ak-较多锥的有关性质

对于有限维Ｅｕｃｌｉｄ空间中带两个参数的ａｋ－较多锥,本文讨论了它与正锥以及有关较多锥类之间的若干关系．同时,还得到此类锥的一些基本性质．     

拓扑向量空间中锥半连续性与锥拟凸映射

对于拓扑向量空间中的几个锥拟凸映射,讨论了它们之间的若干关系,同时,对锥半连续及锥上半连续映射的锥拟凸性给出了一些结果。     

α—较多锥和严格α—较多锥的内部和闭包

对于有限维Euclid空间中带参数α的α－较多锥和严格α－较多锥,本文通过研究其边界的特性,得到了它们的内部和闭包的表示定理。同时,还讨论了这些开锥和闭锥之间的一些关系。     

αk-较多锥的有关性质

对于有限维Euclid空间中带两个参数的αk-较多锥,本文讨论了它与正锥以及有关较多锥类之间的若干关系,同时,还得到此类锥的一些基本性质。     

γ-锥和严格γ-锥

引入有限维向量空间的γ－锥和严格γ－锥的概念．证明了γ－锥是一类闭锥,严格γ－锥是一类开锥．并且,研究了γ－锥和严格γ－锥与较多锥、严格较多锥及它们的闭包和内部之间的关系．     

r-锥和严格r-锥

引入有限维向量空间的r-锥和严格r-锥的概念,证明了r-锥是一类闭锥,严格r-锥是一类开锥。并且,研究了r-锥和严格r-锥与较多锥、严格较多锥及它们的闭包和内部之间的关系。     

实线性锥距离空间中带有锥W-距离的不动点定理

在实线性锥距离空间中给出锥、W-距离的概念及一些性质．由此在实线性锥距离空间中建立了压缩型和扩张型两类不动点定理,其中压缩条件和扩张条件中均含有锥W-距离．     

锥凸集值映射的基本性质

本文首先在R~m的幂集上定义了一种锥序关系并借助这种序关系定义锥凸集值映射,证明了普通单值凸函数的一些基本性质拓广到这种锥凸集值映射时仍成立.     

二阶奇异微分方程边值问题正解的存在性

该文通过构造一个特殊的锥,利用锥压缩与锥拉伸不动点定理,研究了一类二阶奇异微分方程边值问题两个正解的存在性,改进了最近的一些结果.     

体锥与满足角性质锥之间的关系

本文证明：当锥Λ的极锥是尖锥或由不含θ点的闭球体张成时，Λ是体锥；拟多面体锥Λ和极锥Λ*弱*内部非空锥类是一致的并指出了P．Q．Khanh（1992年）的一个错误．     

张量空间中的多面体锥

本文利用文献 [1 ]中的结果给出了张量空间中多面体锥的性质 ,指出当 K1,K2 分别为 V1,V2中的多面体锥时 ,由它们所生成的 V1 V2 中的最小真正锥也是多面体锥 ,这一条件不仅是充分的也是必要的 .并利用这一结果对多面体锥的已有结论给出了新的证明     

拟平移不变拓扑锥与局部β-凸空间的共轭锥

[1]中提出的局部β-凸分析问题从本质上来说是一种非线性凸分析问题 .为了刻画和研究局部β-凸空间 X的共轭锥 X*β ,本文在抽象凸锥上引进具有拟平移不变性质的拓扑结构 ,第一部分重点研究局部生成拓扑锥与赋范拓扑锥 .第二部分将这两种拓扑锥的一般理论应用于局部 β - 凸空间的共轭锥 X*β 的研究 ,得到 (X*β,U| A)与 (X*β ,‖‖ )的局部生成性与完备性定理等 .     

Characterization of subdual latticial cones in Hilbert spaces by the isotonicity of the metric projection

The subdual latticial cones in Hilbert spaces are characterized by the isotonicity of a generalization of the positive part mapping which can be expressed in terms of the metric projection only. Although Németh characterized the positive cone of Hilbert lattices with the metric projection and ordering only [A.B. Németh, Characterization of a Hilbert vector lattice by the metric projection onto its positive cone, J. Approx. Theory 123 (2) (2003), pp. 295–299.], this has been done for the first time for subdual latticial cones in this article. We also note that the normal generating pointed closed convex cones for which the projection onto the cone is isotone are subdual latticial cones, but there are subdual latticial cones for which the metric projection onto the cone is not isotone [G. Isac, A.B. Németh, Monotonicity of metric projections onto positive cones of ordered Euclidean spaces, Arch. Math. 46 (6) (1986), pp. 568–576; G. Isac, A.B. Néemeth, Every generating isotone projection cone is latticial and correct, J. Math. Anal. Appl. 147 (1) (1990), pp. 53–62; G. Isac, A.B. Németh, Isotone projection cones in Hilbert spaces and the complementarity problem, Boll. Un. Mat. Ital. B 7 (4) (1990), pp. 773–802; G. Isac, A.B. Németh, Projection methods, isotone projection cones, and the complementarity problem, J. Math. Anal. Appl. 153 (1) (1990), pp. 258–275; G. Isac, A.B. Németh, Isotone projection cones in Eucliden spaces, Ann. Sci. Math Québec 16 (1) (1992), pp. 35–52].     

On cone characterizations of weak, proper and Pareto optimality in multiobjective optimization

Efficient, weakly and properly Pareto optimal solutions of multiobjective optimization problems can be characterized with the help of different cones. Here, contingent, tangent and normal cones as well as cones of feasible directions are used in the characterizations. The results are first presented in convex cases and then generalized to nonconvex cases by employing local concepts.     

Intersection cuts for convex mixed integer programs from translated cones

We develop a general framework for linear intersection cuts for convex integer programs with full-dimensional feasible regions by studying integer points of their translated tangent cones, generalizing the idea of Balas (1971). For proper (i.e, full-dimensional, closed, convex, pointed) translated cones with fractional vertices, we show that under certain mild conditions all intersection cuts are indeed valid for the integer hull, and a large class of valid inequalities for the integer hull are intersection cuts, computable via polyhedral approximations. We also give necessary conditions for a class of valid inequalities to be tangent halfspaces of the integer hull of proper translated cones. We also show that valid inequalities for non-pointed regular translated cones can be derived as intersection cuts for associated proper translated cones under some mild assumptions.     

Contingent cone to a set defined by equality and inequality constraints at a Fréchet differentiable point

In this paper, we prove equality expression for the contingent cone and the strict normal cone to a set determined by equality and/or inequality constraints at a Fréchet differentiable point. A similar result has appeared before in the literature under the assumption that all the constraint functions are of classC or under the assumption that the functions are strictly differentiable at the point in question. Our result has applications to the calculation of various kinds of tangent cones and normal cones.This research was supported, in part by the National Science and Engineering Research Council of Canada under Grant No. OGP-41983.The authors would like to thank D. E. Ward for his many helpful comments.     

有效点、弱有效点和真有效点的锥刻画

利用集合在某点的相依切锥、法向锥和可行方向锥等研究向量优化问题的有效点、 弱有效点和真有效点的特征,对局部有效点、局部弱有效点和局部真有效点与集合的各 锥之间的关系作了刻画.     

Generalized isotone projection cones

This article extends the notion of isotone projection cones to generalized isotone projection cones by replacing the usual metric projection with a generalized one. It is shown that all such cones are simplicial.     

Generalized binomial expansion on Lorentz cones

We study some properties of generalized binomial coefficients for symmetric cones and we obtain a generalized binomial expansion formula for Lorentz cones.