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&;#215;V2中的最小值正锥也是正多面体锥,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结出了新的证明。     

带约束不可微凸规划的一个次梯度可行方向法

本文提出了一种计算带约束不可微凸规划问题的算法。这是一种利用有关函数的次梯度的可行方向法,它也可以作为[2]中给出的无约束bundle方法在带有不可微凸的约束情形下的推广。本文给出了算法收敛性的证明。对于求解本算法中所用到的计算多面体凸锥与凸多面体间最短距离这个子问题,也给出了一个收敛性得以保证的方法。     

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．     

锥映象的K.Fan逼近定理及其应用

本文在Banach空间中分别就锥内的闭球、环形区域及球面，对半紧的1－集压缩映象证明了著名的K.Fan逼近定理，本质上改进和推广了文[2]的所有结果。并且应用所得结果给出了关于Banach空间中两点边值问题正固有元和正解的几个存在定理，这也是文[3]主要结果的推广和补充。     

非线性非单调二元算子方程组的解及其应用

利用非线性泛函分析中的锥理论和单调迭代的方法,研究了一类非线性非单调二元算子方程组的解的存在性,并给出了收敛于解的迭代序列,然后作为应用,得到了B anach空间中的一类非线性V olterra型积分方程组的解,改进了最近的许多结果.     

紧Riemann对称空间球带函数为实函数的判别

紧对称空间 M=G/K的球带函数的定义首先由 Cartan给出。文献[2]给出了一些一般结果。本文给出一个判断 C~∞(M,C)中的不可约 G子模 V的球带函数φ_v为实函数的充要条件(定理1):V具有实形式。利用这一结果,我们证明了定理4,具体指出了对哪些V,φ_v是实的。 本文利用了文献[3]的结果,该文解决的是实Lie代数实表示的分类,讨论的是更广泛的问题。     

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。     

锥度量空间中锥的非正规性条件(英文)

该文首先给出锥度量空间中的锥为非正规锥的几个充要条件,随后给出一个例子进行验证.并且在锥度量空间中,当不考虑空间的完备性时,在压缩映射条件下,得到非正规锥的存在性.这些结果直接改进前人关于度量空间的一些结果,也补充他们关于锥度量空间的一些结果.     

自反Banach空间中向量优化问题弱有效解集特性的进一步研究

本文分别研究了在无限维自反Banach空间中,当控制结构为多面体锥时,-般凸向量优化问题和锥约束凸向量优化问题的弱有效解集的非空有界性,并且把结论应用到了一类罚函数方法的收敛性分析上.     

锥中调和函数的下界及其应用

本文首先给出锥中一类调和函数的下界,所得结果推广了张艳慧、邓冠铁和高洁欣在半空间中的相关结论;作为应用,接着证明了锥中的Levin型定理;最后,给出了锥中Dirichlet问题解积分表示形式的唯一性定理.     

Polyhedral cones and positive operators

Some results are obtained relating topological properties of polyhedral cones to algebraic properties of matrices whose columns are the extremal vectors of the cone. In addition, several characterizations of positive operators on polyhedral cones are given.     

关于锥理论的一些注记

指出了再生锥和极小锥之间的关系,证明了一些具体锥的全正则性,探讨了半序空间中上确界的一些不同点,推广和发展了已有文献中的相关结论.     

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.     

The cone of quasi-semimetrics and exponent matrices of tiled orders

Finite quasi semimetrics on n can be thought of as nonnegative valuations on the edges of a complete directed graph on n vertices satisfying all possible triangle inequalities. They comprise a polyhedral cone whose symmetry groups were studied for small n by Deza, Dutour and Panteleeva. We show that the symmetry and combinatorial symmetry groups are as they conjectured.Integral quasi semimetrics have a special place in the theory of tiled orders, being known as exponent matrices, and can be viewed as monoids under componentwise maximum; we provide a novel derivation of the automorphism group of that monoid. Some of these results follow from more general consideration of polyhedral cones that are closed under componentwise maximum.     

A method for constructing the polar cone of a polyhedral cone,with applications to linear multicriteria decision problems

The necessary and sufficient conditions for solution sets of linear multicriteria decision problems are given in the first part of this paper. In order to find the solution sets by applying the theorem describing the conditions, the constructions of the open polar cone and the semi-open polar cone of a given polyhedral cone are required.A method of construction of the polar cone, open polar cone, and semi-open polar cone is presented. For this purpose, edge vectors of the polar cone are introduced and characterized in terms of the generating vectors of a given polyhedral cone. It is shown that these polar cones are represented by the edge vectors.Numerical examples of linear multicriteria decision problems are solved to illustrate the construction of the polar cones and to explain the application of the theorem to obtain the solution sets.The author is grateful to Professor P. L. Yu for helpful comments concerning the development of Theorem 2.1.     

Zero polyhedral cones

Properties of zero polyhedral cones are studied by making use of Fourier-Motzkin eliminations. Algorithms are presented for the characterization of zero polyhedral cones.     

Critical angles in random polyhedral cones

This work concerns the angular structure of random polyhedral cones generated by p stochastically independent vectors uniformly distributed on the unit sphere of Rn. We comment on the expected number of critical angles and the mathematical expectation of the extremal angles.     

Second order duality and symmetric duality for non-linear programs in complex space

A second order dual to a non-linear program with linear constraints in complex space over arbitrary polyhedral convex cones is presented and appropriate duality theorems are established. Also, a pair of second order non-linear symmetric dual programs is formulated and appropriate duality results are proved. It is shown that a second order dual gives a better bound for the objective function than does the first order dual. Some special cases are discussed.     

Critical angles in polyhedral convex cones: numerical and statistical considerations

This work concerns the numerical computation of critical angles in polyhedral convex cones. The set of proper critical angles is evaluated explicitly by solving a series of generalized eigenvalue problems involving the generators of the cone. The local maximal angles are identified by using a necessary condition for local maximality. The expected numbers of critical angles in random polyhedral convex cones are estimated experimentally.     

Bifractional inequalities and convex cones

In this paper we give a systematic study of a class of linear inequalities related to convex cones in linear spaces. In particular, Chebyshev and Andersson type inequalities are discussed. Some classical and new inequalities are derived from the results.