Table of Content

30 June 2021, Volume 9 Issue 2

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COVID-19 Pandemic with Human Mobility Across Countries

Cheng Zhang, Li-Xian Qian, Jian-Qiang Hu

2021, 9(2):  229-244.  doi:10.1007/s40305-020-00317-6

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This study develops a holistic view of the novel coronavirus(COVID-19) spread worldwide through a spatial–temporal model with network dynamics. By using a unique human mobility dataset containing 547 166 flights with a total capacity of 101 455 913 passengers from January 22 to April 24, 2020, we analyze the epidemic correlations across 22 countries in six continents and particularly the changes in such correlations before and after implementing the international travel restriction policies targeting different countries. Results show that policymakers should move away from the previous practices that focus only on restricting hotspot areas with high infection rates. Instead, they should develop a new holistic view of global human mobility to impose the international movement restriction. The study further highlights potential correlations between international human mobility and focal countries’ epidemic situations in the global network of COVID-19 pandemic.

Optimal Reinsurance and Investment Strategy with Delay in Heston’s SV Model

Chun-Xiang A, Ai-Lin Gu, Yi Shao

2021, 9(2):  245-271.  doi:10.1007/s40305-020-00331-8

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In this paper, we consider an optimal investment and proportional reinsurance problem with delay, in which the insurer’s surplus process is described by a jump-diffusion model. The insurer can buy proportional reinsurance to transfer part of the insurance claims risk. In addition to reinsurance, she also can invests her surplus in a financial market, which is consisted of a risk-free asset and a risky asset described by Heston’s stochastic volatility (SV) model. Considering the performance-related capital flow, the insurer’s wealth process is modeled by a stochastic differential delay equation. The insurer’s target is to find the optimal investment and proportional reinsurance strategy to maximize the expected exponential utility of combined terminal wealth. We explicitly derive the optimal strategy and the value function. Finally, we provide some numerical examples to illustrate our results.

Inexact Operator Splitting Method for Monotone Inclusion Problems

Yuan-Yuan Huang, Chang-He Liu, You-Lin Shang

2021, 9(2):  274-306.  doi:10.1007/s40305-020-00296-8

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The Douglas–Peaceman–Rachford–Varga operator splitting methods are a class of efficient methods for finding a zero of the sum of two maximal monotone operators in a real Hilbert space; however, they are sometimes difficult or even impossible to solve the subproblems exactly. In this paper, we suggest an inexact version in which some relative error criterion is discussed. The corresponding convergence properties are established, and some preliminary numerical experiments are reported to illustrate its efficiency.

Local Linear Convergence of an ADMM-Type Splitting Framework for Equality Constrained Optimization

Jun-Feng Yang, Yin Zhang

2021, 9(2):  308-319.  doi:10.1007/s40305-019-00271-y

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We establish local convergence results for a generic algorithmic framework for solving a wide class of equality constrained optimization problems. The framework is based on applying a splitting scheme to the augmented Lagrangian function that includes as a special case the well-known alternating direction method of multipliers (ADMM). Our local convergence analysis is free of the usual restrictions on ADMM-like methods, such as convexity, block separability or linearity of constraints. It offers a much-needed theoretical justification to the widespread practice of applying ADMM-like methods to nonconvex optimization problems.

Transient Behavior of a Single-Server Markovian Queue with Balking and Working Vacation Interruptions

Arumugam Azhagappan, Thirunavukkarasu Deepa

2021, 9(2):  322-341.  doi:10.1007/s40305-019-00288-3

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This paper studies the time-dependent analysis of an M/M/1 queueing model with single, multiple working vacation, balking and vacation interruptions. Whenever the system becomes empty, the server commences working vacation. During the working vacation period, if the queue length reaches a positive threshold value ‘k’, the working vacation of the server is interrupted and it immediately starts the service in an exhaustive manner. During working vacations, the customers become discouraged due to the slow service and possess balking behavior. The transient system size probabilities of the proposed model are derived explicitly using the method of generating function and continued fraction. The performance indices such as average and variance of system size are also obtained. Further, numerical simulations are presented to analyze the impact of system parameters.

Generalizations of Sobolev’s Consistency and Values for TU-Games

Jun Su, Theo S. H. Driessen, Gen-Jiu Xu

2021, 9(2):  344-357.  doi:10.1007/s40305-019-00279-4

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In the framework of cooperative game theory, Sobolev (Advances in game theory, Izdat., “Minitis”, Vilnius, pp 151–153, 1973) axiomatized the well-known Shapley value by means of consistency property with reference to a specifically chosen reduced game. The goal of this paper is to generalize Sobolev’s consistency approach to the class of efficient, symmetric and linear values.

A Novel MILP Model for N-vehicle Exploration Problem

Guo-Jun Zhang, Jin-Chuan Cui

2021, 9(2):  359-373.  doi:10.1007/s40305-019-00289-2

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The N-vehicle exploration problem (NVEP) is a nonlinear discrete scheduling problem, and the complexity status remains open. To our knowledge, there is no literature until now employing mixed integer linear programming (MILP) technology to solve this problem except for Wang (J Oper Res Soc China 3(4):489–498, 2015). However, they did not give numerical experiments since their model existed strictly inequalities and the number of constraints was up to O(n³), which was inefficient to solve practical problems. This paper establishes a more concise MILP model, where the number of constraints is just O(n²). Therefore, the existing efficient MILP algorithms can be used to solve NVEP. Secondly, we provide some properties of N-vehicle problem and give three methods for cutting plane construction, which can increase the solving speed significantly. Finally, a numerical experiment is provided to verify the effectiveness and robustness for different instances and scales of acceleration techniques.

Optimality and Duality for Multiobjective Semi-infinite Variational Problem Using Higher-Order B-type I Functions

Promila Kumar, Jyoti Dagar

2021, 9(2):  375-393.  doi:10.1007/s40305-019-00269-6

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The notion of higher-order B-type I functional is introduced in this paper. This notion is utilized to study optimality and duality for multiobjective semi-infinite variational problem in which the index set of inequality constraints is an infinite set. The concept of efficiency is used as a tool for optimization. Mond–Weir type of dual is proposed for which weak, strong, and strict converse duality theorems are proved to relate efficient solutions of primal and dual problems.

The Optimal Investment, Liability and Dividends in Insurance

Ping-Jin Deng, Xiu-Fang Li, Xiao-Wei Chen

2021, 9(2):  395-409.  doi:10.1007/s40305-020-00292-y

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In this paper, we build an optimal control model with the objective to maximize the expected value of the time discount utility by selecting optimal investment, liability and dividend strategies for insurance companies. We then use the techniques from Merton (J Econ Theory 3(4):373–413, 1971) to solve our optimal control problem and deduce the optimal control solutions. Finally, we analyze the economic impacts on the optimal controls of the parameters in insurance market.

An Adaptive Three-Term Conjugate Gradient Method with Sufficient Descent Condition and Conjugacy Condition

Xiao-Liang Dong, Zhi-Feng Dai, Reza Ghanbari, Xiang-Li Li

2021, 9(2):  411-425.  doi:10.1007/s40305-019-00257-w

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In this paper, an adaptive three-term conjugate gradient method is proposed for solving unconstrained problems,which generates sufficient descent directions at each iteration. Different from the existent methods, a dynamical adjustment between Hestenes–Stiefel and Dai–Liao conjugacy conditions in our proposed method is developed. Under mild condition, we show that the proposed method converges globally. Numerical experimentation with the new method indicates that it efficiently solves the test problems and therefore is promising.

On the Vertex Cover Number of 3-Uniform Hypergraph

Zhuo Diao

2021, 9(2):  427-440.  doi:10.1007/s40305-019-00284-7

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Given a hypergraph H(V, E), a set of vertices S ⊆ V is a vertex cover if every edge has at least one vertex in S. The vertex cover number is the minimum cardinality of a vertex cover, denoted by τ(H). In this paper, we prove that for every 3-uniform connected hypergraphH(V, E), τ(H) ≤ 2m/3+1 holds on where m is the number of edges. Furthermore, the equality holds on if and only if H(V, E) is a hypertree with perfect matching.

Semicontinuity of the Minimal Solution Set Mappings for Parametric Set-Valued Vector Optimization Problems

Xin Xu, Yang-Dong Xu, Yue-Ming Sun

2021, 9(2):  441-454.  doi:10.1007/s40305-019-00275-8

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With the help of a level mapping, this paper mainly investigates the semicontinuity of minimal solution set mappings for set-valued vector optimization problems. First, we introduce a kind of level mapping which generalizes one given in Han and Gong (Optimization 65:1337–1347, 2016). Then, we give a sufficient condition for the upper semicontinuity and the lower semicontinuity of the level mapping. Finally, in terms of the semicontinuity of the level mapping, we establish the upper semicontinuity and the lower semicontinuity of the minimal solution set mapping to parametric setvalued vector optimization problems under the C-Hausdorff continuity instead of the continuity in the sense of Berge.

The Generic Uniqueness and Well-Posedness of Nash Equilibria for Stable Population Games

Wen-Sheng Jia, Xiao-Ling Qiu, Ding-Tao Peng

2021, 9(2):  455-464.  doi:10.1007/s40305-019-00281-w

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This paper aims at studying a new kind of stable population games introduced by J. Hofbauer and H. Sandholm in 2009. We first construct a complete distance space M consisting of stable population games and show that most of stable population games have unique Nash equilibrium point that according to Baire’s category theorem. It implies that every stable population game that possesses more than one Nash equilibrium can be approached arbitrarily by a sequence of the stable population game each of which has a unique Nash equilibrium. Then, we construct a bounded rationality function and deduce some results on the generic well-posedness implying Tikhonov well-posedness and Hadamard well-posedness for stable population games.

Inverse Maximum Flow Problem Under the Combination of the Weighted l₂ Norm and the Weighted Hamming Distance

Long-Cheng Liu, Han Gao, Chao Li

2021, 9(2):  465-474.  doi:10.1007/s40305-019-00273-w

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The idea of the inverse optimization problem is to adjust the values of the parameters so that the observed feasible solutions are indeed optimal. The modification cost is measured by different norms, such as l₁, l₂, l_∞ norms and the Hamming distance, and the goal is to adjust the parameters as little as possible. In this paper, we consider the inverse maximum flow problem under the combination of the weighted l₂ norm and the weighted Hamming distance, i.e., the modification cost is fixed in a given interval and depends on the modification out of the given interval. We present a combinatorial algorithm which can be finished in O(nm) to solve it due to the minimum cut of the residual network.