Minimax原理在完全非线性椭圆型方程中的应用

利用临界点理论中的极小极大原理，研究了Ｒ＾ｎ上一类完全非线性椭圆型方程的ｇｒｏｕｎｄｓｔａｔｅ解和结点解的存在性问题。通过构造适当的Ｂａｎａｃｈ空间，给出了ｇｒｏｕｎｄｓｔａｔｅ解和结点解存在的充分条件，证明了这两类解都是Ｃ＾２解。     

Optimal scheduling of reservoir releases during flood: Deterministic optimization problem,part 1, procedure

In this paper, we are concerned with the optimal scheduling of water releases from retention reservoirs during flood, with the objective of minimizing flood damages at the important damage centers downstream of the reservoirs. Unlike in most other papers devoted to this subject, the flood routing equations are nonlinear. The performance index of the problem leads to a minimax optimal control problem. For this problem, the necessary optimality conditions are provided and a version of the feasible directions method is proposed.The research reported here has been supported by the Central Basic Research Program CPBP-03.09, Metody Analizy i Uytkowania Zasobow Wodnych, Polish Academy of Sciences, Warsaw, Poland. This support is kindly acknowledged.     

二阶非齐次非线性差分方程与方程组的次调和周期解的多解性

通过应用由赵培浩等提出的乘积空间的环绕定理.提出了一种研究非线性差分方程及方程组的次调和周期解的存在性与多解性的新方法.对于二阶非齐次非线性差分方程组{-△2un-1=μ1 f1(n,un) λh1(n,un,vn), n∈z,一△2un-1=μ2 f2(n,vn) λh2(n,un,vn),n∈z,得到了一些新的结果.特别地,给出了此方程组存在至少两个非平凡周期解的充分条件.     

静态结构化不确定性极小极大控制在网络中的应用

研究了具有静态结构化不确定性时滞系统的极小极大鲁棒控制问题.针对乘时二次型性能指标,运用Lyapunov方法得到极小极大鲁棒控制器的存在条件,并引入凸优化算法求解控制器最优参数和性能指标的最小上界.最后,将该算法应用于带有时滞因素的TCP网络拥塞控制中,使路由器的队列长度能够更快地收敛于期望值,并且稳态时的振荡很小.通过与其他方法的比较,说明了该方法在实际应用中的有效性与优越性.     

Dynamic System for Solving Saddle Point Problems in Hilbert Spaces and Its Application to Neural Computing

This paper studies the existence and uniqueness of solutions and the stability and convergence of a dynamic system for solving saddle point problems (SPP) in Hilbert spaces. The analysis first converts the SPP into a problem of searching for equilibriums of a dynamic system using a criterion for solutions of the SPP, then shows the existence and uniqueness of the solutions by creating a positive function whose Fréchet derivative is decreasing along any solution. The construction of positively invariant subsets gives the global stability and convergence of this dynamic system, that is, the dynamic system globally converges to some exact solution of the SPP. Finally, the paper also shows that the obtained results can be applied to neural computing for solving SPP.     

Weak KKM theorems in generalized finitely continuous space with applications

Some new weak Knaster-Kuratouski-Mazurkiewicz （KKM） theorems are proved under the noncompact situation in the generalized finitely continuous space （GFC-space） without any convexity. As applications, the minimax inequalities of the Ky Fan type are also given under some suitable conditions. The results unify and generalize some known results in recent literatures.     

Duality for Semi-Infinite Minimax Fractional Programming Problem Involving Higher-Order (Φ, ρ)-V-Invexity

In this paper, we introduce the concept of higher-order (Φ, ρ)-V-invexity and present two types of higher-order dual models for a semi-infinite minimax fractional programming problem. Weak, strong, and strict converse duality theorems are discussed under the assumptions of higher-order (Φ, ρ)-V-invexity to establish a relation between the primal and dual problems.     

MINIMAX THEOREM AND SADDLE POINT THEOREM WITHOUT LINEAR STRUCTURE

I.IntroductionFanKyinequalityisaveryusefultoolinnoolinearanalysiswhichasserts:LetXbeanonemptycompactconvexsetinatopologicallinearspaceandWbeareal-valuedfunctiondefinedonXxX.Assumethat(i)9(x,y)islowersemicontinuousinac;(n)9(x,y)isquasiconcaveiny.ThenthereisboaXsuchthatsHPg(xo'Y)$sZPp(x,x).SinceFanKyprovedtheinequalityin1972,variousg...,.li..tlon,havebeen;v..byseveralauthors(see[l-3]andreferencestherein).Thepreviousgeneralizationsallremainedtheconditions(i)-'9(x,y)beinglowersemicontinuous…     

L-凸空间的一个极大极小不等式及应用

运用L-凸空间中的一个极大极小不等式,对L-凸空间中的抽象变分不等式和似变分不等式解的存在性,Ky Fan型截口定理,以及具有扰动的二人零和博弈和多人非合作博弈均衡的存在性进行研究,从而得到没有线性结构的L-凸空间中一些新的抽象变分不等式和似变分不等式解的存在性结果和一个Ky Fan型截口定理.最后得到了一个具有扰动的二人零和博弈和一个多人非合作博弈的均衡存在性结果.计算结果与其他相关结果相比,条件是比较弱的.     

一类二阶常p-Laplace系统周期解的存在性

Hamilton系统理论是经典而又现代化的研究领域,其广泛存在于数理科学,生命科学及社会科学等各个领域,特别是经典力学和场论中很多模型都以Hamilton系统的形式出现.本文通过应用临界点理论中的极小极大方法,研究一类常p-Laplace系统非平凡周期解的存在性,所得结构推广了二阶Hamilton系统的相关结果.