The Alternative Property and Vector Optimization Problem in Ordered Locally Convex Topological Vector Spaces

ＴｈｅＡｌｔｅｒｎａｔｉｖｅＰｒｏｐｅｒｔｙａｎｄＶｅｃｔｏｒＯｐｔｉｍｉｚａｔｉｏｎＰｒｏｂｌｅｍｉｎＯｒｄｅｒｅｄＬｏｃａｌｙＣｏｎｖｅｘＴｏｐｏｌｏｇｉｃａｌＶｅｃｔｏｒＳｐａｃｅｓＷＡＮＧＱｉＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓａｎ...     

多目标主从向量集值优化Benson真有效解的最优性条件

借助 Aubin的 Contingent切导数建立了可微多目标主从向量集值优化弱 Benson真有效元的Fritz-John型最优性条件.     

Generalized invexity-type conditions in constrained optimization

This paper defines a new class of generalized type I functions, and obtains Kuhn-Tucker necessary and sufficient conditions and duality results for constrained optimization problems in the presence of the aforesaid weaker assumptions on the objective and constraint functions involved in the problem.     

交互式广义目标规划决策方法─—满意度决策方法

本文针对社会经济系统中多目标决策问题, 提出了交互式广义目标规决策方法。通过引入满意度的概念, 将决策者对各个目标函数的满意水平数量化, 给出了交互式规划决策算法。     

极小化不可行量函数的Flow Shop变异问题

讨论一类Flowshop的变异问题。在这类变异问题中 ,给定一个截止工期 ,该工期比Flowshop最优调度中的最大完工时间小。讨论的问题是在全部工件的完工时间不超过截止工期的限制下 ,极小化不可行量函数。这类问题与矩阵函数因子分解有着密切联系。基于对问题的分析 ,证明了这一问题等价于单机调度中极小化类似的延迟量函数。推广了已有的结论。     

用投影收缩算法求解考虑排放的交通分配模型

给出一种考虑排放约束条件下的交通分配均衡模型,在所定义的广义出行费用中明确考虑排放因素,通过将变分不等式问题转换成等价的非线性互补问题,采用一种自适应的投影收缩算法求解该模型,所给出的数值算例得到广义费用下的UE最优解,在同样收敛精度的要求下,和其他投影算法相比,采用该算法收敛速度较快.     

MINIMAX PROGRAMMING UNDER GENERALIZED （p, r）-INVEXITY

Minimax programming problems involving generalized （p, r）-invex functions are consid- ered. Parametric sufficient optimality conditions and duality results are established under the aforesaid assumptions on the objective and constraint functions.     

ROLE OF α-PSEUDO-UNIVEX FUNCTIONS IN VECTOR VARIATIONAL-LIKE INEQUALITY PROBLEMS

In this paper, we introduce a new class of generalized convex function, namely, a-pseudounivex function, by combining the concepts of pseudo-univex and α-invex functions. Further, we establish some relationships between vector variational-like inequality problems and vector optimization problems under the assumptions of α-pseudo-univex functions. Results obtained in this paper present a refinement and improvement of previously known results.     

THE SECOND-ORDER CONDITIONS OF NONDOMINATED SOLUTIONS FOR C~(1,?) GENERALIZED MULTIOBJECTIVE MATHEMATICAL PROGRAMMING

In this paper,the generalized Hessian matrix and the generalized second-order directional(?)erivative for C~(1,1)vector functions are defined.The extension of the vector second-order Taylorexpansion is derived.The second-order necessary and sufficient conditions for the local nondominatedsolutions associated with the given convex cone and polyhedral convex cone of the generalizedmultiobjective mathematical programming problem with C~(1,1)constrained functions are discussed.     

NON-CLASSICAL GENERALIZED SOLUTIONS FOR SOME HYPERBOLIC SYSTEMS

1.IntroductionThemostspecialfeatureofconservationlawsofhyperbolicsystemsisthattheirsolutionsalwayshavediscolltinuities.ThiskindofdiscontinuityrepresentstheshoCkwavephenomena.Sopeopleintroducetheideaofgeneralizedsolutionwhichsatisfiesequationsinthesenseofdistribution.Underthisdefinition,alotofachievementshavebeenobtainedsince1950'sinthisfield.However,inrecelltyears,manyauthors(see[l--6])discoveredthatthereisnoexistenceanduniqllenessofsolutionstoRiemannproblemsforsomeconservationlaws.Bynumeric…     

新型小波支持向量机在波动率预测中的实证研究

运用支持向量机进行广义自回归条件异方差(GARCH)模型预测所面临的一个主要问题就是普通核函数难以准确捕捉股指波动率的聚集特征.然而小波函数却具备以任意时间粒度在任意位置刻画任一时间序列的能力.因此,本文基于小波分析与核函数理论,构造了一个满足mercer条件的多尺度小波核来解决这一问题.通过真实股指数据分析,小波支持向量机在波动率预测中的有效性获得了证实.     

广义计算理论研究

概要讨论广义计算的一般化理论 ,包括广义计算模型、广义计算系统、广义学习模型等 ,同时介绍广义计算系统实例 .     

An Exact Solution and its Extensions for Generalized Linear Least Squares Problems

ＡｎＥｘａｃｔＳｏｌｕｔｉｏｎａｎｄｉｔｓＥｘｔｅｎｓｉｏｎｓｆｏｒＧｅｎｅｒａｌｉｚｅｄＬｉｎｅａｒＬｅａｓｔＳｑｕａｒｅｓＰｒｏｂｌｅｍｓＬＩＵＸｉａｏｍｉｎＤｅｐｔｏｆＡｐｐｌｉｅｄＭａｔｈ．，ＢｅｉｊｉｎｇＵｎｉｖｅｒｓｉｔｙｏｆＡｅｒｏｎａ...     

Existence of solutions of generalized quasi-variational relation problems by the inductive relations and some applications

By the inductive relations, this paper first obtains some existence theorems of solutions for generalized quasi-variational relation problems, which are different from other papers. As applications, some existence theorems of solutions for generalized quasi-equilibrium problems and NS-equilibria for noncooperative games under uncertainty are obtained.     

Viability criteria for differential inclusions

A method of verifying the viability criterion at a given point for a region with nonsmooth boundary, which is expressed by a quasidifferentiabl function, under a differential inclusion which is a convex hull of finitely many functions, is proposed. By this method, determining the viability is transformed into solving a number of systems of linear inequalities, or equivalently solving a number of linear programming problems. For the other differential inclusion, called the generalized convex process, it is shown that viability condition holds for a polytope if and only if it holds at all of its vertices. This result is an extension of corresponding one for a linear control system.     

Generalization of the linguistic aggregation operator and its application in decision making

A generalization of the linguistic aggregation functions (or operators) is presented by using generalized and quasiarithmetic means.Firstly,the linguistic weighted generalized mean (LWGM) and the linguistic generalized ordered weighted averaging (LGOWA) operator are introduced.These aggregation functions use linguistic information and generalized means in the weighted average (WA) and in the ordered weighted averaging (OWA) function.They are very useful for uncertain situations where the available information cannot be assessed with numerical values but it is possible to use linguistic assessments.These aggregation operators generalize a wide range of aggregation operators that use linguistic information such as the linguistic generalized mean (LGM),the linguistic OWA (LOWA) operator and the linguistic ordered weighted quadratic averaging (LOWQA) operator.We also introduce a further generalization by using quasi-arithmetic means instead of generalized means obtaining the quasi-LWA and the quasi-LOWA operator.Finally,we develop an application of the new approach where we analyze a decision making problem regarding the selection of strategies.     

KUHN-TUCKER NECESSARY CONDITIONS FOR (h, ψ)-MULTIOBJECTIVE OPTIMIZATION PROBLEMS

Five kinds of cones are introduced, which are used to establish the constraints qualifications, under which the generalized Kuhn-Tucker necessary conditions are developed for a class of generalized (h, (?))-differentiable single-objective and multiobjective programming problems by using Motzkin's alternative theorem and Ben-Tal generalized algebraic operations.     

THE GENERALIZED SOLUTIONS OF PBVP FOR INTEGRO-DIFFERENTIAL EQUATIONS

ＴＨＥＧＥＮＥＲＡＬＩＺＥＤＳＯＬＵＴＩＯＮＳＯＦＰＢＶＰＦＯＲＩＮＴＥＧＲＯ－ＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＺＨＵＡＮＧＷａｎ；ＣＨＥＮＹｕｂｏ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｈａｎｄｏｎｇＮｏｒｍａｌＵｎｉｖｅｒｓ...     

变时滞广义神经网络的指数稳定性

讨论具有可变时滞的Cohen Grossberg广义神经网络平衡态的稳定性问题。以推广的Halanay微分不等式为工具,通过构造合适的Lyapunov函数,结合Dini导数和不等式技巧,对具有可变时滞(适合于任何时滞有界情况)的广义神经网络平衡态的指数稳定性进行分析。在适当的假设条件下,得到了系统渐近指数稳定的几个充分性判据,与此同时也给出了相应的Lyapunov指数。     

具有多值映射的两级优化问题的广义算法研究

两级优化问题是一种非凸非光滑问题，绝大多数问题的求解都是建立在下层有唯一解的基础之上的。而本文针对多值映射，即下层非唯一解的情形，利用隐函数理论，将两级优化问题转化为带有隐函数的非光滑问题，提出求解这类问题的广义算法框架，并证明其收敛性，最后通过实例验证该方法的实用性．