Benson Proper Efficiency in the Vector Optimization of Set-Valued Maps

This paper extends the concept of cone subconvexlikeness of single-valued maps to set-valued maps and presents several equivalent characterizations and an alternative theorem for cone-subconvexlike set-valued maps. The concept and results are then applied to study the Benson proper efficiency for a vector optimization problem with set-valued maps in topological vector spaces. Two scalarization theorems and two Lagrange multiplier theorems are established. After introducing the new concept of proper saddle point for an appropriate set-valued Lagrange map, we use it to characterize the Benson proper efficiency. Lagrange duality theorems are also obtained  

Characterizations of the Benson Proper Efficiency for Nonconvex Vector Optimization

Under generalized cone-subconvexlikeness for vector-valued mappings in locally-convex Hausdorff topological vector spaces, a Gordan-form alternative theorem is derived. Some characterizations of the Benson proper efficiency under this generalized convexity are established in terms of scalarization, Lagrangian multipliers, saddle-point criterion, and duality.  

熵函数法的数学理论

１．引言考虑复合函数其中ｇ；：Ｒ"－Ｒ，ｉ＝１，２，...；。连续可微．因的ｘ）的不可微性，涉及的ｘ）的优化问题，如极大极小问题Ｉｒｌｍｌｎｏｔｘｊ．ｆｉｊＺＦＲ"通常属不可微优化范畴．文山借助最大嫡原理推导出一类一致逼近一（Ｘ）的可微函数（称之为妨函数）Ｏ。ｉｌｌ--一ｉｆｌｙｌｌＸＤＣＱ．ｌｏｌｌ．ＩＪｊ容易证明ｔｉｍ人一中且对任意ｘＥＲ"，ＣＭ＋ＯＯｇｂｃｌ（ｌ＞ｏｆｃ。（ｌ，ＶＣＺ＞ＣＩ＞０，（４ｉｌｌｆｆｉ０＜ｕｌ。（）ｄｉ（］＜．（５基于该性质，文山一【４］通过一次取定较大有限值Ｃ。＞０，将…  

微分多项式系统的近微分特征列集

本文对微分多项式系统的近微分特征列集与微分特征列集之间的一些关系进行了研究,给出了在某些条件下近微分特征列集是微分特征列集的结论,从而对微分多项式系统特征列集理论（吴方法）进行了改进,并且建立的算法较大地提高了计算微分特征列集的效率.  

P0-函数箱约束变分不等式的正则半光滑牛顿法

1引言设X C R~n,F：R~n→R~n,变分不等式Ⅵ(X,F)是指：求x∈X,使F(x)~T(y-x)≥0,(?)_y∈X．(1)记i∈N={1,2,…,n},当X=[a,b]：={x∈(?)~n|a_i≤x_i≤b_i,i∈N}时,称Ⅵ(X,F)为箱约束变分不等式(也有些文献称为混合互补问题),记为Ⅵ(a,b,F)．若a_i=0,b_i= ∞,i∈N,即X=(?)_ ~n：={x∈(?)~n|x≥0}时,Ⅵ(a,b,F)化为非线性互补问题NCP(F)：求x∈(?)_ ~n,使x≥0,F(x)≥0,x~TF(x)=0．(2)  

华蘅芳数在幂和问题中的新应用

自然效的幂和问题具有悠久的历史,亦不乏现代的兴趣.一般学者不了解清代数学家华蘅芳的成果.本文改进了华氏数的定义;针对该问题建立了新的取盒-放球模型,给出幂和的组合解释;应用华氏数获得了简捷的幂和公式.文末介绍了华氏数的历史来源.  

四阶强阻尼波方程的新混合元方法

构造半线性四阶强阻尼波动方程的新H1-Galerkin混合有限元方法,得到一维情况下半离散和全离散格式最优收敛阶误差估计,并且推广到二维和三维情况,不用验证LBB相容性条件.  

非线性互补问题的一种新的光滑价值函数及牛顿类算法

A new smooth merit function was constructed for nonlinear complementarity problems (NCPs). Like as the merit function based on the famous FischerBurmeister function, the stationary point of the merit function is the solution of NCP when the function is only a P0-function, and the merit function has good coercive property. A damped Newton-type algorithm which based on the merit function was presented. The global and local superlinear or quadratic convergence results were obtained under suitable conditions. Furthermore, the finite termination property was obtained for affine case with P-matrix without using the hybrid switch technique or additional step as corrector Newton step as usual. Numerical results suggest that the method is promising.