向量均衡问题的超有效性的对偶形式

在局部凸空间中引进了向量均衡问题的强超有效解、C-强超有效解、弱超有效解, C-弱超有效解、齐次超有效解、 C-齐次超有效解的概念,并在局部凸空间中用极理论为工具讨论了向量均衡问题的 C-弱超有效解, C-超有效解, C-齐次超有效解,以及C-强超有效解的对偶形式. 又在赋范线性空间中讨论了向量均衡问题的以上各种超有效解之间的等价性,并且在赋范线性空间具正规锥的条件下讨论了向量均衡问题的以上各种超有效解的对偶形式. 作为它的应用,给出了向量优化问题各种超有效解的对偶形式.     

压电材料圆锥顶端作用集中载荷的解

从压电材料三维问题的通解出发,用凑合法求解了圆锥顶端作用集中力、点电荷和集中力矩的解,此解形式简单便于应用。当圆锥顶角2α=π时,集中力、点电荷和扭矩的解可退化得到半空间问题的解。     

二阶非线性微分方程边值问题的同伦分析解

研究了结合变量替换应用同伦分析方法,去求解二阶非线性微分方程的两点边值问题,并得到了逼近解析解的函数级数形式.给出了应用同伦分析方法求解二阶非线性问题的三个实例,显示了同伦分析方法可以比较有效地求解非线性问题.     

无穷时滞泛函微分方程的正周期解

利用范数形式的锥拉伸和锥压缩不动点定理讨论具有无穷时滞泛函微分方程的周期解问题,获得了正周期解的存在性定理,并给出了定理的若干应用.     

两相材料空间问题基本解的显式张量表示*

本文应用张量运算将文献中的三维两相无限体的集中力基本解表示为张量形式,从而使其能够直接用于边界积分方程和边界元方法,以分析两相材料空间弹性力学问题.本文结果包括了Mindlin问题、Lorentz问题和均质体空间问题的基本解.     

无穷时滞泛函微分方程的正周期解

利用范数形式的锥拉伸和锥压缩不动点定理讨论具有无穷时滞泛函微分方程的周期解问题,获得了正周期解的存在性定理,并给出了定理的若干应用.     

奇摄动半线性Robin问题的多重解

研究了一类奇摄动半线性Robin问题.在适当的条件下,分析了该问题出现多重解现象.利用合成展开法构造出问题的形式渐近解,并应用微分不等式理论证明了解的存在性以及当ε→0时解的渐近性质.     

一类具非线性边值条件的微分方程的奇摄动问题

研究了一类非线性三阶微分方程的奇摄动问题.运用合成展开法构造了问题的形式渐近解,并运用不动点原理证明了原问题解的存在性及所得形式渐近解的一致有效性.     

一类常微分方程解的存在唯一性及其应用

提出并证明了一类常微分方程解的存在唯一性成立的一个充要条件,并给出了多项式形式增长函数的一列上界.最终将此结果应用到证明一类倒向随机微分方程的唯一解问题.     

一类具非线性边界条件的高阶方程的双参数奇摄动问题

研究了一类含双参数的非线性高阶微分方程的奇摄动问题.运用合成展开法构造了问题的形式渐近解,并运用微分不等式理论证明了原问题解的存在性及所得形式渐近解的一致有效性.     

Nash Equilibria for the Multiobjective Control of Linear Partial Differential Equations

This article is concerned with the numerical solution of multiobjective control problems associated with linear partial differential equations. More precisely, for such problems, we look for the Nash equilibrium, which is the solution to a noncooperative game. First, we study the continuous case. Then, to compute the solution of the problem, we combine finite-difference methods for the time discretization, finite-element methods for the space discretization, and conjugate-gradient algorithms for the iterative solution of the discrete control problems. Finally, we apply the above methodology to the solution of several tests problems.     

Pointwise Control of the Burgers Equation and Related Nash Equilibrium Problems: Computational Approach

This article is concerned with the numerical solution of multiobjective control problems associated with nonlinear partial differential equations and more precisely the Burgers equation. For this kind of problems, we look for the Nash equilibrium, which is the solution to a noncooperative game. To compute the solution of the problem, we use a combination of finite-difference methods for the time discretization, finite-element methods for the space discretization, and a quasi-Newton BFGS algorithm for the iterative solution of the discrete control problem. Finally, we apply the above methodology to the solution of several tests problems. To be able to compare our results with existing results in the literature, we discuss first a single-objective control problem, already investigated by other authors. Finally, we discuss the multiobjective case.     

The system of generalized vector equilibrium problems with applications

In this paper, we introduce the system of generalized vector equilibrium problems which includes as special cases the system of generalized implicit vector variational inequality problems, the system of generalized vector variational and variational-like inequality problems and the system of vector equilibrium problems. By using a maximal element theorem, we establish existence results for a solution of these systems. As an application, we derive existence results for a solution of a more general Nash equilibrium problem for vector-valued functions.     

Optimality conditions for vector equilibrium problems

In this paper, we present the necessary and sufficient conditions for weakly efficient solution, Henig efficient solution, globally efficient solution, and superefficient solution to the vector equilibrium problems with constraints. As applications, we give the necessary and sufficient conditions for corresponding solution to the vector variational inequalities and vector optimization problems.     

Bilevel programming with discrete lower level problems

In this article, we investigate bilevel programming problems with discrete lower level and continuous upper level problems. We will analyse the structure of these problems and discuss both the optimistic and the pessimistic solution approach. Since neither the optimistic nor the pessimistic solution functions are in general lower semicontinuous, we introduce weak solution function. By using these functions we are able to discuss optimality conditions for local and global optimality.     

Variational relation problems and equivalent forms of generalized Fan-Browder fixed point theorem with applications to Stampacchia equilibrium problems

In this paper, we study the existence theorems of solution for variational relation problems. From the existence theorems of solution for variational relation problems, we study equivalent forms of generalized Fan-Browder fixed point theorem, existence theorems of solutions for Stampacchia vector equilibrium problems and generalized Stampacchia vector equilibrium problems. Our results contains many orginal results and have many applications in Nonlinear Analysis.     

Characterizations of Solutions for Vector Equilibrium Problems

In this paper, we characterize the solutions of vector equilibrium problems as well as dual vector equilibrium problems. We establish also vector optimization problem formulations of set-valued maps for vector equilibrium problems and dual vector equilibrium problems, which include vector variational inequality problems and vector complementarity problems. The set-valued maps involved in our formulations depend on the data of the vector equilibrium problems, but not on their solution sets. We prove also that the solution sets of our vector optimization problems of set-valued maps contain or coincide with the solution sets of the vector equilibrium problems.     

奇摄动问题中阶梯状解的缝接法

In view of singularly perturbed problems with complex inner layer phenomenon,including contrast structures(step-step solution and spike-type solution),corner layer behavior and right-hand side discontinuity,we carry out the process with sewing connection.The presented method of sewing connection for singularly perturbed equations is based on the two points singularly perturbed simple boundary problems.By means of sewing orbit smoothness,we get the uniformly valid solution in the whole interval.It is easy to prove the existence of solutions and deal with the high dimensional singularly perturbed problems.     

Reduced order solution of structured linear systems arising in certain PDE-constrained optimization problems

The solution of PDE-constrained optimal control problems is a computationally challenging task, and it involves the solution of structured algebraic linear systems whose blocks stem from the discretized first-order optimality conditions. In this paper we analyze the numerical solution of this large-scale system: we first perform a natural order reduction, and then we solve the reduced system iteratively by exploiting specifically designed preconditioning techniques. The analysis is accompanied by numerical experiments on two application problems.     

On complexity of unconstrained hyperbolic 0-1 programming problems

Single- and multiple-ratio unconstrained hyperbolic 0-1 programming problems are considered. We prove that checking whether these problems have a unique solution is NP-hard. Furthermore, we show that finding the global maximizer of problems with unique solution remains NP-hard. We also discuss complexity of local search and approximability for multiple-ratio problems.