向量值映射锥鞍点存在定理

本文首次通过借助Kakutani-Fan-Glicksberg固定点定理和非线性标量化,研究了向量值映射的Benson锥鞍点定理.然后,通过使用该Kakutani-Fan-Glicksberg固定点定理,同样得到了集值映射的锥松鞍点定理.     

A minimax theorem for vector-valued functions in lexicographic order

In this paper, a minimax theorem and a saddle point theorem are obtained for vector-valued functions in the sense of lexicographic order, respectively. An equivalent relationship between the minimax inequality and the saddle point is established. Some examples are given to illustrate our results.     

Minimax Problems for Set-Valued Mappings

In this article, by virtue of the Fan-Browder fixed point theorem, we first obtain a minimax theorem and establish an equivalent relationship between the minimax theorem and a cone saddle point theorem for scalar set-valued mappings. Then, by using scalarization functions, we investigate an existence theorem of the cone saddle point for set-valued mappings. Simultaneously, we also establish a minimax theorem for set-valued mappings.     

A local saddle point theorem and an application to a nonlocal PDE

We prove a local saddle point theorem that can be viewed as a generalization of the saddle point theorem of Rabinowitz. A difficulty to overcome is that there isn’t any linking. We then apply the theorem to show the existence of solutions of a nonlocal partial differential equations.     

非紧L-凸度量空间中的一个新的不动点定理及其对极大极小不等式和鞍点的应用

In this paper,a new fixed point theorem is established in noncompact complete Lconvex metric spaces.As applications,a maximal element theorem,a minimax inequality and a saddle point theorem are obtained.     

向量最优化问题的Lagrange对偶与择一定理

本文讨论无限维向量最优化问题的Lagrange对偶与弱对偶，建立了若干鞍点定理与弱鞍点定理．作为研究对偶问题的工具，建立了一个新的择一定理．     

非紧超凸度量空间中的一个新的不动点定理及其对鞍点问题的应用

在非紧超凸度量空间中建立了一个新的不动点定理.作为应用,研究了连续选择及其不动点定理,极大元定理、Ky Fan极大极小不等式和鞍点定理.     

非紧超凸度量空间中的一个新的不动点定理及其对鞍点问题的应用

In this paper,a new fixed point theorem is established in noncompact hyperconvex metric spaces.As applications,a continuous selection and its fixed point theorem,an existence theorem for maximal elements,a Ky Fan minimax inequality and an existence theorem for saddle points are obtained.     

Super efficiency in vector optimization with nearly convexlike set-valued maps

In this paper, we establish a scalarization theorem and a Lagrange multiplier theorem for super efficiency in vector optimization problem involving nearly convexlike set-valued maps. A dual is proposed and duality results are obtained in terms of super efficient solutions. A new type of saddle point, called super saddle point, of an appropriate set-valued Lagrangian map is introduced and is used to characterize super efficiency.     

一类非自治二阶系统的多重周期解

利用广义鞍点定理讨论了一类非自治二阶系统的多重周期解．     

矩阵对策鞍点定理的归纳法证明

Many proofs have been published for the minimax theorem, and all the published inductive proofs have been indirect ones. It has been pointed out that a direct inductive proof is needed, especially for instructional purposes, since indirect proofs are more or less implicit in nature. Such a direct proof is given in [4]. Now the minimax theorem can be stated equivalently in terms of saddle point; And it is the object of the present paper to give a direct inductive proof for the saddle point version of this theorem.     

多目标半定规划的互补弱鞍点和G-鞍点最优性条件

对于含矩阵函数半定约束和多个目标函数的多目标半定规划问题，给出Lagrange函数在弱有效意义下的互补弱鞍点和Geofrrion恰当有效意义下的G-鞍点的定义及其等价定义．然后，在较弱的凸性条件下，利用含矩阵和向量约束的择一性定理，建立多目标半定规划的互补弱鞍点和G-鞍点充分必要条件．     

非紧超凸度量空间中的极大元定理及其对极大极小问题和鞍点问题的应用

在非紧超凸度量空间中的非紧次允许子集中建立了一个极大元定理．作为应用,研究了Fan-Browder型不动点定理、KyFan极大极小不等式和鞍点定理．     

Loose saddle points of set-valued maps in topological vector spaces

We give a new existence theorem for loose saddle point of set-valued map having values in a partially ordered topological vector space which is based on continuity and quasiconvexity- quasiconcavity of its scalarized maps. Moreover, we prove a new saddle point theorem for vector-valued functions in locally convex topological vector spaces under weak condition that is the semicontinuity of two function scalarization.     

非紧L-凸空间中的一个新的极大元定理及其对鞍点的应用(英文)

在非紧L-凸空间中建立一个新的极大元定理.作为应用,获得了非紧L-凸空间中的极大极小不等式和鞍点定理.     

An intersection theorem in L-convex spaces with applications

A new intersection theorem is obtained in L-convex spaces without linear structure. As its applications, a fixed point theorem, a maximal element theorem, a coincidence theorem, some new minimax inequalities and a saddle point theorem are given in L-convex spaces. Our results generalize many known theorems in the literature.     

The existence of solutions for a class of semilinear elliptic systems

In this paper, some new existence theorems of weak solutions for a class of semilinear elliptic systems are obtained by means of the local linking theorem and the saddle point theorem.     

精确罚函数和极小极大问题

在这篇文章中我们研究了对于不等式约束的非线性规划问题如何根据极小极大问题的鞍点来找精确罚问题的解。对于一个具有不等式约束的非线性规划问题,通过罚函数,我们构造出一个极小极大问题,应用交换“极小”或“极大”次序的策略,证明了罚问题的鞍点定理。研究结果显示极小极大问题的鞍点是精确罚问题的解。     

集值映射多目标半定规划问题的epsilon-弱有效性

对于集值映射多目标半定规划问题, 在近似锥-次类凸的框架下, 建立了含矩阵和向量的择一性定理, 给出了问题的epsilon-弱有效解的epsilon-Lagrange乘子定理及标量化定理和epsilon-弱鞍点定理．     

Generalized saddle point theorem and asymptotically linear problems with periodic potential

We prove a critical point theorem, which is an infinite dimensional generalization of the classical saddle point theorem of P. H. Rabinowitz. As an application we obtain solution of asymptotically linear Schrödinger equations with periodic potential.