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Approximations for a Queueing Game Model with Join-the-Shortest-Queue Strategy Qi-Hui Bu, Li-Wei Liu, Jia-Shan Tang, Yi-Qiang Q. Zhao Journal of the Operations Research Society of China    2023, 11 (3): 489-504.   DOI: 10.1007/s40305-021-00382-5 Abstract （146）      PDF       Knowledge map    Save This paper investigates a partially observable queueing system with N nodes in which each node has a dedicated arrival stream. There is an extra arrival stream to balance the load of the system by routing its customers to the shortest queue. In addition, a reward-cost structure is considered to analyse customers' strategic behaviours. The equilibrium and socially optimal strategies are derived for the partially observable mean field limit model. Then, we show that the strategies obtained from the mean field model are good approximations to the model with finite N nodes. Finally, numerical experiments are provided to compare the equilibrium and socially optimal behaviours, including joining probabilities and social benefits for different system parameters. Reference | Related Articles | Metrics | Comments（0）

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Competitive Resource Allocation Among Urban Congestion Areas in a Modern Big City Alexander Krylatov, Anastasiya Raevskaya Journal of the Operations Research Society of China    2024, 12 (1): 133-153.   DOI: 10.1007/s40305-023-00530-z Abstract （129）      PDF       Knowledge map    Save The continuing growth of modern big cities leads to their spatial expansion and the emergence of new road connections and urban areas. Areas where large transportation flows of pedestrians, passengers, and drivers come together create demand points, which attract business companies that strive to allocate their resources in the most sought-after places. However, the law of supply and demand restrains companies from allocating all their resources solely in the most popular congestion areas since the more valuable an urban area, the higher the cost to be paid for a resource unit allocation there. As a result, companies act in a non-cooperative manner and try to minimize their own overall costs when allocating resources across available commercial areas in a big city. Non-cooperative behavior of companies leads to the problem of Nash equilibrium search in the game of competing entrepreneurs. In this paper, we study the corresponding resource allocation game under affine cost functions and obtain Nash equilibrium strategies in explicit form. These findings allow us to develop a simple procedure for computing Nash equilibria in the game of companies allocating their resources among urban congestion areas. The computational study demonstrates the dependence of the average price for resource allocation on the number of players and their resource volumes. The outcome of the paper contributes to flow theory and seems to be fresh and useful for managers. Reference | Related Articles | Metrics | Comments（0）

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Approximation of the Shannon Capacity Via Matrix Cone Programming Shi-Tong Wu, Zhen-Nan Zhou, Zhong-Yi Huang, Bo Bai Journal of the Operations Research Society of China    2023, 11 (4): 875-889.   DOI: 10.1007/s40305-022-00408-6 Abstract （205）      PDF       Knowledge map    Save This paper proposes a novel formulation using the matrix cone programming to compute an upper bound of the Shannon capacity of graphs, which is theoretically superior to the Lovász number. To achieve this, a sequence of matrix cones is constructed by adding certain co-positive matrices to the positive semi-definite matrix cones during the matrix cone programming. We require the sequence of matrix cones to have the weak product property so that the improved result of the matrix cone programming remains an upper bound of the Shannon capacity. Our result shows that the existence of a sequence of suitable matrix cones with the weak product property is equivalent to the existence of a co-positive matrix with testable conditions. Finally, we give some concrete examples with special structures to verify the existence of the matrix cone sequence. Reference | Related Articles | Metrics | Comments（0）

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Preface: The Special Issue on Dynamic and Networking Games Hong-Wei Gao, Vladimir Mazalov Journal of the Operations Research Society of China    2024, 12 (1): 1-3.   DOI: 10.1007/s40305-023-00536-7 Abstract （117）      PDF       Knowledge map    Save Related Articles | Metrics | Comments（0）

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A Mini-Batch Proximal Stochastic Recursive Gradient Algorithm with Diagonal Barzilai–Borwein Stepsize Teng-Teng Yu, Xin-Wei Liu, Yu-Hong Dai, Jie Sun Journal of the Operations Research Society of China    2023, 11 (2): 277-307.   DOI: 10.1007/s40305-022-00436-2 Abstract （1028）      PDF       Knowledge map    Save Many machine learning problems can be formulated as minimizing the sum of a function and a non-smooth regularization term. Proximal stochastic gradient methods are popular for solving such composite optimization problems. We propose a minibatch proximal stochastic recursive gradient algorithm SRG-DBB, which incorporates the diagonal Barzilai–Borwein (DBB) stepsize strategy to capture the local geometry of the problem. The linear convergence and complexity of SRG-DBB are analyzed for strongly convex functions. We further establish the linear convergence of SRGDBB under the non-strong convexity condition. Moreover, it is proved that SRG-DBB converges sublinearly in the convex case. Numerical experiments on standard data sets indicate that the performance of SRG-DBB is better than or comparable to the proximal stochastic recursive gradient algorithm with best-tuned scalar stepsizes or BB stepsizes. Furthermore, SRG-DBB is superior to some advanced mini-batch proximal stochastic gradient methods. Reference | Related Articles | Metrics | Comments（0）

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The Generalized Stackelberg Equilibrium of the Two-Person Stopping Game Marek Skarupski, Krzysztof J. Szajowski Journal of the Operations Research Society of China    2024, 12 (1): 155-168.   DOI: 10.1007/s40305-023-00460-w Abstract （107）      PDF       Knowledge map    Save In modeling the bilateral selection of states of the process, Dynkin (Dokl Akad Nauk USSR 185:241–288, 1969) proposed a two-person game in which players use stopping moments as strategies. The purpose of this work is to present a model of the game in which the players have different information about the process itself, as well as various laws to stop the process and accept its state. The game model uses the stochastic process apparatus, in particular, the ability to create different filters for the same process. The sets of stopping moments based on different filters are not identical, which allows us to model different sets of strategies for players. We show that the follower, by observing the behavior of a rational leader, can recover information that is lost due to the lack of complete observation of the state of the process. In the competition of two opponents for the maximum of the i.i.d. sequence, one of whom has access to full information and the other only knows their relative ranks, we found the generalized Stackelberg equilibrium. If the priority of a player observing the relative ranks is less than 50%, then that player modifies his strategy based on the behavior of the second player. For a player with full information, information about the behavior of the player observing the relative ranks is useless. Reference | Related Articles | Metrics | Comments（0）

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An Automatic Fuzzy Clustering Algorithm for Discrete Elements Tai Vovan, Yen Nguyenhoang, Sang Danh Journal of the Operations Research Society of China    2023, 11 (2): 309-325.   DOI: 10.1007/s40305-021-00388-z Abstract （983）      PDF       Knowledge map    Save This research proposes a measure called cluster similar index (CSI) to evaluate the similarity of cluster for discrete elements. The CSI is used as a criterion to build the automatic fuzzy clustering algorithm. This algorithm can determine the suitable number of clusters, find the elements in each cluster, give the probability to belong to the clusters of each element, and evaluate the quality of the established clusters at the same time. The proposed algorithm can perform quickly and effectively by the established MATLAB procedure. Several numerical examples illustrate the proposed algorithm and show the advantages in comparing with the existing ones. Finally, applying the proposed algorithm in the image recognition shows potentiality in the reality of this research. Reference | Related Articles | Metrics | Comments（0）

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A Gradient Descent Method for Estimating the Markov Chain Choice Model Lei Fu, Dong-Dong Ge Journal of the Operations Research Society of China    2023, 11 (2): 371-381.   DOI: 10.1007/s40305-021-00365-6 Abstract （1043）      PDF       Knowledge map    Save In this paper, we propose a gradient descent method to estimate the parameters in a Markov chain choice model. Particularly, we derive closed-form formula for the gradient of the log-likelihood function and show the convergence of the algorithm. Numerical experiments verify the efficiency of our approach by comparing with the expectation-maximization algorithm. We show that the similar result can be extended to a more general case that one does not have observation of the no-purchase data. Reference | Related Articles | Metrics | Comments（0）

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Strong Subgame Consistency of the Core in Stochastic Network Formation Games Ping Sun, Elena Parilina Journal of the Operations Research Society of China    2024, 12 (1): 189-213.   DOI: 10.1007/s40305-022-00442-4 Abstract （108）      PDF       Knowledge map    Save We consider a model of network formation as a stochastic game with random duration proposed initially in Sun and Parilina (Autom Remote Control 82(6):1065–1082, 2021). In the model, the leader first suggests a joint project to other players, i.e., the network connecting them. Second, the players are allowed to form fresh links with each other updating the initially proposed network. The stage payoff of any player is defined depending on the network structure. There are two types of randomness in the network formation process: (i) links may fail to be formed with different probabilities although players intend to establish them, (ii) the game process may terminate at any stage or transit to the next stage with a certain probability distribution. Finally, a network is formed as a result of players’ decisions and realization of random variables. The cooperative version of the stochastic game is investigated. In particular, we examine the properties of subgame consistency as well as strong subgame consistency of the core. We provide a payment mechanism or regularization of the core elements to sustain its subgame consistency and avoid the player’s deviations from the cooperative trajectory. In addition, the distribution procedure of the core elements is regularized in case there are negative payments to achieve only nonnegative payments to the players at any stage. The sufficient condition of a strongly subgame consistent core is also obtained. We illustrate our theoretical results with a numerical example. Reference | Related Articles | Metrics | Comments（0）

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Approximate Weak Minimal Solutions of Set-Valued Optimization Problems S. Khoshkhabar-amiranloo Journal of the Operations Research Society of China    2023, 11 (3): 673-692.   DOI: 10.1007/s40305-022-00401-z Abstract （141）      PDF       Knowledge map    Save This paper deals with approximate weak minimal solutions of set-valued optimization problems under vector and set optimality criteria. The relationships between various concepts of approximate weak minimal solutions are investigated. Some topological properties and existence theorems of these solutions are given. It is shown that for set-valued optimization problems with upper (outer) cone-semicontinuous objective values or closed objective maps the approximate weak minimal and strictly approximate lower weak minimal solution sets are closed. By using the polar cone and two scalarization processes, some necessary and sufficient optimality conditions in the sense of vector and set criteria are provided. Reference | Related Articles | Metrics | Comments（0）

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The Rate of Convergence of Augmented Lagrangian Method for Minimax Optimization Problems with Equality Constraints Yu-Hong Dai, Li-Wei Zhang Journal of the Operations Research Society of China    2024, 12 (2): 265-297.   DOI: 10.1007/s40305-022-00439-z Abstract （127）      PDF       Knowledge map    Save The augmented Lagrangian function and the corresponding augmented Lagrangian method are constructed for solving a class of minimax optimization problems with equality constraints. We prove that, under the linear independence constraint qualification and the second-order sufficiency optimality condition for the lower level problem and the second-order sufficiency optimality condition for the minimax problem, for a given multiplier vector μ, the rate of convergence of the augmented Lagrangian method is linear with respect to ||μ - μ*|| and the ratio constant is proportional to 1/c when the ratio ||μ - μ*/c is small enough, where c is the penalty parameter that exceeds a threshold c* > 0 and μ* is the multiplier corresponding to a local minimizer. Moreover, we prove that the sequence of multiplier vectors generated by the augmented Lagrangian method has at least Q-linear convergence if the sequence of penalty parameters {ck} is bounded and the convergence rate is superlinear if {ck} is increasing to infinity. Finally, we use a direct way to establish the rate of convergence of the augmented Lagrangian method for the minimax problem with a quadratic objective function and linear equality constraints. Reference | Related Articles | Metrics | Comments（0）

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Degree Conditions on Copies of Forests in Graphs Xiao-Dong Chen, Shuai-Jun Chen, Ming-Chu Li Journal of the Operations Research Society of China    2023, 11 (3): 667-672.   DOI: 10.1007/s40305-022-00404-w Abstract （188）      PDF       Knowledge map    Save For a graph G, let $ \mu (G)=\min \{\max \{{d}(x),{d}(y)\}:x\ne y,xy\notin E(G), x,y\in V(G)\} $ if G is non-complete, otherwise, $ \mu (G)=+\infty. $ For a given positive number s, we call that a graph G satisfies Fan-type conditions if $ \mu (G)\geqslant s. $ Suppose $ \mu (G)\geqslant s, $ then a vertex v is called a small vertex if the degree of v in G is less than s. In this paper, we prove that for a forest F with m edges, if G is a graph of order $ n\geqslant |F| $ and $ \mu (G)\geqslant m $ with at most $ \max \{n-2m,0\} $ small vertices, then G contains a copy of F. We also give examples to illustrate both the bounds in our result are best possible. Reference | Related Articles | Metrics | Comments（0）

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A Hybrid Conjugate Gradient Algorithm for Nonconvex Functions and Its Applications in Image Restoration Problems Gong-Lin Yuan, Ying-Jie Zhou, Meng-Xiang Zhang Journal of the Operations Research Society of China    2023, 11 (4): 759-781.   DOI: 10.1007/s40305-022-00424-6 Abstract （199）      PDF       Knowledge map    Save It is prominent that conjugate gradient method is a high-efficient solution way for large-scale optimization problems. However, most of the conjugate gradient methods do not have sufficient descent property. In this paper, without any line search, the presented method can generate sufficient descent directions and trust region property. While use some suitable conditions, the global convergence of the method is established with Armijo line search. Moreover, we study the proposed method for solving nonsmooth problems and establish its global convergence. The experiments show that the presented method can be applied to solve smooth and nonsmooth unconstrained problems, image restoration problems and Muskingum model successfully. Reference | Related Articles | Metrics | Comments（0）

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A Framework of Convergence Analysis of Mini-batch Stochastic Projected Gradient Methods Jian Gu, Xian-Tao Xiao Journal of the Operations Research Society of China    2023, 11 (2): 347-369.   DOI: 10.1007/s40305-019-00276-7 Abstract （1003）      PDF       Knowledge map    Save In this paper, we establish a unified framework to study the almost sure global convergence and the expected convergencerates of a class ofmini-batch stochastic(projected) gradient (SG) methods, including two popular types of SG: stepsize diminished SG and batch size increased SG. We also show that the standard variance uniformly bounded assumption, which is frequently used in the literature to investigate the convergence of SG, is actually not required when the gradient of the objective function is Lipschitz continuous. Finally, we show that our framework can also be used for analyzing the convergence of a mini-batch stochastic extragradient method for stochastic variational inequality. Reference | Related Articles | Metrics | Comments（0）

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The Non-Inclusive Diagnosability of Regular Graphs Yu-Long Wei, Tong-Tong Ding, Min Xu Journal of the Operations Research Society of China    2023, 11 (4): 891-910.   DOI: 10.1007/s40305-022-00415-7 Abstract （113）      PDF       Knowledge map    Save Fault diagnosis is an important area of study with regard to the design and maintenance of multiprocessor systems. A new measure for fault diagnosis of systems, namely, non-inclusive diagnosability (denoted by tN(G)), was proposed by Ding et al. In this paper, we establish the non-inclusive diagnosability of a class of regular graphs under the PMC model and the MM* model. As applications, the non-inclusive diagnosabilities of hypercubes, hierarchical hypercubes, folded hypercubes, star graphs, bubble-sort graphs, pancake graphs and dual cubes are determined under the PMC model and the MM* model. Reference | Related Articles | Metrics | Comments（0）

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Remarks on Component Factors Wei Gao, Wei-Fan Wang Journal of the Operations Research Society of China    2023, 11 (3): 657-666.   DOI: 10.1007/s40305-021-00357-6 Abstract （141）      PDF       Knowledge map    Save In this remark, we first simply survey the important results on component factors in graphs. Then, we focus on the binding number condition of component factors in some special settings. The main contributions in this remark are two folded: (1) we reveal that the existence of some special component factors is equal to some specific binding number conditions; (2) the parameter conditions for a graph G with a $ P_{\tiny {\geqslant 3}} $-factor are determined. Reference | Related Articles | Metrics | Comments（0）

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An Overview of Stochastic Quasi-Newton Methods for Large-Scale Machine Learning Tian-De Guo, Yan Liu, Cong-Ying Han Journal of the Operations Research Society of China    2023, 11 (2): 245-275.   DOI: 10.1007/s40305-023-00453-9 Abstract （1097）      PDF       Knowledge map    Save Numerous intriguing optimization problems arise as a result of the advancement of machine learning. The stochastic first-ordermethod is the predominant choicefor those problems due to its high efficiency. However, the negative effects of noisy gradient estimates and high nonlinearity of the loss function result in a slow convergence rate. Second-order algorithms have their typical advantages in dealing with highly nonlinear and ill-conditioning problems. This paper provides a review on recent developments in stochastic variants of quasi-Newton methods, which construct the Hessian approximations using only gradient information. We concentrate on BFGS-based methods in stochastic settings and highlight the algorithmic improvements that enable the algorithm to work in various scenarios. Future research on stochastic quasi-Newton methods should focus on enhancing its applicability, lowering the computational and storage costs, and improving the convergence rate. Reference | Related Articles | Metrics | Comments（0）

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Equilibrium Arrivals to Preemptive Queueing System with Fixed and Random Population Size Julia Chirkova, Vladimir Mazalov Journal of the Operations Research Society of China    2024, 12 (1): 77-92.   DOI: 10.1007/s40305-023-00461-9 Abstract （113）      PDF       Knowledge map    Save A single-server queueing system with preemptive access is considered. Each customer has one attempt to enter the system at its working interval [0, T]. As soon as the customer request enters the system, the server immediately starts the service. But when the next request arrives in the system, the previous one leaves the system even he has not finished his service yet. We study a non-cooperative game in which the customers wish to maximize their probability of obtaining service within a certain period of time. We characterize the Nash equilibrium and the price of anarchy, which is defined as the ratio between the optimal and equilibrium social utility. Two models are considered. In the first model the number of players is fixed, while in the second it is random and obeys the Poisson distribution. We demonstrate that there exists a unique symmetric equilibrium for both models. Finally, we calculate the price of anarchy for both models and show that the price of anarchy is not monotone with respect to the number of customers. Reference | Related Articles | Metrics | Comments（0）

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The Perturbation Bound of the Extended Vertical Linear Complementarity Problem Shi-Liang Wu, Wen Li, He-Hui Wang Journal of the Operations Research Society of China    2024, 12 (3): 601-625.   DOI: 10.1007/s40305-023-00456-6 Abstract （172）      PDF       Knowledge map    Save In this paper, we discuss the perturbation analysis of the extended vertical linear complementarity problem (EVLCP). Under the assumption of the row $\mathcal{W}$-property, we derive several absolute and relative perturbation bounds of EVLCP, which extend some existing results. Several numerical examples are given to show the proposed bounds. Reference | Related Articles | Metrics | Comments（0）

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The Minimum Centroid Branch Spanning Tree Problem Hao Lin, Cheng He Journal of the Operations Research Society of China    2024, 12 (2): 528-539.   DOI: 10.1007/s40305-022-00419-3 Abstract （112）      PDF       Knowledge map    Save For a spanning tree T of graph G, the centroid of T is a vertex v for which the largest component of T - v has as few vertices as possible. The number of vertices of this component is called the centroid branch weight of T. The minimum centroid branch spanning tree problem is to find a spanning tree T of G such that the centroid branch weight is minimized. In application to design of communication networks, the loads of all branches leading from the switch center should be as balanced as possible. In this paper, we prove that the problem is strongly NP-hard even for bipartite graphs. Moreover, the problem is shown to be polynomially solvable for split graphs, and exact formulae for special graph families, say Kn1,n2,…,nk and Pm×Pn, are presented. Reference | Related Articles | Metrics | Comments（0）