小参数时变非线性系统的技术稳定性

分析一类含小参数的时变非线性系统关于给定状态约束集合的技术稳定性.根据向量微分比较原理和基本的单调性准则,利用向量V函数方法给出由系统系数表达的技术稳定性判据.并讨论了基于派生系统和线性化方法研究非线性系统技术稳定性的条件.另外,对于派生时变线性系统的指数稳定性给出了简单的代数判据.最后给出示例说明文中方法.     

向量参变量的约束集族最大元的通有稳定性

利用集值映射方法定义约束广义最大元,在约束条件和向量参变量意义下,讨论了约束最大元映射、向量参数扰动时,特别是约束条件受到扰动时,向量参变量的约束集族最大元的通有稳定性,在最广的扰动下,获得了通有稳定性定理.     

离散扰动下向量均衡问题的稳定性

利用集合序列P—K收敛的概念,讨论了离散扰动下的向量均衡问题弱有效解的稳定性．提出了一个新的向量均衡问题的极小化序列的概念．给出了各种充分条件以确保集合的包含关系,并举例阐述相应的结论．     

平衡问题解的存在性

主要研究平衡问题解的存在性.通过对目标函数和可行集合的渐近分析,给出拟单调平衡问题解集非空的条件.进而用类似的方法研究了向量平衡问题解存在的条件,并将其应用到向量优化问题上.     

物元可拓集集合性质研究

在可拓集合概念基础上,提出了向量可拓集和区间可拓集概念,研究了物元可拓集合的交、并、求补等集合运算及其性质.     

一类具有相同对称/反对称中心的正交平衡向量小波系统的不存在性

本文得到两个结果:首先证明尺度因子m与重数r的乘积为奇数时,具有相同对称/反对称中心1/2(1+μ+μ/m-1)(μ∈N)的正交向量小波系统的不存在性;其次证明尺度因子m=3,重数r为偶数时,具有相同对称/反对称中心1/2(1+μ+μ/m-1)的正交平衡向量小波系统的不存在性,这里N是正整数集合.     

参数非光滑优化的微分稳定性

本文研究了含有向量参数的非光滑优化问题的极值函数或叫做边缘函数的连续性及某种意义下的微分性质。给出了目标函数及不等式约束为李普希兹函数,等式约束为连续可微函数,并且带有闭凸约束集C的非凸非光滑问题的最优值函数的几种方向导数的界,把[4],[1]中关于一个参数的单边扰动推广到向量参数的扰动,亦可认为是把[2]由光滑函数类推广到李普希兹函数类。     

基于最近边界向量的SVM增量学习算法

为了减少求支持向量过程中二次规划的复杂度,利用训练样本集的几何信息,选出两类中离另一类最近的边界向量集合,它是样本中最有可能成为支持向量的一部分,用它代替原样本集进行训练.对新增样本,若存在违反KKT条件的样本,只对这部分新样本进行学习.同时找出原样本中可能转化为支持向量的非支持向量样本.基于分析结果,提出了一种新的基于最近边界向量的增量式支持向量机学习算法.对标准数据集的实验结果表明,算法是可行的,有效的.     

强向量拟均衡问题的存在性

设X是一个实的Hausdorff拓扑向量空间,Y是一个实的局部凸向量空间,C是Y中的闭凸锥,K X是一个紧子集.FX×X→Y是一个双向量函数,GK→2K是一个集合值映射.我们考虑下面的强拟均衡问题存在x∈G(x),使得对任意的y∈G(x),成立F(x,y)∈C.本文证明了当F是半连续时,上述问题解的存在性结论.     

向量互补问题和极小元问题

本文不仅引入了非空集的有效下界的概念,而且引入了新的严格C-伪单调映射,在C-伪单调性的假设下,文内证明了向量互补问题（VCP）的可行集及其相关集合的有效下界和下有效点的存在性。     

Optimality Conditions and Lagrange Duality for Vector Extremum Problems with Set Constraint

The necessary and sufficient optimality conditions for vector extremum problems with set constraint in an ordered linear topological space are given. Finally, Lagrange duality is established.     

Classifying convex extremum problems over linear topologies having separation properties

It is shown that any convex or concave extremum problem possesses a subsidiary extremum problem which has certain homogeneous properties. Analogous to the given problem, the “homogenized” extremum problem seeks the minimum of a convex function or the maximum of a concave function over a convex domain. By using homogenized extremum problems, new relationships are developed between any given convex extremum problem (P) and a concave extremum problem (P¹) (also having a convex domain), called the “dual” problem of (P). This is achieved by combining all possibilities in tabular form of (1) the values of the extremum functions and (2) the nature of the convex domains including perturbations of all problems (P), (P¹), and each of their respective homogenized extremum problems.This detailed and refined classification is contrasted to the relationships obtainable by combining only the possible values of the extremum functions of the problems (P) and (P¹) and the possible limiting values of these functions stemming from perturbations of the convex constraint domains of (P) and (P¹), respectively.The extremum problems in this paper and classification results are set forth in real topologically paired vector spaces having the Hahn-Banach separation property.     

Generalized Clarke Epiderivatives of Parametric Vector Optimization Problems

This paper deals with the generalized Clarke epiderivative of the extremum (or efficient point) multifunction in parametric vector optimization problems. The formulas for computing and/or estimating the generalized Clarke epiderivative of this extremum multifunction are given in terms of the Clarke tangent cone to the graph of a multifunction or the constraint mapping and/or the Fréchet derivative of the objective function. An application to semi-infinite programming is given.     

Constrained Extremum Problems,Regularity Conditions and Image Space Analysis. Part I: The Scalar Finite-Dimensional Case

Image space analysis has proved to be instrumental in unifying several theories, apparently disjoint from each other. With reference to constraint qualifications/regularity conditions in optimization, such an analysis has been recently introduced by Moldovan and Pellegrini. Based on this result, the present paper is a preliminary part of a work, which aims at exploiting the image space analysis to establish a general regularity condition for constrained extremum problems. The present part deals with scalar constrained extremum problems in a Euclidean space. The vector case as well as the case of infinite-dimensional image will be the subject of a subsequent part.     

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.     

Optimal control problems of hyperbolic systems with operator and nonoperator equality constraints

In the paper two kinds of optimal control problems of hyperbolic systems with additional equality constraints are considered: a problem with the operator equality constraint in the form of terminal condition and a problem with nonoperator equality constraint in the u(.)ε U where - some set. The extremum principles are proved: for the first problem - by using some specification of the Dubovitskii-Milyutin method in the case of n equality constraints in the operator form and for the second one - by using some generalization of the Dubovitskii-Milyutin theory     

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。     

Semicontinuity and convergence for vector optimization problems with approximate equilibrium constraints

This paper mainly intends to present some semicontinuity and convergence results for perturbed vector optimization problems with approximate equilibrium constraints. We establish the lower semicontinuity of the efficient solution mapping for the vector optimization problem with perturbations of both the objective function and the constraint set. The constraint set is the set of approximate weak efficient solutions of the vector equilibrium problem. Moreover, upper Painlevé–Kuratowski convergence results of the weak efficient solution mapping are showed. Finally, some applications to the optimization problems with approximate vector variational inequality constraints and the traffic network equilibrium problems are also given. Our main results are different from the ones in the literature.     

Generalized abstract economy and systems of generalized vector quasi-equilibrium problems

The present paper is in two-fold. The first fold is devoted to the existence theory of equilibria for generalized abstract economy with a lower semicontinuous constraint correspondence and a fuzzy constraint correspondence defined on a noncompact/nonparacompact strategy set. In the second fold, we consider systems of generalized vector quasi-equilibrium problems for multivalued maps (for short, SGVQEPs) which contain systems of vector quasi-equilibrium problems, systems of generalized mixed vector quasi-variational inequalities and Debreu-type equilibrium problems for vector valued functions as special cases. By using the results of first fold, we establish some existence results for solutions of SGVQEPs.     

Generalized Hadamard well-posedness for infinite vector optimization problems

In this paper, we study the generalized Hadamard well-posedness of infinite vector optimization problems (IVOP). Without the assumption of continuity with respect to the first variable, the upper semicontinuity and closedness of constraint set mappings are established. Under weaker assumptions, sufficient conditions of generalized Hadamard well-posedness for IVOP are obtained under perturbations of both the objective function and the constraint set. We apply our results to the semi-infinite vector optimization problem and the semi-infinite multi-objective optimization problem.