First , locally invex set is defined and based on it a class of new generalized convex function called semilocally - subinvex function is defined 摘要首先引入了局部不变凸集的概念，在此基础之上，定义了一类新的广义凸函数一半局部-次不变凸函数。
The detail contents were as follows ( a ) firstly , based on the convex modeling of uncertainties , interval finite element methods for uncertain structures were studied 具体内容如下： ( 1 )基于不确定性的凸集模型描述，研究了不确定结构的区间有限元解法。
In the light of the weakness of the traditional method , this thesis improves the point spread function ( psf ) of the imaging system . meanwhile , this thesis adds line process as a priori to set up several convex constraint sets 针对传统凸集投影估计法的缺点,本文提出了改进的点扩散函数,同时利用图像的先验知识,提出了加入线过程作为凸约束。
Chapter 2 established derivatives of a class of set - valued maps and differentials of subdifferential maps of convex functions in the sense of tyurin ( 1965 ) and banks & jacobs ( 1970 ) based on theories of convex pairs space 在第2章中，建立了一类基于凸集对空间的理论在tyurin ( 1965 )和banks & jacobs ( 1970 )意义下集值映射的导数的计算公式和凸函数的次微分映射的微分。
Alike with the convex modeling of uncertainties , the presented method requires less for available information than probabilistic method , thereby , which provided a possible choice for the reliability analysis and design of structures when available information is lack or limited 和不确定性的凸集模型描述一样，所提方法对不确定参量已知数据的要求较低。且直观、简捷。从而为掌握数据信息较少时结构的可靠性评估提供了依据。
Although some results on convex and concave iterative roots are known , there are no results about convexity for more general iterative equations . in this chapter , convexity of both increasing solutions and decreasing solutions is investigated by the divided difference theory and fixed point theory 本章在连续函数构成的紧凸集上构造一个连续自映射算子，利用均差理论和不动点理论证明了线性型迭代方程的凹凸解的存在唯一性及连续依赖性。
In this thesis , some topics in vector optimization theory with set - valued maps are discussed . the concept of generalized subconvexlike set - valued map is defined , and some important properties of the new concept are discussed in linear space . under the assuption of generalized subconvexlikeness , a gordan - farkas type alternative theorem is proved 在线性空间中定义了广义次似凸集值映射的概念，并讨论了它的一些重要性质。在广义次似凸性假设下，证明了gordan - farkas型的择一性定理。
The character of the constraints ( i . e . , the feasible domain of the constraints ) is analysed in this paper . an important conclusion is that the feasible domain of frequency constraints is no convex , while the others are convex . therefore , the frequency constraint is the key constraint for the existence of the solution 对结构优化设计的约束的性质(即约束的可行域)进行了分析，得出了固频约束的可行域是非凸集，其余约束的可行域是凸集，固频约束是决定优化解是否存在的关键约束等有益结论； 3
General convex sets and convex functions : g - convex sets and g - convcx functions are investigated , some properties of which arc achieved , the cti - tcrions of g - convcx functions and g - quasiconvcx functions arc given , the theory of general convexity is deepen : two kinds of general variational inequality problems are studied 讨论了一类广义的凸集和凸函数： g -凸集和g -凸函数，得出了若干性质，给出了g -凸函数和g -拟凸函数的判别准则，丰富了广义凸性的内容；研究了两类广义的变分不等式问题。
Abstract : in this paper , we investigate some properties of cone - continuous vector - valued functionsand the greatest cone lower bound , and prove the connectedness of the cone efficient solutionset for a cone - continuous vector - valued cone - quasiconcave function under the condition thatthe image set is cone - convex 文摘:本文讨论了锥连续函数及锥最大下界的性质,在此基础上讨论了锥连续锥拟凹向量函数最大化问题有效解集的连通性,证明了当象集为锥凸集时锥有效解集是连通的
