cryptography, computer science, economics, and operations research and has increasingly attracted attention from both academia and industry. Though the operations research has been widely adopted in the blockchain technology, there is a lack of comprehensive survey on the operations research in blockchain-related issues. In order to fill the gap, we analyze the blockchain technology through the perspective of operations research and present a comprehensive review of the operations research problems from the aspects of security and stability, efficiency and performance, and resource allocation. This paper aimed to help the relevant readers in the field of operations research find their own points of interest and conduct in-depth research on the blockchain technology, hoping to promote the rapid development and wider application of the blockchain technology in the near future.