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A Conic Programming Approach for Robust Portfolio Optimization Problems BAI Yan-Qin, SHU Xuan-Yu, ZHANG Hong-Jie Operations Research Transactions    2010, 14 (4): 21-31.   Abstract （2720）      PDF（pc） （588KB）（16741）       Knowledge map    Save This paper deals with the robust portfolio optimization problems with linear transaction costs. The model is based on the worst-case Conditional Value-at-Risk (CVaR) risk measure and uncertainty for the portfolio return distribution. We show that the robust portfolio optimization problems with box uncertainty  and ellipsoidal uncertainty structures can be reformulated as linear programming and second-order cone programming, respectively. Moreover, we illustrate our model by an example of market data simulation.   Related Articles | Metrics | Comments（0）

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Introduction to compressive sensing and sparse optimization WEN Zaiwen YIN Wotao LIU Xin ZHANG Yin Operations Research Transactions    2012, 16 (3): 49-64.   Abstract （9028）      PDF（pc） （669KB）（3495）       Knowledge map    Save We briefly introduce the basic principle and theory of compressive sensing and sparse optimization. Compressive sensing is a new paradigm of signal acquisition, which senses a sparse signal by taking a set of incomplete measurements and  recovers the signal by solving an optimization problem. This article first illustrates the compressive sensing paradigm through a synthetic example. Then we describe two sufficient conditions,  the null space property and restricted isometry principle, for l1 convex minimization to give the sparsest solution. Finally, we summarize a few typical algorithms for solving the optimization models arising from compressive sensing. Reference | Related Articles | Metrics | Comments（0） Cited: Baidu(16)

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Research report on the development of operations research in China The Operational Research Society of China Operations Research Transactions    2012, 16 (3): 1-48.   Abstract （4159）      PDF（pc） （1123KB）（2902）       Knowledge map    Save Operations Research (OR) is an interdisciplinary subject emerged in the 1930s. It mainly studies how to make optimal or satisfactory solutions through mathematical and computational theories and methods for social and engineering systems. In order to promote the research and  application of OR in China, we invite a dozen of experts in OR and related areas to complete this report  making reference to the review of OR development by many top experts in representative areas in OR. In this  report, we first summarize the features and methodology of OR and make a brief review on the development of  OR with analysis on successful experiences in OR study. Then, we survey the status of some main directions  of this discipline along with some its typical open problems. In the end of the survey we prospect for the  trend of OR in the future. We hope that this report could motivate readers to reflect upon what is the essence  of OR and how OR has grown up and will develop in next decades, and in such a way advance OR development in  China. Reference | Related Articles | Metrics | Comments（0） Cited: Baidu(3)

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Global convergence of the Levenberg-Marquardt method with Goldstein line search DU Shouqiang Operations Research Transactions    2012, 16 (4): 105-111.   Abstract （2104）      PDF（pc） （411KB）（2756）       Knowledge map    Save In this paper, we consider the Levenberg-Marquardt method for solving nonlinear equations. We use Goldstein line search on every iteration to guarantee the global convergence of the Levenberg-Marquardt method. Under mild conditions, we prove that the Levenberg-Marquardt method is globally convergent. And we also apply the method to solve generalized complementarity problems. Reference | Related Articles | Metrics | Comments（0） Cited: Baidu(4)

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A new augmented lagrangian function based on inequalty constraints problem LIU Mu-Hua, SHANG You-Lin, LI Pu Operations Research Transactions    2011, 15 (4): 115-123.   Abstract （2182）      PDF（pc） （1062KB）（2398）       Knowledge map    Save A new kind of augmented lagrangian function is proposed in this paper. We proved that there are the 1-1 corresponding relationships between the stable point of the lagrangian function and KKT point of the original problem. The same results are obtained for the both global minimum point. The local minimum point of the augmented lagrangian function is the local minimum point of the original problem. Related Articles | Metrics | Comments（0） Cited: Baidu(3)

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Reverse Point Algorithm of Assignment Problem on Assignment Less Than Jobs and Persons WANG Li-Zhu, LIU Yang Operations Research Transactions    2011, 15 (3): 124-128.   Abstract （3494）      PDF（pc） （267KB）（2330）       Knowledge map    Save Abstract：In this paper, we propose a new algorithm on a special assignment problem in which the real assigned jobs are less than or equal to both the total persons and the total jobs. To this special assingment problem we pose the concept of reserve point, discussed the character of reserve point and accessed to relevant conclusion.a new method to solve this special assignment problem is given through increasing reserve points finally. Related Articles | Metrics | Comments（0） Cited: Baidu(3)

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Optimal investment strategy with stochastic  volatility and  dynamic VaR constraint YI Bo, LI Zhong-Fei, ZENG Yan Operations Research Transactions    2012, 16 (2): 77-90.   Abstract （2805）      PDF（pc） （242KB）（2323）       Knowledge map    Save This paper considers an optimal  portfolio choice problem under Stein-Stein stochastic volatility model and dynamic VaR constraint. The investor aims to maximize the expected power utility of the terminal wealth, and the financial  market consists of one risk-free asset and one risky asset whose price process is described by   Stein-Stein stochastic volatility model. At the same time, the investor hopes to limit the potential   risk over investment horizon by a dynamic VaR constraint. Adopting the stochastic dynamic programming    approach and Lagrange multiple method, we derive the closed-form expressions of the optimal strategy    as well as the optimal value function in a special case. Moreover, economic implications and numerical    analysis are proposed to illustrate the impacts of stochastic volatility and dynamic VaR constraint    on the investor's optimal strategy. Reference | Related Articles | Metrics | Comments（0）

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Advances in linear and nonlinear programming DAI Yuhong, LIU Xinwei Operations Research Transactions    2014, 18 (1): 69-92.   Abstract （2665）      PDF（pc） （782KB）（2212）       Knowledge map    Save Linear and nonlinear programming is a classical branch in mathematical programming. We introduce some backgrounds on linear and nonlinear programming, and some new methods and new research advances in linear programming, unconstrained and constrained optimization. The alternating direction method of multipliers is very efficient in solving some constrained optimization problems with special structure and has been attracted much attentions in recent years. Global optimization is specially important for applications of optimization. These two topics are also involved. Reference | Related Articles | Metrics | Comments（0） Cited: Baidu(10)

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Optimization in many-to-one two-sided matching market LI Jianrong Operations Research Transactions    2013, 17 (4): 1-10.   Abstract （1581）      PDF（pc） （550KB）（2039）       Knowledge map    Save The game-theoretic solutions defined in two-sided market allow the interests of agents on the same side of the market to be simultaneously maximized. The theoretic basis of such kind of optimization is the stability of the selection matching. This paper uses game-theoretic method to study the optimization in many-to-one two-sided matching market. Under the presence of substitutable and LAD(Law of Aggregate Demand) preferences, we prove that the selections made by firms produce a stable matching, so do the selections made by workers. Reference | Related Articles | Metrics | Comments（0） Cited: Baidu(2)

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Algorithm design and the fair incentive mechanism in Chinese college admissions matching market LI Jianrong Operations Research Transactions    2019, 23 (2): 75-85.   DOI: 10.15960/j.cnki.issn.1007-6093.2019.02.007 Abstract （1143）      PDF（pc） （575KB）（2029）       Knowledge map    Save This paper, using matching game theoretic methods, studies the algorithm design and the fair incentive mechanism in Chinese college admissions market. Based on the admissions procedure, we design the Chinese college admissions algorithm, which we proved is feasible. We prove that every stable allocation can be produced by a Nash equilibrium, but not vice versa. We demonstrate the relationship between fairness and stability, and prove that stability implies fairness but not vice versa. Then we construct a (Gale and Shapley) deferred-acceptance algorithm in our market and show that it is both stable and strategy-proof. Therefore, it is a fair incentive mechanism. Reference | Related Articles | Metrics | Comments（0）

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Recent advances in integer programming SUN Xiaoling, LI Duan Operations Research Transactions    2014, 18 (1): 39-68.   Abstract （2343）      PDF（pc） （803KB）（1940）       Knowledge map    Save Integer programming deals with optimization problems with decision variables being all integer or partly integer. Integer programming has been one of the most active research directions in optimization due to its wide applications in operations research and management science. In this survey paper, we first briefly review the background of integer programming and summarize the fundamental results of linear and nonlinear integer programming. We then focus on some recent progress in several research topics, including semi-definite programming relaxation and randomized methods for 0-1 quadratic programs, optimization problems with cardinality and semi-continuous variables, and co-positive cone program representations and approximations of 0-1 quadratic programs. Finally, we indicate some research perspectives and open problems in integer programming. Reference | Related Articles | Metrics | Comments（0） Cited: Baidu(2)

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An Approximation Agorithm for the Stochastic Fault-Tolerant Fcility Placement Problem SHAO Jia-Ting, Xu-Da-Chuan Operations Research Transactions    2012, 16 (1): 13-20.   Abstract （3024）      PDF（pc） （180KB）（1890）       Knowledge map    Save In the deterministic fault-tolerant facility placement problem (FTFP),  we are given a set of locations  and a set of clients. We can open any number of different facilities with the same opening cost at each location. Each client j has an integer requirement rj. Connecting  client j to different facilities at the same location is permitted. The objective is to open some facilities and connect each client j to rj different facilities such that the total cost is minimized. In this paper, we consider the two-stage stochastic fault-tolerant facility placement problem (SFTFP)  with recourse in which the set of clients are unknown in advance. But there are finite scenarios materialized by a probability distribution. Each scenario specifies a subset of clients to be assigned. Moreover, each facility has two kinds of opening cost. In the first stage, we open a subset of facilities according to the stochastic information of the clients. In the second stage, we can open additional number of facilities when the actual information of the clients is revealed. We give a linear integral program and an LP-rounding based 5-approximation algorithm for the SFTFP. Reference | Related Articles | Metrics | Comments（0）

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Second-order characterizations for local weakly nondominated points with variable ordering structure XU Yihong, MEI Fang Operations Research Transactions    2019, 23 (1): 45-52.   DOI: 10.15960/j.cnki.issn.1007-6093.2019.01.005 Abstract （691）      PDF（pc） （437KB）（1834）       Knowledge map    Save A kind of second-order tangent derivatives is introduced, with which a second-order necessary optimality condition is established for set-valued optimization with variable ordering structure in the sense of local weakly nondominated points. Under special circumstances, a first-order necessary optimality condition is obtained. The relationship to second-order contingent tangent derivatives for the sum of two set-valued maps is given under some constraint qualification indued by modified Dubovitskij-Miljutin tangent cones. Further more, a necessary optimality condition is obtained where the objective and constraining functions are considered separately with respect to second-order contingent tangent derivatives. Reference | Related Articles | Metrics | Comments（0）

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CRS algorithm based on the simulated annealing TANG Dan Operations Research Transactions    2011, 15 (4): 124-128.   Abstract （2397）      PDF（pc） （267KB）（1829）       Knowledge map    Save In this paper, a new algorithm is proposed for the nonlinear programming problems, The algorithm applied the simulated annealing to the CRS algorithm, According to the simulated annealing reflects on concentrates and proliferates in each iteration, Enables the CRS algorithm to search the global optimization more easier rather than the local optimization. Finally, the proposed algorithm is applied to two typical function optimization problems, and the numerical results illustrate the accuracy and efficiency of the algorithm. Related Articles | Metrics | Comments（0）

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Efficiency for a Class of Multiobjective Optimization Problems ZHAO Ke-Quan, Yang Xin-Min Operations Research Transactions    2011, 15 (3): 1-8.   Abstract （3057）      PDF（pc） （152KB）（1823）       Knowledge map    Save In this paper, a class of multiobjective optimization problems in which involved inequality constraints is considered. Some necessary and sufficient conditions are established for an efficient solution. Moreover, the equivalence is established between efficiency and properly efficiency by linear scalarization method under some suitable conditions. Our results improves naturally and extends some previously known results. Related Articles | Metrics | Comments（0） Cited: Baidu(10)

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Simulation of Levy-driven models and  its application in finance CHEN Ruidi, PENG Yijie, HU Jianqiang Operations Research Transactions    2013, 17 (1): 1-9.   Abstract （2876）      PDF（pc） （566KB）（1821）       Knowledge map    Save Levy processes have been widely used to model financial assets since the 1990s. The reason of their widespread applications is mainly due to the fact that they provide more realistic models that capture discontinuous behaviors and stylized empirical statistical characteristics of time series data in economy and finance. However, when applied to derivative pricing, very few analytical results are available except for European options.  Therefore, one usually has to resort to numerical methods such as Monte Carlo simulation method.  The simulation method is so attractive  that it is very general and can also handle high dimensional problems very well.  In this short survey paper, we first provide an overview on Levy processes.  We then introduce Monte Carlo simulation method for Levy processes.  Finally, we discuss the two main simulation based gradient estimation methods: perturbation analysis and likelihood ratio method. Reference | Related Articles | Metrics | Comments（0）

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An LVI-based Numerical Algorithm for Solving Quadratic Programming Problems ZHANG Yu-Nong, LI Xue-Zhong, ZHANG Zhi-Jun, LI Jun Operations Research Transactions    2012, 16 (1): 21-30.   Abstract （2639）      PDF（pc） （206KB）（1808）       Knowledge map    Save This paper presents and investigates a numerical algorithm (termed as 94LVI algorithm) for solving quadratic programming (QP) problems with linear equality and bound constraints. To do this, the constrained QP problems are firstly converted into linear variational inequalities (LVI), which are then converted into equivalent piecewise-linear projection equations (PLPE). After that, the resultant PLPE is solved by the presented 94LVI algorithm. The optimal numerical solutions to the QP problems are thus obtained. Furthermore, the theoretical proof of the global convergence of the 94LVI algorithm is presented. The numerical comparison results between the 94LVI algorithm and the active set algorithm are provided as well, which further demonstrates the efficacy and superiority of the presented algorithm for solving such QP problems. Reference | Related Articles | Metrics | Comments（0） Cited: Baidu(6)

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Optimization Methods for a Class of Integer Polynomial Programming Problems TIAN Jing, WU Zhi-You, J. Ugon Operations Research Transactions    2011, 15 (4): 23-35.   Abstract （3044）      PDF（pc） （209KB）（1781）       Knowledge map    Save In this paper, a class of integer polynomial programming problems is considered. This class of integer polynomial programming problems has a wide range of practical applications and is NP hard. For these problems, necessary global optimality conditions and sufficient global optimality conditions have been presented recently. We will design some optimization methods to this class of integer polynomial programming problems by using these global optimality conditions. Firstly, a local optimization method is designed according to the necessary global optimality conditions for these integer polynomial programming problems. Moreover, a new global optimization method for this class of integer polynomial programming problems is presented by combining the sufficient global optimality conditions, the local optimization method and an auxiliary function. Some numerical examples are presented to illustrate the efficiency and reliability of these optimization methods. Related Articles | Metrics | Comments（0） Cited: Baidu(9)

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Approximation algorithms for the  priority facility location problem with submodular penalties WANG Ying, WANG Fengmin, XU Dachuan, XU Wenqing Operations Research Transactions    2015, 19 (2): 1-14.   DOI: 10.15960/j.cnki.issn.1007-6093.2015.02.001 Abstract （1075）      PDF（pc） （647KB）（1735）       Knowledge map    Save In this paper, we study priority facility location problem with submodular penalties where each client has a level-of-service requirement. An open facility must satisfy the requirement of the clients served by it, and there is a submodular penalty cost corresponding with the unserved clients. The objective is to minimize the sum of the opening cost, the connection cost and the submodular penalty cost. We present the integer program, the linear programming relaxation and the dual program for the problem. Using the primal-dual and greedy augmentation techniques, we then propose two approximation algorithms and obtain the approximation ratios of 3 and 2.375 respectively. Reference | Related Articles | Metrics | Comments（0）

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A class of limited memory BFGS-type algorithms for large-scale unconstrainedoptimization QIAN Xiao-Yan, SHI Qing-Sheng, LIU Hao, SHI Kui-Ran Operations Research Transactions    2011, 15 (3): 9-18.   Abstract （4617）      PDF（pc） （187KB）（1734）       Knowledge map    Save In this paper, objective function value information is exploited in limited memory BFGS-type algorithms. we first construct a new quadratic function satisfying some interpolation conditions to approximate the objective function, get a new weak secant equation. Combining the new weak secant equation and that obtained by Yuan\cite{yuan1991}, a class of limited memory BFGS--type algorithms including the classic LBFGS algorithm based on a new weak secant equation are proposed. The convergence of this class limited memory BFGS-type algorithms is proved. Numerical results for standard test problems from CUTE are reported, which indicate that all the algorithms in the proposed class perform quiet well. Related Articles | Metrics | Comments（0）