集值向量优化问题ε-超有效解的性质

本文讨论了ε-超有效点的性质，并给出了ε-超有效解集连通性的证明．     

多目标最优化恰当有效解的稳定性

主要研究当两种类型的参数扰动时,多目标最优化问题中恰当有效解的稳定性.在点集映射的连续性意义下,分析讨论这种稳定性问题并分别给出引起扰动的两参数u,v所对应的点集映射Q1(u)和Q2(v),同时严格证明了在两个闭凸锥U,V上Q1(u)和Q2(v)的连续性定理.最后,通过附注对其进行补充和改进.     

集值映射向量优化问题ε-超有效解集的连通性

本文在赋范向量空间中讨论集值映射向量优化问题的ε-超有效性，在锥-半连续和广义锥-次类凸的假设条件下，获得了ε-超有效点(解)集的连通性结果．     

目标函数扰动的集值优化问题的稳定性

本文研究了由目标函数扰动的集值优化问题的有效点集所定义的集值映射的半连续性.讨论了目标函数扰动的集值优化问题在上半连续意义下的稳定性.特别地,在广义适定性条件下,证明了集值优化问题在上半连续意义下的稳定性.     

扰动集值优化问题超有效点集的次微分稳定性

在锥序Banach向量空间引入了集值映射在超有效意下的次微分(次梯度);在一定的条件下,证明次微分(次梯度)的存在性;得到了序扰动、双扰动集值优化问题超有效点集在次微分意义下的稳定性．     

关于超有效点的注记

本文首先给出了赋范空间中Ｂｏｒｗｅｉｎ超有效点定义的二个与范数无关的等价形式,从而得出推广超有效点到局部凸空间的二个途径,并通过例子说明其中之一是不恰当的．我们还给出了超有效点集连通的二个结果．最后,我们指出文［１］引入的严有效点就是Ｈｅｎｉｇ有效点,其主要定理（［１］定理７）是［２］中定理３．３的特例     

多目标规划α—较多有效解的稳定性

本文借助于对非凸的α─较多锥的分解，得到多目标规划的卜较多有效解在半连续意义下的稳定性结果．     

集值映射最优化问题超有效解集的连通性

本文在局部凸空间中对集值映射最优化问题引入超有效解的概念．首先研究了超 有效点的一些重要特性．其后证明了当目标函数为锥类凸的集值映射时，其目标空间里 的超有效点集是连通的；若目标函数为锥凸的集值映射时，其超有效解集也是连通的．     

含约束集值映射超有效解集的连通性

在局部凸拓扑线性空间中给出了含约束集值映射超有效解的连通性定理,当目标函数及约束映射为锥弧连通的集值映射时,其超有效解集是连通的.     

Orlicz空间中支撑映射的上(下)半连续点

该文给出了赋Ｏｒｌｉｃｚ范数的Ｏｒｌｉｃｚ空间Ｌ°Ｍ中的点是支撑映射的上（下）半连续点的充分必要条件；推出了支撑映射为上（下）半连续的判别准则．     

The Ekeland variational principle for Henig proper minimizers and super minimizers

In this paper we consider, for the first time, approximate Henig proper minimizers and approximate super minimizers of a set-valued map F with values in a partially ordered vector space and formulate two versions of the Ekeland variational principle for these points involving coderivatives in the sense of Ioffe, Clarke and Mordukhovich. As applications we obtain sufficient conditions for F to have a Henig proper minimizer or a super minimizer under the Palais-Smale type conditions. The techniques are essentially based on the characterizations of Henig proper efficient points and super efficient points by mean of the Henig dilating cones and the Hiriart-Urruty signed distance function.     

锥上半连续锥拟凸集值映射多目标优化超有效解集的连通性

本文研究集值映射多目标优化超有效解集的连通性,在目标映射为锥上半连续和锥拟凸的条件下,证明了其超有效解集是连通的.     

Super efficiency in convex vector optimization

We establish a Lagrange Multiplier Theorem for super efficiency in convex vector optimization and express super efficient solutions as saddle points of appropriate Lagrangian functions. An example is given to show that the boundedness of the base of the ordering cone is essential for the existence of super efficient points.Research is supported partially by NSERC.Research is supported partially by NSERC and Mount St. Vincent University grant.     

STABILITY OF MAJORLY EFFICIENT POINTS AND SOLUTIONS IN MULTIOBJECTIVE PROGRAMMING

ＳＴＡＢＩＬＩＴＹＯＦＭＡＪＯＲＬＹＥＦＦＩＣＩＥＮＴＰＯＩＮＴＳＡＮＤＳＯＬＵＴＩＯＮＳＩＮＭＵＬＴＩＯＢＪＥＣＴＩＶＥＰＲＯＧＲＡＭＭＩＮＧＧＵＧＵＯＨＵＡＡＮＤＨＵＹＵＤＡ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓａｎｄＭｅｃｈａｎｉｃｓ...     

Non-autonomous perturbation of autonomous semilinear differential equations: Continuity of local stable and unstable manifolds

In this paper we prove a result on lower semicontinuity of pullback attractors for dynamical systems given by semilinear differential equations in a Banach space. The situation considered is such that the perturbed dynamical system is non-autonomous whereas the limiting dynamical system is autonomous and has an attractor given as union of unstable manifold of hyperbolic equilibrium points. Starting with a semilinear autonomous equation with a hyperbolic equilibrium solution and introducing a very small non-autonomous perturbation we prove the existence of a hyperbolic global solution for the perturbed equation near this equilibrium. Then we prove that the local unstable and stable manifolds associated to them are given as graphs (roughness of dichotomy plays a fundamental role here). Moreover, we prove the continuity of this local unstable and stable manifolds with respect to the perturbation. With that result we conclude the lower semicontinuity of pullback attractors.     

向量优化问题有效解的稳定性

运用标量化的方法,通过锥正定真有效解的上半连续性讨论了无限维赋范空间中锥有效解的部分上半连续性,证明了锥有效解的通有稳定性.在此基础上,进一步证明,在Baire纲的意义下,绝大多数的向量优化问题至少存在一个锥正定真有效解是本质的有效解,换句话说,绝大多数的向量优化问题锥有效解是几乎下半连续的.     

向量优化问题有效点集的稳定性

在不需要紧性假设下,利用拟C-凸函数及回收锥的性质,建立了向量优化问题有效点集的稳定性, 获得了一列目标函数和可行集均扰动情形下的向量优化问题与对应的向量优化问题有效点集的Painlevé Kuratowski内收敛性结果．所得结果推广和改进了相关文献(Attouch H, Riahi H. Stability results for Ekeland’s ε-variational principle and cone extremal solution; Huang X X. Stability in vector-valued and set-valued optimization)中的相应结果, 并给出例子说明了所得结果的正确性.     

赋范线性空间集合的严有效点

本文引入一个新的有效点概念一严有效点,它是Borwein超有效点的推广.此外还讨论了严有效点的基本性质:存在性条件、纯量化特征、稠密性定理以及与Borwein超有效点的关系.     

Upper semicontinuity of pullback attractors for multi-valued random cocycle

In this paper we study the upper semicontinuity of random attractors for multi-valued random cocycle when small random perturbations approach zero or small perturbation for random cocycle is considered. Furthermore, we consider the upper semicontinuity of random attractors for multi-valued random cocycle under the condition which the metric dynamical systems is ergodic.