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  relative interior
    Based on concepts of relative algebraic interior and relative topological interior of sets,some conditions assuring Ari+B(A+B)ri in a linear space and conditions assuring riA+Bri(A+B) in a linear topological space are given respectively,according to Tanaka and Kuroiwa' s conclusions. Therefore,Tanaka and Kuroiwa' s conclusions about interior are generalized to the situation of relative interior.
    根据Tanaka和Kuroiwa的结论,在集合相对代数内部和相对拓扑内部概念的基础上,分别讨论了线性空间中Ari+B(A+B)ri和线性拓扑空间中riA+Bri(A+B)成立的条件,从而将Tanaka和Kuroiwa关于内部的结论推广到了相对内部的情形;
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    Conditions Assuring Properties of the Relative Interior of Sets in a Linear Space
    线性空间中集合相对内部性质成立的条件
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    Then relative interior is introduced and an alternative theorem of generalized convex set-valued maps is established by using the separation theorem.
    引进了相对内部, 应用凸集分离定理建立了一个广义凸集值映射的择一性定理.
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    Under the assuption of -generalized convexity,relative interior is introduced,and a Farkas-Minkowski type alternative theorem is proved.
    在 -广义锥凸性假设下,引进相对内部,证明了Farkas-Minkowski型的择一性定理。
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    Some new properties of explicitly quasiconcave functions are presented. These newproperties are expressed in terms of the properties of arid relationships between the levelset, the upper level set, the relative interior, and the relative boundary of the upper levelset.
    本文提出了显拟凹函数的若干新性质.这些新性质是用水平集、上水平集及其相对内部、相对边界的性质与它们之间的关系来表述的.
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  “相对内部”译为未确定词的双语例句
    In this paper we discuss the properties of strongly decomposable operators and prove that strong decomposition of T implies strong decomposition of T~* if every set spectrum F of T~* equal to Fo.
    本文讨论了强可分解算子的若干性质,证明了当T的集合谱为其关于σ(T)的相对内部的闭包时,T强可分解蕴含T强可分解,最后给出了T为强可分解的一个充要条件。
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  relative interior
The relative interior of the base polyhedron and the core
      
In this paper we present an infinite dimensional nonlinear duality theory obtained by using new separation theorems based on the notion of quasi-relative interior, which, in all the concrete problems considered, is nonempty.
      
An interior point of a triangle is calledCP-point if its orthogonal projection on the line containing each side lies in the relative interior of that side.
      
We develop the notion of the quasi relative interior of a convex set, an extension of the relative interior in finite dimensions.
      
Our result depended on a constraint qualification involving the notion ofquasi relative interior.
      
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  relative interiors
Partially finite convex programming, Part I: Quasi relative interiors and duality theory
      
We show that the GIT-classes are the relative interiors of rational polyhedral convex cones, which form a fan in the G-ample cone.
      
They exploit the key facts that the transition probabilities of queueing networks are shift invariant on the relative interiors of faces and the cost functions of interest are linear in the state.
      
A systematic procedure for choosing different quadratic functions on the relative interiors of faces to serve as surrogates of the differential costs in an inequality relaxation of the average cost function leads to linear program bounds.
      


In this paper we discuss the properties of strongly decomposable operators and prove that strong decomposition of T implies strong decomposition of T~* if every set spectrum F of T~* equal to Fo.

本文讨论了强可分解算子的若干性质,证明了当T的集合谱为其关于σ(T)的相对内部的闭包时,T强可分解蕴含T强可分解,最后给出了T为强可分解的一个充要条件。

In this papers the definition of Benson-proper efficient points is generalized. A characterization of the relative interior of a convex cone is given. Without the pointedness assumption, the equivalence between Hartley-proper efficient points and the generalized Bensonproper efficient points is proved by the characterization of relative interiors of convex cones. Several results of scalarization of efficient points and proper efficient points are derived.

本文推广了Benson真有效点的定义,给出了凸锥相对内部的一个刻划,并在无尖性假设情况下,利用凸锥相对内部的刻划,证明了Hartley真有效点与改进的Benson真有效点是等价的;同时给出了一些有效点与真有效点标量化的一些结果.

Some new characterizations of explicitly convex and strictly convex functionsare presented. These new characterizations are expressed in terms of the properties of andrelationships between the graph I the eplgraph, the relative interior, the relative boundary Iand the extreme points of the epigraph.

提出了显凸函数和严格凸函数的若干新特征,这些新特征是用函数的图象、上图象及其相对内部、相对边界、极点的性质与它们之间的关系来表述的。

 
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