2010 Vol.14

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A Note on The Steiner Problem ---An Approach to Find The Minimal Network Yue Minyi, Cheng Congdian Operations Research Transactions    2010, 14 (1): 1-14.   Abstract （1585）            Knowledge map    Save This article addresses the problem how to find a minimal  network connecting 5 given points in the plane. The related results with four points have been given by Pollack (1978) and  Yue Minyi.  The present work  proposes a fast algorithm to solve the problem. Related Articles | Metrics | Comments（0）

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Utility-based Differential Game for Portfolio  in CIR Framework Non-uniformly Bounded Costs Wan Shuping Operations Research Transactions    2010, 14 (1): 15-23.   Abstract （1512）            Knowledge map    Save Utility-based differential game for portfolio with Cox-Ingersoll-Ross (CIR) stochastic interest rate in continuous time between two investors is developed. The market interest rate has the dynamics of CIR interest rate. The prices of risky stocks are affected by CIR interest rate. There is a single payoff function which depends on both investors' wealth processes. One player chooses a dynamic portfolio strategy in order to maximize this expected payoff, while his opponent is simultaneously choosing a dynamic portfolio strategy so as to minimize the same quantity. The optimal strategies for the utility-based game are obtained by the stochastic control theory. Especially for the constant relative risk aversion utility game with fixed duration, the explicit optimal strategies and value of the game are derived. The numerical example and simulation are provided to illustrate the results obtained in this paper. Related Articles | Metrics | Comments（0）

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Extremal Graphs about Bipartite Matching Extendability WANG Xiu-Mei, SHANG Wei-苹, LIN Yi-Xun Operations Research Transactions    2010, 14 (1): 23-30.   Abstract （1571）            Knowledge map    Save Let $G$ be a simple  graph containing a perfect matching.  $G$ is said to be bipartite matching extendable (BM-extendable) if every matching $M$ whose induced subgraph is a bipartite graph extends to a perfect matching. Extremal graph problems are at the core  of graph theory. In this paper, we characterize maximally BM-unextendable graphs, maximally BM-extendable graphs in the class of complete $k$-partite graphs with $k\geq 2$. Related Articles | Metrics | Comments（0）

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Strong NP-hardness of the Single-variable-resource Scheduling Problem to Minimize the Total Weighted Completion Time Yuan-Jin-Jiang, WANG Qin Operations Research Transactions    2010, 14 (1): 31-36.   Abstract （1560）            Knowledge map    Save Baker and Nuttle studied the following single-variable-resource scheduling problem: sequencing $n$ jobs for processing by a single resource to minimize a function of job  completion times, when the availability of the resource varies over time.  When the objective function to be minimized is the total weighted completion time,   Baker and Nuttle conjectured that the problem is NP-hard. Recently, Yuan, Cheng and Ng   showed that this problem is NP-hard in the binary sense, but the   exact complexity of the problem is still open. We show in this paper  that this problem is strongly NP-hard. Related Articles | Metrics | Comments（0）

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Algorithm for Nonlinear Integer programming YANG Hua-Yun, YANG Yong-Jian Operations Research Transactions    2010, 14 (1): 37-45.   Abstract （1455）            Knowledge map    Save  In this paper, a novel  filled function is proposed for nonlinear integer programming  problem. This function contains only one parameter. We also  discuss the properties of the proposed function and using this filled function  to solve the nonliner integer programming problem. Numerical experiments on  several test problems have demonstrated the reliability and efficiency of  the proposed method. Related Articles | Metrics | Comments（0）

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Set in Constrained Convex Vector Optimization Chen-Yao, HUANG Xue-Xiang, GUO Li Operations Research Transactions    2010, 14 (1): 46-54.   Abstract （1296）            Knowledge map    Save In this paper, we first characterize the nonemptiness and boundedness of the efficient solution set of a cone-constrained convex vector optimization problem whose domination cone is  polyhedral.  Then, we apply a key condition in the characterizations to the convergence analysis of a class of penalty methods. Related Articles | Metrics | Comments（0）

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A Weighted-Path-Following Interior-Point Algorithm for Convex JIN Zheng-Jing, BAI Yan-Qin, HAN Bo-Shun Operations Research Transactions    2010, 14 (1): 55-65.   Abstract （1639）            Knowledge map    Save Inspired by Darvay's work that developed a weighted path-following interior point algorithm for solving Linear Programming, we extend in this paper the algorithm of Darvay to solve convex quadratic optimization problem and show that this algorithm has local quadratic convergence rate and the favorable polynomial complexity bound.   Related Articles | Metrics | Comments（0）

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A Linearization Technique for Quadratic Integer Programming with Box Constrain REN Yan, CHEN Wei Operations Research Transactions    2010, 14 (1): 66-76.   Abstract （1599）            Knowledge map    Save In this paper, we discusses the linearization technique for the quadratic integer programming problem. Under the objective function is quadratic function, we consider the linearization strategy for the  problem with quadratic constrain, and extend the method for quadratic $0-1$problem to the quadratic problem with box constrains.  We consider the reduction of quadratic integer programming problems to linear mixed $0-1$ programming problems,and then solve the linear mixed $0-1$ programming problems with ilog-cplex or Excel. Related Articles | Metrics | Comments（0）

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The Ruin Probability for Markov Risk Model with  Claim Amounts Being Exponentially Distributed JIN Shi-Wei Operations Research Transactions    2010, 14 (1): 77-84.   Abstract （1368）            Knowledge map    Save The ruin probability for a Markov risk model is considered in the paper. In the case where the claim distribution is exponential or mixed exponential, the explicit form of the ruin probability is given by solving the differential-integral systems satisfied by the ruin probability. Related Articles | Metrics | Comments（0）

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Total Dominating Functions on Subclasses    of Chordal Graphs ZHOU Li-Gang, DAN 而Fang, WANG Hai-Chao Operations Research Transactions    2010, 14 (1): 85-94.   Abstract （1282）            Knowledge map    Save  In this paper we show that the $k$-total domination and signed total domination problems are NP-complete on doubly chordal graphs. Also, we present an unified approach to slove the signed total domination, minus total domination, $k$-total domination and $\{k\}$-total domination problems on a strongly chordal graph in linear-time, if the strong elemination ordering for the strongly chordal graph is given. Related Articles | Metrics | Comments（0）

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A Condition for Strong Average Optimality  of MDP with Non-uniformly Bounded Costs XIAO Qing-Chu, TAN Hang-Sheng Operations Research Transactions    2010, 14 (1): 95-105.   Abstract （1369）            Knowledge map    Save In this paper, we consider the Markov decision processes under an average cost criterion with non- uniformly bounded cost,  denumerable state and arbitrary action spaces. Some sufficient conditions are given under which every average optimal policy is strong average optimal. We improve the main results obtained by Cavazos-Cadena R.and Fernandez-Gaucheran E. (Math. Meth. Oper. Res., 1996, 43: 281-300).   Related Articles | Metrics | Comments（0）

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Mean-Variance-Approximate Skewness Portfolio  Model and Empirical Analysis Yu-Jing Operations Research Transactions    2010, 14 (1): 106-114.   Abstract （1639）            Knowledge map    Save The classical Markowitz's mean-variance model in modern investment science uses variance as  risk measure while it ignores the asymmetry of the return istribution. When skewness is adopted to measure the asymmetry,  the portfolio optimization model becomes very difficult due to the nonconvex and non-quadratic features of skewness.In this paper,  we propose a mean-variance-approximate skewness (MVAS) model which measures the asymmetry by the radio of positive semi-variance and negative semi-variance. Empirical analysis of Chinese stock market shows that the portfolio models which consider  the asymmetry of the return distribution  outperform  MV and MAD models when the market has non-normal feature. Related Articles | Metrics | Comments（0）

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An Introduction to the Cost for Multistage  Rocket of Series Type ZHU Xue-Jun, CHEN Shu, ZHANG Lian-Sheng Operations Research Transactions    2010, 14 (1): 115-128.   Abstract （1293）            Knowledge map    Save  On basis of the maximum velocity's regularity of a multistage rocket we reform the commonly used mathematical model for the cost problem: the least least propellant plan. We analyze the cost problems for multistage rocket of series type in all cases, and verify the effectivity of the new model by some examples Related Articles | Metrics | Comments（0）

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Dense Schedule for Open Shop Problems with at Most   Two Idle Intervals on the Last Complete Machine CHEN Rong-Jun, HUANG Wan-Zhen, TANG Guo-Chun Operations Research Transactions    2010, 14 (2): 1-10.   Abstract （1531）            Knowledge map    Save For open shop problem, if the principle of avoiding unnecessary machine idleness is applied when arranging jobs, a dense schedule is obtained. It is conjectured that the makespan of any dense schedule is at most $2-1/m$ times the optimal makespan of the problem, where m is the number of machines. The conjecture remains unproved when the number of machine is greater than six. In this paper, by introducing characteristic functions of jobs and machines and non-interruption of machines about jobs, we propose  sufficient conditions under which the conjecture is true for general number of machines, provided that the last complete machine in the dense schedule has no more than two idle intervals. Related Articles | Metrics | Comments（0）

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A Smoothing Approximation to the Lower Order Exact Penalty Function HE Zhen-Hua, BAI Fu-Sheng Operations Research Transactions    2010, 14 (2): 11-22.   Abstract （1808）            Knowledge map    Save In this paper, we propose a smoothing approximation to the lower order exact penalty functions for inequality-constrained optimization problems. An algorithm is presented to obtain an approximate global solution of the original optimization problem by searching a global solution of the smoothed penalty problem. Several numerical examples are given to illustrate the effectiveness of the present smoothing method.   Related Articles | Metrics | Comments（0）

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The Pos/Neg-weighted 2-Median Problem on Interval Graphs CHENG Yu-Kun Operations Research Transactions    2010, 14 (2): 23-36.   Abstract （1679）            Knowledge map    Save This paper deals with the facility location problem on interval graphs with ositive and negative interval weights. We consider two different objective functions: the sum of the minimum weighted distances (MWD) of the intervals from the facilities and the sum of the weighted minimum distances (WMD). Two $O(n^2)$ time algorithms for both models of the 2-median problem have been developed.     Related Articles | Metrics | Comments（0）

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A Hybrid  PSO Algorithm Based on Penalty Function for Solving Zero-One Nonlinear Programming Problems Gao-Yue-Lin, LEI Fan-Fan, LI Hui-Rong Operations Research Transactions    2010, 14 (2): 37-44.   Abstract （2667）            Knowledge map    Save Using penalty function,we transform  zero-one nonlinear programming problems into unconstrained optimization problem. Then we combine particle swarm optimization with penalty function method  to produce a PSO hybrid algorithm based on penalty function. It can be shown by the numerical results that the proposed algorithm is effective.     Related Articles | Metrics | Comments（0）

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Optimality and Duality for a Class of  Nonsmooth  Optimization Problems ZHAO Ke-Quan, TANG Li-Ping, YANG Xin-Min Operations Research Transactions    2010, 14 (2): 45-54.   Abstract （1690）            Knowledge map    Save In this paper, a class of nonsmooth multiobjective optimization problems in which involved equality constraints and inequality constraints is considered. The generalized Karush-Kuhn-Tucker necessary and sufficient optimality conditions are given. Furthermore, mixed type dual model is discussed, and theorems of weak duality, strong duality, converse duality, strict converse duality and restricted converse duality are presented. Related Articles | Metrics | Comments（0）

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On the Extremal Wiener Indices of Some Graphs LIN Xiao-Xia Operations Research Transactions    2010, 14 (2): 55-60.   Abstract （1691）            Knowledge map    Save  The Wiener index of a graph is defined as the sum of distances between all pairs of vertices of the graph. It has been found extensive applications in chemistry. In this paper, we characterize the graphs which minimize the Wiener index among all graphs with given order and specific parameter, such as the chromatic number or clique number, and the graphs which maximize the Wiener index among all graphs with given order and clique number. Related Articles | Metrics | Comments（0）

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Analysis of a Discrete-Time Preemptive Priority Queue LI Gang, ZHANG Hua-Juan Operations Research Transactions    2010, 14 (2): 61-69.   Abstract （1718）            Knowledge map    Save In this paper, we consider a discrete-time preemptive priority queue with a single server and two types of customers. The stationary probabilities are presented in a matrix form with respect to the background state space. Applying the matrix analytic method, it is shown that certain reasonable conditions lead to a geometric decay of the tail probabilities as the level goes to infinity. Related Articles | Metrics | Comments（0）

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A System Equations Method with Arbitrary Initial Point for Semi-infinite Programming SUN Qing-Ying, GAO Bao, SANG Zhao-Yang, TIAN Feng-Ting Operations Research Transactions    2010, 14 (2): 70-78.   Abstract （1637）            Knowledge map    Save  Based on discretization technique and  diagonal-sparse quasi-Newton method, an improved system equations method with arbitrary initial point for semi-infinite programming is presented. The global and super-linear convergence properties of the new method are discussed. The numerical results illustrate that the new method is more effective than the original algorithm. Related Articles | Metrics | Comments（0）

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Bounding the Efficiency Loss with Mixed Equilibrium Associated  with User Equilibrium and Logit-Based LUO Wen-Chang Operations Research Transactions    2010, 14 (2): 79-86.   Abstract （1693）            Knowledge map    Save In a transportation network with users classified into two categories, the first category chooses the route according to user equilibrium(UE)  principle and the second category chooses the route according to Logit-based stochastic user  equilibrium(LSUE)  principle. In this paper, a variational inequality is proposed to  formulate the mixed equilibrium travel behavior associated with user equilibrium and Logit-based stochastic user  equilibrium. Likewise, the upper bound of efficiency loss for the  mixed equilibrium is described as a general formula. It is shown that the upper bound is related to the  topological structure of networks, transportation demand and the demand  ratio.   Related Articles | Metrics | Comments（0）

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A Problem on Electricity Distribution and Payment   Related to Electricity Bidding Price System QIU Xiao-Ling Operations Research Transactions    2010, 14 (2): 87-94.   Abstract （1503）            Knowledge map    Save This article is to set up the ambulant equation of electricity supply and demand on the basis of electric exchange centres; and then prove  the existence, uniqueness of the clearing price, discuss the continuity of clearing price and profits nctions about price function, finally to demonstrate the  existence theorem of  equilibria in different power plants' profits according to the theory of Schauder fixed points. The payment on clearing price may realize the economic Pareto optimizing.   Related Articles | Metrics | Comments（0）

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The Cone Optimization Analysis of Coherent Risk Measures REN Feng-Ying, LI Xing-Si Operations Research Transactions    2010, 14 (2): 95-105.   Abstract （1746）            Knowledge map    Save The axiomatic system of coherent risk measures has set up by Artzner et.al. owever, the mathematics underlying it is closely related to the ideas of convex otimization, specifically the duality theory. This paper simply proved the general  expression of coherent risk measures by the cone duality theorem in finite dimension space.  We have analyzed the core role of acceptable set in coherent risk measure and the properties  of conventional risk measures. In spite of the size of acceptable set may be used for controlling the risk management strictly or loosely, but we do not know how to express it quantitatively.   The paper suggest  In addition we suggest relaxing no arbitrage condition in view of the flexibility of coherent  risk measures and the achieved results may be used to pricing option in incomplete market.   Related Articles | Metrics | Comments（0）

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Optimal   Investment Strategy for  Insurers under Linear Constraint ZENG Yan, LI Zhong-Fei Operations Research Transactions    2010, 14 (2): 106-118.   Abstract （1759）            Knowledge map    Save In practice, investment behaviors of  an insurer will be subjected to some constraints from Insurance Law and the insurer's own risk management. Additionally,  an insurer should draw certain reserve to satisfy regulatory requirements. Therefore, in this paper we suppose the time when its surplus first comes up to the floor level of reserve as the ``ruin'' time; the target of the insurance company is to minimize the ``ruin'' probability; the surplus process of the insurer is derived by a diffusion model and its investment behaviors are subjected to a linear constraint. By solving the corresponding HJB equation,  the optimal investment strategy and value function are derived explicitly when the insurer is allowed to investment on a risk-free asset and a risky asset. In the end, economic analysis and numerical examples are provided. Related Articles | Metrics | Comments（0）

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A Class of Filled Function for Constrained  Global Optimization ZHAO De-Fen, WANG Wei Operations Research Transactions    2010, 14 (2): 119-128.   Abstract （1601）            Knowledge map    Save In this paper, a class of filled function for constrained global optimization is proposed.Also,its filled properties and other analytical properties are proved under several mild assumptions. In addition, according to the theoretical analysis, a new algorithm and two numerical experiments are presented , the computational results show that our algorithm is effective. Related Articles | Metrics | Comments（0）

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On a Primal-Dual Neural Network for Online Solution of Linear Programming Operations Research Transactions    2010, 14 (3): 1-10.   Abstract （2186）            Knowledge map    Save  This paper investigates the theory of primal linear-programming (LP) problem and its dual problems, which could be used to develop a kind of recurrent neural network for solving online LP problems as well as kinematic control of redundant manipulators. For example, a so-called usual primal-dual neural network (PDNN) initiated by Tang et al. However, due to the complexity and diversity of duality theory, that PDNN needs to be improved so as to obtain the optimal solution(s) instead of feasible solutions. Computer-simulation results substantiate the efficacy and correctness of the improved PDNN model for online solution of LP problems. Related Articles | Metrics | Comments（0）

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The Minimal Genus of Circular Graph C(n,m) Operations Research Transactions    2010, 14 (3): 11-18.   Abstract （1731）            Knowledge map    Save The orientable and nonorientable minimal genus of all the circular graphs are given in this paper. In the meanwhile, the strong  minimal genus of some circular graphs are discussed too. Related Articles | Metrics | Comments（0）

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Online Scheduling with Reassignment under  Non-Simultaneous Machine Available Times Hou Liying, Kang Liying Operations Research Transactions    2010, 14 (3): 19-30.   Abstract （1750）            Knowledge map    Save In this paper, we consider online scheduling problems on two parallel machines with reassignment under non-simultaneous machine available times. The objective is to minimize the maximum completion time (makespan). We study two different versions and propose the best possible algorithms. Related Articles | Metrics | Comments（0）

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The Elimination Cutwidth Problem for Graphs ZHANG Zhen-Kun, GAO Feng-Xin Operations Research Transactions    2010, 14 (3): 32-40.   Abstract （1611）            Knowledge map    Save The graph-searching problem is a well-known $NP-$complete problem in combinatorial optimization. Now we make a restriction on the graph-searching problem that an edge is closed as soon as it is searched and need not be searched again. The problem arises from epidemic prevention,  the maintenance and repairing of pipeline networks, etc. This restrictive graph-searching problem can be transformed into the elimination cutwidth problem for graphs. In this paper, a polynomial-time algorithm and some fundamental properties of elimination cutwidth $EC(G)$ are mainly presented. Also, the relations with other parameters (such as treewidth and pathwidth) and some special graph results are discussed.   Related Articles | Metrics | Comments（0）

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Inexact Newton  Method for  Semismooth Operator  Equations in Banach Space LIU Jing, GAO Yan Operations Research Transactions    2010, 14 (3): 41-47.   Abstract （1672）            Knowledge map    Save In this paper, we propose two inexact Newton methods for locally Lipschitzian semismooth function and prove  their local convergence results under some conditions. The present inexact Newton methods could be viewed as the extensions of previous ones with same convergent results in finite-dimensional space.   Related Articles | Metrics | Comments（0）

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YUAN Wan-Lian, DI Ming-Qing Operations Research Transactions    2010, 14 (3): 48-54.   Abstract （1454）            Knowledge map    Save An L(3,2,1)-labeling of a graph G is a function from the vertex set V(G) to the set of all nonnegative integers such that |f(u)-f(v)|> 3 if d_G(u,v)=1,|f(u)-f(v)|> 2 if d_G(u,v)=2, and |f(u)-f(v)|> 1, if d_G(u,v)=3. The L(3,2,1)-labeling problem is to find the smallest number _3(G) such that there exists an L(3,2,1)-labeling function with no label greater than it. In this paper, we study this problem for chordal graphs. We obtain bounds of \lambda_3 number for chordal graphs and its subclasses, such as fan, r-path, r-tree and so on. Related Articles | Metrics | Comments（0）

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A New Vehicle Routing Problem and It's Two Stage Algorithm WANG Ke-Feng, YE Chun-Ming, TANG Guo-Chun Operations Research Transactions    2010, 14 (3): 55-63.   Abstract （2122）            Knowledge map    Save In this paper, a new vehicle routing problem, split and simultaneous pickup and delivery vehicle routing problem with time windows constraints (SVRPSPDTW), was provided for the first time under the actual background in the third party logistics of auto parts. Then the mathematic model of this problem and the heuristic algorithm to solve the problem, i.e. two stage algorithm,  was given. In the end, the computational experiment was done based on the modified Solomn's benchmark. Related Articles | Metrics | Comments（0）

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rojected Self-Scaling Symmetric Rank One Quasi－Newton Methods for Nonlinear Monotone Equations LIU Hao, QIAN Xiao-Yan, NI Qin Operations Research Transactions    2010, 14 (3): 64-72.   Abstract （1963）            Knowledge map    Save  In this paper, two self-scaling symmetric rank one algorithms  with projection are proposed for solving nonlinear monotone equations. In the two algorithms, a simple  rule in choosing parameters in symmetric rank one is modified and  a cautious update rule is used. Under the condition that the nonlinear  monotone function is Lipschitz  continuous, the global convergence of these two algorithms is proved.  Compared with the same type BFGS algorithms, some preliminary numerical  experiments  are also done. The results indicate that the numerical performance of   SSR1 class algorithms may be competitive with that of the counterparts. Related Articles | Metrics | Comments（0）

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A Polynomial Time Algorithm for the Economic Lot－size  Problem with Multiple Transportation Channels BAI Qing-Guo, XU Jian-Teng, ZHANG Yu-Zhong Operations Research Transactions    2010, 14 (3): 73-82.   Abstract （1924）            Knowledge map    Save For the centralization of management,reduction in cost,and  reinforcement of the competitive advantage,the supplier usually concentrates on production and utsources the transportation of products to a Distribution Center. The Distribution Center decides the modes and the time to transport  according to the demand of the retailer.  Hence the supplier, Distribution Center and the retailer form   a two-echelon supply chain system.  This paper considers the economic lot-size problem of   the two-echelon supply chain in which the transportation modes   are characterized by different all-unit quantity discount cost structures.   Several optimality properties are proposed for this problem,  and a polynomial time algorithm is developed for a special case.   Related Articles | Metrics | Comments（0）

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Simulated Annealing Algorithm for Vehicle Routing  Problem with Time Window under Time-Dependent YANG Shan-Lin, MA Hua-Wei, GU Tie-Jun Operations Research Transactions    2010, 14 (3): 83-90.   Abstract （2108）            Knowledge map    Save The vehicle routing problem with time window (VRPTW) is one of the routing optimization problems with capacity and time window constraints. Most of the literatures about it suppose that vehicle's speed is constant and ignore the influence of dynamic factors. We consider the speed as a time-dependent piecewise function, and use simulated annealing algorithm to solve the VRPTW under time-dependent.Experiment results show that the algorithm can solve the problem efficiently.   Related Articles | Metrics | Comments（0）

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Rule of Fictitious Play in the Learning Process  with Incomplete Learning Times DING Zhan-Wen, CAI Chao-Ying, YANG Hong-Lin, JIANG Shu-Min Operations Research Transactions    2010, 14 (3): 91-100.   Abstract （1935）            Knowledge map    Save In this paper we have generalized the time frequency of learning in the repeated games to study the problems of strategy converging and utility consistency under the fictitious play rule.  We have showed that in the process of incomplete learning, the strict Nash Equilibria are absorbing for the fictitious play provided they are played by uniform learning and the fictitious play has the property of utility consistency when the learning times are frequent enough and the fictitious play exhibits infrequent switches. Related Articles | Metrics | Comments（0）

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Models to Hedge Whole Period Risks   and Empirical Analysis Operations Research Transactions    2010, 14 (3): 101-108.   Abstract （2139）            Knowledge map    Save The traditional hedging models only consider the asset risk at the end of hedging period and the information supplied by the sample of assets prices are not fully taken into account. A kind of hedging models,called whole period hedging models, are proposed to fully take the information of assets prices into account and to consider the risks of hedging assets at the whole hedging period. The whole period hedging models control the risks in a stable level during the whole hedging period by minimizing the asset risks of different time periods within the hedging period. Empirical analyses and comparisons are made based on Hu-Shen 300 index and it's simulated stock index future. GARCH curves are presented to show the dynamic ffects of these hedging models. Empirical and comparison results show that the effects of the whole period hedging models are better than those of the traditional hedging models, and that the whole period hedging models can reduce the risks when the hedging is terminated ahead of the hedging period.  Related Articles | Metrics | Comments（0）

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A Filter Algorithm for Minimax Problems YANG Xiao-Hui Operations Research Transactions    2010, 14 (3): 109-121.   Abstract （1614）            Knowledge map    Save In this paper, a filiter algorithm is proposed to solve Minimax problems with inequality constrains.  Based on the sequential quadratic programming method, the penalty function is not  required by filter strategy. Under some suitable conditions, the global convergence and superlinear  convergence are obtained. Some numerical results show that the method in this paper is effective. Related Articles | Metrics | Comments（0）

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Extended AS-GN Hybrid Conjugate Gradient Method YAN Hui, Chen-Lan-Ping Operations Research Transactions    2010, 14 (3): 122-128.   Abstract （1692）            Knowledge map    Save In this paper, we propose a new algorithm for unconstrained optimization.It makes  Touati-Ahmed and Storey's  and Nocedal and Gilbert's hybrid conjugate gradient methods to be special cases under precise line search.From the construction of the new formula $\beta_{k}$, the   new algorithm satisfies descent  conditions turally. And this property depends neither on the line search used nor on the convexity of the objective function.Under normal conditions, we prove the new method  can ensure the global convergence. Numerical results also show its efficiency.   Related Articles | Metrics | Comments（0）

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