A POTENTIAL REDUCTION ALGORITHM FOR MONOTONE VARIATIONAL INEQUALITY PROBLEMS

1.IntroductionLetKbeanonemptyclosedconvexsubsetofR"andletF:R"-R"beacontinuousmapping.Avariationalinequalityproblem(VIP)istofindapointx*eKsuchthatThevariationalinequalityproblemmakesitswideappearanceinthestudyofvariousequilibriummodelsineconomics,oper...     

HIGHLY NONCONFORMING FINITE ELEMENT APPROXIMATIONS FOR A FOURTH ORDERVARIATIONAL INEQUALITY WITH CURVATURE OBSTACLE

The purpose of this paper is to obtain the optimal error estimates of O(h) for the highly nonconforming elements to a fourth order variational inequality with curvature obstacle in a convex domain with simply supported boundary by using the novel function splitting method and the orthogonal properties of the nonconforming finite element spaces.Morley‘s element approximation is our special case.     

ON THE CONVERGENCE ANALYSIS OF ALGORITHMS FOR GENERALIZED SET-VALUEDVARIATIONAL INCLUSIONS IN BANACH SPACES

In this paper, we are devoted to the convergence analysis of algorithms forgeneralized set-valued variational inclusions in Banach spaces. Our results improve, extend,and develop the earlier and recent corresponding results.     

CONVERGENCE RATE ANALYSIS OF MULTIPLICATIVE SCHWARZ ALGORITHM FOR ELLIPTIC VARIATIONAL INEQUALITIES

1 IntroductionWith the development of computer science, decomposition methods have been widely usedin solving large sparse lineax systems arising from the discretization of seifadjoint or nonseifad-joint elliptic boundary value problems (see, e.g., [1--6]). These methods have also been used tosolve variational inequalities (see [7--13] and the references therein). Recently, decompositiontechniques have been introduced to solve discrete problems of variational inequalities. An algthrithm of thi…     

A NEW ALGORITHM FOR PURX O-1 LINEAR PROGRAMS WITH INEQUALITY CONSTRAINTS

ＡＮＥＷＡＬＧＯＲＩＴＨＭＦＯＲＰＵＲＸＯ－１ＬＩＮＥＡＲＰＲＯＧＲＡＭＳＷＩＴＨＩＮＥＱＵＡＬＩＴＹＣＯＮＳＴＲＡＩＮＴＳ￥ＣＨＥＮＪｉａｎｆｅｉ（ＢｉｏｃｈｅｍｉｃａｌＥｎｇｉｎｅｅｒｉｎｇＳｔａｔｅＫｅｙＬａｂｏｒａｔｏｒｙ，Ｂｅｉｊｉｎｇ１０...     

POSITIVE SOLUTIONS FOR DIRICHLET PROBLEMS OF SINGULAR SEMILINEAR ELLIPTIC EQUATIONS

ＰＯＳＩＴＩＶＥＳＯＬＵＴＩＯＮＳＦＯＲＤＩＲＩＣＨＬＥＴＰＲＯＢＬＥＭＳＯＦＳＩＮＧＵＬＡＲＳＥＭＩＬＩＮＥＡＲＥＬＬＩＰＴＩＣＥＱＵＡＴＩＯＮＳ￥ＣＵＩＳｈａｎｇｂｉｎ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＬａｎｚｈｏｕＵｎｉｖｅｒｓ...     

SENSITIVITY ANALYSIS IN BILEVEL LINEAR PROGRAMMING

1.IntroductionMultilevelprogrammingmodelsdescribesdecisionmakingsituationswhereahierarchyexists.Inabilevelsystem,thedecisionofthehigherlevel(leader)mayaffectthechoiceofstrategyavailabletothelowerlevel(follower)whoattemptstooptimizehisobjectivefunction.Inthissystem,theleaderalsoconsidersthefollower'sresponsewhichisbasedonoptimizingthefollower'sobjectivefunction,forinstance,see[1].Asanextensionandavariationofmathematicalprogramming,multilevelprogrammingwasfirstintroducedbyCandlerandTownsley[2].…     

CONVEXIFICATION AND CONCAVIFICATION METHODS FOR SOME GLOBAL OPTIMIZATION PROBLEMS

In this paper, firstly, we propose several convexification and concavification transformations to convert a strictly monotone function into a convex or concave function, then we propose several convexification and concavification transformations to convert a non-convex and non-concave objective function into a convex or concave function in the programming problems with convex or concave constraint functions, and propose several convexification and concavification transformations to convert a non-monotone objective function into a convex or concave function in some programming problems with strictly monotone constraint functions. Finally, we prove that the original programming problem can be converted into an equivalent concave minimization problem, or reverse convex programming problem or canonical D.C. programming problem. Then the global optimal solution of the original problem can be obtained by solving the converted concave minimization problem, or reverse convex programming problem or canonical D.C     

A MATHEMATICAL PROGRAMMING MODEL FOR THE COEXISTENCE OF COMPETITIONS AND COOPERATIONS PROBLEMS

We study in this paper a mathematical programming model for the coexistence of competitions and cooperations problems. We introduce a new solution concept, s-optimal solution for the problem, which always exists under compact and continuous conditions. It is shown that an s-optimal solution can be obtained by solving a nonlinear programming problem. Some examples are given to explain how to compute an s-optimal solution.     

AN ANALYSIS OF SPLITTING EXTRAPOLATION FOR MULTIDIMENSIONAL PROBLEMS

The splitting extrapolation is an important technique for solving multidimensionalproblems.In the case that error u~h-u has an asymptotic expansion of form Σc_αh~(2α),whereα=(α_1,…,α_s) and h~α=h_1~(α_1),…h_s~(α_s),the method gives an approximation involving less computerstorage and less computational work in comparison with the classical Richardson extrapolation.In this paper we present a recurrence rule of the splitting extrapolation and discuss itsapplications in the fields of multiple integrals,multidimensional integral equations,partialdifferential equations and singular perturbation problems.     

THEORETICAL AND NUMERICAL COMPARISON ON DOUBLE-PROJECTION METHODS FOR VARIATIONAL INEQUALITIES

Recently, double projection methods for solving variational inequalities have received much attention clue to their fewer projection times at each iteration. In this paper, we unify these double projection methods within two unified frameworks, which contain the existing double projection methods as special cases. On the basis of this unification, theoretical and numerical comparison between these double projection methods is presented.     

带有参数的C~2R模型的灵敏度分析

文献［１］“带有参数的数据包络分析Ｃ２Ｒ模型”的研究中，要求被评价决策单元的输入或输出指标按同比例变化，而实际总是按一定的比例变化的同时并带有一定的摄动，尤其在多输入、多输出问题上更为普遍。因此本文给出了带有摄动的参数数据包络分析模型，讨论了这种模型的有关性质，同样也给出了阀值的概念，并给出了求解阀值的方法。实际上也从另一个角度提供了一种ＤＥＡ灵敏度分析方法。     

求解模糊线性规划问题的拟人化算法

提出一种求解模糊线性规划的拟人化算法．它模拟人的调节过程,将模糊控制思想嵌入到遗传算法的变异与交叉算子之中求解出一个模糊优解,取代了以往利用单纯形求解模糊线性规划问题的一个最优解．实验结果表明,算法有潜力解决实际的规划问题．     

OPTIMALITY CONDITIONS FOR NONCONVEX BILEVEL PROGRAMMING PROBLEMS

Recomendation.ThisworkisrecomendedbyamemberiftheEditorialBoard,ProfWANGShouyang.1.IntroductionThebilevelprogrammingproblemcanbestatedasfollows:whereS(x),foreachx,isthesolutionsetofthefollowingparametricprogrammingproblem:whereF,f:Re ~-R,g'Re ~-R"andG:Re ~…     

MAXIMUM ENTROPY METHODS FOR CONSTRAINED OPTIMIZATION AND MINIMAX PROBLEMS

ＭＡＸＩＭＵＭＥＮＴＲＯＰＹＭＥＴＨＯＤＳＦＯＲＣＯＮＳＴＲＡＩＮＥＤＯＰＴＩＭＩＺＡＴＩＯＮＡＮＤＭＩＮＩＭＡＸＰＲＯＢＬＥＭＳ￥ＴＡＮＧＨｕａｎｗｅｎ；ＺＨＡＮＧＬｉｗｅｉ；ＷＡＮＧＸｕｅｈｕａ（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄｍａｔｈｅｍ...     

DUALITY FOR A CLASS OF NONSMOOTHMULTIOBJECTIVE PROGRAMMING PROBLEMS

In this paper, two new dual models of nonsmooth multiobjective programmingare constructed and two duality results are derived.     

AN SQP METHOD BASED ON SMOOTHING PENALTY FUNCTION FOR NONLINEAR OPTIMIZATION WITH INEQUALITY CONSTRAINT

1 IntroductionIn tabs paper, we consider the following nonlinear optbostion problem:where j: Re - R, g: Re - Re are continuously ~ntiable functinns. SoP method forproblem (1) generates a sequence of points which converges to a K--T point of problem (1)through the following iterate formulaxk 1 = x* adds (2)adhere da is the solution of the following quadratic Prograrxuning problemin which Bh is a sylnlnetric positive deflate lllatris and A* is a stepsise obtained by some lineseaxch to redu…     

BOOLEAN LATTICE CONDITIONS OF SYSTEM RECONSTRUCTABILITY ANALYSIS PROBLEMS WITH LOGICAL RELATIONS

The concepts of logically constrained overall systems and subsystems of recon-structability analysis are introduced. Then the paper gave an important basis for furtherresearches of the author-the sufficient conditions for their structural representation graphsto become Boolean lattices, and proved it.     

POSITIVE SOLUTIONS OF SINGULAR SUBLINEAR SECOND ORDER BOUNDARY VALUE PROBLEMS

1.IntroductionBoundaryvaluepr0blemsconcerningthegeneralizedEmden-F0wlerequationsx p(t)x'=O,(1)wherep(t)eC(O,1),p(t)20f0rtE(O,1),AER,havebeenstudiedbymanyauthors(see[1-51andthereferencestherein).InthispaperwetreattheDirichletproblem(1)withax(0)-bx'(0)=O,c…     

A ROBUST SQP METHOD BASED ON A SMOOTHING APPROXIMATE PENALTY FUNCTION FOR INEQUALITY CONSTRAINED OPTIMIZATION

1 IntroductionConsider the following inequality constrained optiInization problem:Inin f(x)xeRn(1)s.t. g(x) 5 0where f: R1'-R, g: R"-Rm are cofltinuousIy differentiable functions.SQP method for soIving problem(1) is to gellerate a sequence {xk} converging…