序线性空间中向量极值问题的最优性条件

本文在序线性空间中建立了广义次似凸映射下的择一定理,运用此定理,得出一类向量极值问题的最优性条件.     

线性空间中向量极值问题的鞍点

首先在序线性空间中引入广义次似凸映射 ,建立其择一定理 .然后 ,在这种空间中定义向量 Fritz-John鞍点和向量 Kuhn- Tucker鞍点 ,我们讨论了其二者之间以及向量极值问题的弱有效解与他们的关系 .     

线性拓扑空间中向量极值问题的广义 Kuhn-Tucker 条件

文[1]对 n 维欧氏空间 R~n,建立了在次似凸(Subconvexlike)映射下的择一定理,并以此证明具有弱凸性的极大极小定理.本文将择一定理推广到序线性拓扑空间,从而得出向量极值问题的广义 Kuhn-Tucker 条件和 Lagrange 乘子存在定理.     

一类向量极值问题的最优性条件

本文利用序线性空间中关于次似凸集值映射的择一性定理,得出了具有广义等式和不等式约束的向量极值问题的最优性条件.     

(u,02)-广义次似凸映射的择一定理及其对向量优化的应用

在序线性拓扑空间中,引入（u,02）-广义次似凸映射,建立了（u,02）-广义次似凸映射的一个择一定理.最后,利用此定理,在序线性拓扑空间中得到了带广义不等式约束的向量极值问题的最优性必要条件和充分条件.     

乘积Banach空间中等式约束向量极值问题的最优性必要条件

本文利用Banach空间中的隐函数定理和序线性拓扑空间中对于次似凸向量值映射的择一定理,得出了乘积Banach空间中具有等式约束向量极值问题的若干最优性必要条件.     

Banach空间中向量极值问题的Lagrange定理及Kuhn-Tucker条件

Lin讨论了有限维空间中带约束的向量极值问题有效解的一阶必要条件.最近,Minami讨论了变量在局部凸拓扑空间,有限个目标的一类多目标问题弱有效解的必要条件.Borwein利用切锥强化了Goffrion 真有效解概念,进而得到了从局部凸空间到局部凸空间(或Banach空间)的映象的带约束的向量极值问题真有效解的Lagrange乘子定理和Kuhn-Tucker条件.这些结果基于中证明的一个凸锥分离性定理及真有效解     

向量极值问题的一种含有梯度的最优性条件

本文在赋范空间中引入 G-可微函数的梯度概念 ,利用择一定理 ,我们获得了向量极值问题含有梯度的的最优性条件     

线性空间中具有集到集映射的向量极值问题的Lagrange乘子定理

本文在没有任何拓扑结构的条件下，即在非常一般的线性空间中，首先利用Ｍｏｒｒｉｓ序列定义了集到集凸映射的概念，其次证明了集到集映射的Ｆａｒｋａｓ－Ｍｉｎｋｏｗｓｋｉ定理，然后讨论了具有集到集映射的向量极值问题的Ｌａｇｒａｎｇｅ乘子定理。     

序凸锥为非点式锥时向量极值问题的Lagrange乘子定理

本文在非常一般的偏序线性空间中,利用Morris序列以及商空间理论,讨论了序凸锥为非点式锥,且所含映射的均为集到集映射的向量极值问题的Lagrange乘子定理。     

Characterizations of ultrabarrelledness and barrelledness involving the singularities of families of convex mappings

Summary The paper reveals that ultrabarrelled spaces (respectively barrelled spaces) can be characterized by means of the density of the so-called weak singularities of families consisting of continuous convex mappings that are defined on an open absolutely convex set and take values in a locally full ordered topological linear space (respectively locally full ordered locally convex space). The idea to establish such characterizations arose from the observation that, in virtue of well-known results, the density of the singularities of families of continuous linear mappings allows to characterize both the ultrabarrelled spaces and the barrelled spaces.     

The Solvability of Nonlinear Split Ordered Variational Inequality Problems in Partially Ordered Vector Spaces

The concept of nonlinear split ordered variational inequality problems on partially ordered Banach spaces extends the concept of the linear split vector variational inequality problems on Banach spaces, while the latter is a natural extension of vector variational inequality problems on Banach spaces. In this article, we prove the solvability of some nonlinear split vector variational inequality problems by using fixed-point theorems on partially ordered Banach spaces. It is important to notice that in the results obtained in this article, the considered mappings are not required to have any type of continuity and they just satisfy some order-monotonic conditions. Consequently, both the solvability of linear split vector variational inequality problems and vector variational inequality problems will be immediately obtained from the solvability of nonlinear split vector variational inequality problems. We will apply these results to solving nonlinear split vector optimization problems. The underlying spaces of the considered variational inequality problems may just be vector spaces which do not have topological structures, the considered mappings are not required to satisfy any continuity conditions, which just satisfy some order-increasing conditions.     

A Brézis-Browder principle on partially ordered spaces and related ordering theorems

Through a simple extension of Brézis-Browder principle to partially ordered spaces, a very general strong minimal point existence theorem on quasi ordered spaces, is proved. This theorem together with a generic quasi order and a new notion of strong approximate solution allow us to obtain two strong solution existence theorems, and three general Ekeland variational principles in optimization problems where the objective space is quasi ordered. Then, they are applied to prove strong minimal point existence results, generalizations of Bishop-Phelps lemma in linear spaces, and Ekeland variational principles in set-valued optimization problems through a set solution criterion.     

序线性空间中向量极值的标量化定理

文[1]在B anach空间中讨论了向量优化问题的标量化问题。本文在序线性空间由凸集分离定理得到了序线性空间中向量极值的标量化定理。     

Stochastische dynamische Optimierung als Spezialfall linearer Optimierung in halbgeordneten Vektorräumen

In his papers [3], [4], [5], Krabs treats general linear programming problems in partially ordered vector spaces. Assuming the closedness of certain cones, he obtains duality and existence theorems. In the present paper, a linear programming problem fulfilling this assumption is derived. Furthermore, it is shown that dynamic programming problems can be treated by linear programming techniques even in the case of general state and action spaces.     

Order Structures in Banach Spaces of Analytic Functions

In this paper we consider some Banach spaces of analytic functions on the unit disk generated by the cone of analytic functions with monotone decreasing Taylor coefficients. We get that some of these spaces are Banach lattices with respect to this cone. Different ordered spaces of linear bounded operators acting between the previous spaces are also investigated, with emphasis on the so-called regular multipliers and Hankel operators.     

Many Familiar Categories can be Interpreted as Categories of Generalized Metric Spaces

The simple concepts of (general) distance function and homometry (a map that preserves distances up to a calibration) are introduced, and it is shown how some natural distance functions on various mathematical objects lead to concrete embeddings of the following categories into the resulting category DIST°: quasi-pseudo-metric, topological, and (quasi-)uniform spaces with various kinds of maps; groups and lattice-ordered abelian groups; rings and modules, particularly fields; sets with reflexive relations and relation-preserving maps (particularly directed loop-less graphs and quasi-ordered sets); measured spaces with Radon-continuous maps; Boolean, Brouwerian, and orthomodular lattices; categories with combined objects, for example topological groups, ordered topological spaces, ordered fields, Banach spaces with linear contractions or linear continuous maps and so on.     

A Theorem of the Alternative and Its Application to the Optimization of Set-Valued Maps

In this paper, we establish a theorem of the alternative in ordered linear topological spaces. Then, optimality conditions for the optimization of set-valued maps are obtained.     

Stability criteria for positive linear discrete-time systems

Positivity - We prove new characterisations of exponential stability for positive linear discrete-time systems in ordered Banach spaces, in terms of small-gain conditions. Such conditions have...