模糊均衡问题的求解及应用

根据实际均衡问题研究的需要,给出了模糊向量、模糊值函数、模糊矩阵等新概念,建立了模糊均衡问题的数学模型,即模糊线性互补问题。在引入新的模糊期望的基础上,研究了其性质,并据此给出了模糊线性互补问题的一种确定型等价式及此类问题的均衡解的概念。用实例说明了所提模型和方法的合理性及应用前景。     

线性互补问题与多目标优化

本文研究了求解线性互补问题的一类新方法:把线性互补问题转化为多目标优化问题,利用多目标优化有效解的定义,给出了零有效解的概念;进而获得多目标优化问题的零有效解就是线性互补问题的最优解.最后给出了有解、无解线性互补问题,并分别把这些问题转化为多目标优化,采用极大极小方法求解转化后的多目标优化问题.数值实验结果表明了该方法的正确性和有效性,完善了文献[19]的数值结果.     

二阶锥线性互补问题的低阶罚函数算法

本文研究了二阶锥线性互补问题的低阶罚函数算法.利用低阶罚函数算法将二阶锥线性互补问题转化为低阶罚函数方程组,获得了低阶罚函数方程组的解序列在特定条件下以指数速度收敛于二阶锥线性互补问题解的结果,推广了二阶锥线性互补问题的幂罚函数算法.数值实验结果验证了算法的有效性.     

非线性互补约束规划问题的一个新的QP-free算法

本文研究了非线性互补约束均衡问题.利用互补函数以及光滑近似法,把非线性互补约束均衡问题转化为一个光滑非线性规划问题,得到了超线性收敛速度,数值实验结果表明本文提出的算法是可行的.     

求解一类隐线性互补问题的投影MAOR算法

用MAOR迭代算法求解一类L-矩阵的隐线性互补问题.证明了由此算法产生的迭代序列的聚点是隐线性互补问题的解.并且当问题中的矩阵是M-矩阵时,算法产生的迭代序列单调收敛于隐互补问题的解.     

B-矩阵线性互补问题的误差界估计

正1引言线性互补问题在诸多领域具有广泛的应用,如二次规划、市场均衡、最优停步、双矩阵对策等~([1-3]),线性互补问题的数学模型为求x∈R~n,满足(Mx+q)~Tx=0,Mx+q≥0,x≥0,记作LCP(M,q),其中M=(m_(ij))∈R~(n×n)和q∈R~n为给定的矩阵和向量.线性互补问题解的性质主要取决于所定义矩阵的性质.例如,当矩阵是P-矩阵(即它     

隐式形式多值向量均衡问题解的存在性

考虑一类隐式形式多值向量均衡问题的解的存在性,该类问题包含了多值均衡问题、隐式向量均衡问题、多值变分不等式问题、向量变分不等式问题以及向量互补问题作为其特殊情形.利用广义Fan-Browder不动点定理,得到了拓扑向量空间中该类问题解的存要性定理,该结果推广并统一了已有问题解的存在性结果.     

半线性椭圆互补问题的上解与下解(英文)

本文针对半线性椭圆互补问题,提供几种获取该问题的一个上解和下解的方式.在求解过程中,仅仅需要求解一个线性互补问题或线性方程组.所得结果可应用于众多单调算法的初始化.     

单调线性互补问题的一种内点算法

本文研究了单调线性互补问题的一种内点算法.利用牛顿方向和中心路径方向,获得了求解单调线性互补问题的一种内点算法,并证明该算法经过多项式次迭代之后收敛到原问题的一个最优解.数值实验表明此方法是有效的.     

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.     

A new resolution method for the parametric linear complementarity problem

An original method is presented to solve the parametric linear complementarity problem. To solve such a problem requires to identify the values taken by the solution of a linear complementarity problem where some of its right-hand side terms vary in a prescribed domain. This class of problems allows, among others, to deal with linear market equilibrium problems with varying prices: it allows to identify how does the equilibrium point varies when the prices vary over a set of given values. This method is illustrated through an application related to the institution of ecological taxes on the Western European natural gas market.     

Equivalence of the Generalized Vertical Block Linear Complementarity Problems and Linear Complementarity Problems

In this paper, generalization of a vertical block linear complementarity problem associated with two different types of matrices, one of which is a square matrix and the other is a vertical block matrix, is proposed. The necessary and sufficient conditions for the existence of the solution of the generalized vertical block linear complementarity problem is derived and the relationship between the solution set of the generalized vertical block linear complementarity problem and the linear complementarity problem is established. It is proved that the generalized vertical block linear complementarity problem has the P-property if and only if the vertical block linear complementarity problem has the P-property.     

Stability of the linear complementarity problem at a solution point

In this paper we study the behavior of a solution of the linear complementarity problem when data are perturbed. We give characterizations of strong stability of the linear complementarity problem at a solution. In the case of stability we give sufficient and necessary conditions.     

The basic theorem of complementarity revisited

The basic theorm of (linear) complementarity was stated in a 1971 paper [6] by B.C. Eaves who credited C.E. Lemke for giving a constructive proof based on his almost complementary pivot algorithm. This theorem asserts that associated with an arbitrary linear complementarity problem, a certain augmented problem always possesses a solution. Many well-known existence results pertaining to the linear complementarity problem are consequences of this fundamental theorem.In this paper, we explore some further implications of the basic theorem of complementarity and derive new existence results for the linear complementarity problem. Based on these results, conditions for the existence of a solution to a linear complementarity problem with a fully-semimonotone matrix are examined. The class of the linear complementarity problems with aG-matrix is also investigated.The work of this author was based on research supported by the National Science Foundation under grant ECS-8717968.     

Smoothing approach to Nash equilibrium formulations for a class of equilibrium problems with shared complementarity constraints

The equilibrium problem with equilibrium constraints (EPEC) can be looked on as a generalization of Nash equilibrium problem (NEP) and the mathematical program with equilibrium constraints (MPEC) whose constraints contain a parametric variational inequality or complementarity system. In this paper, we particularly consider a special class of EPECs where a common parametric P-matrix linear complementarity system is contained in all players?? strategy sets. After reformulating the EPEC as an equivalent nonsmooth NEP, we use a smoothing method to construct a sequence of smoothed NEPs that approximate the original problem. We consider two solution concepts, global Nash equilibrium and stationary Nash equilibrium, and establish some results about the convergence of approximate Nash equilibria. Moreover we show some illustrative numerical examples.     

Upper semicontinuity of the solution maps in homogeneous vector quasi-equilibrium problems

The aim of this work was to study the solution maps in the vector homogeneous quasi-equilibrium problems. Here, we establish some sufficient and necessary conditions for upper semicontinuity of the solution maps in the vector homogeneous quasi-equilibrium problems. The results presented extend and improve the preceding results of Oetlli and Yen [Oetlli, W. and Yen, N.D., 1995, Continuity of the solution set of homogeneous equilibrium problems and linear complementarity problems. In: F. Giannessi and A. Maugeri (Eds) Variational Inequalities and Network Equilibrium Problems (New York: Plenum Press)].     

Linear Complementarity Problems on Extended Second Order Cones

In this paper, we study the linear complementarity problems on extended second order cones. We convert a linear complementarity problem on an extended second order cone into a mixed complementarity problem on the non-negative orthant. We state necessary and sufficient conditions for a point to be a solution of the converted problem. We also present solution strategies for this problem, such as the Newton method and Levenberg–Marquardt algorithm. Finally, we present some numerical examples.     

Locally unique solutions of quadratic programs,linear and nonlinear complementarity problems

It is shown that McCormick's second order sufficient optimality conditions are also necessary for a solution to a quadratic program to be locally unique and hence these conditions completely characterize a locally unique solution of any quadratic program. This result is then used to give characterizations of a locally unique solution to the linear complementarity problem. Sufficient conditions are also given for local uniqueness of solutions of the nonlinear complementarity problem.Research supported by National Science Foundation Grant MCS74-20584 A02.     

Fixed Point Methods for the Complementarity Problem

This paper is concerned with iterative procedures for the monotone complementarity problem. Our iterative methods consist of finding fixed points of appropriate continuous maps. In the case of the linear complementarity problem, it is shown that the problem is solvable if and only if the sequence of iterates is bounded in which case summability methods are used to find a solution of the problem. This procedure is then used to find a solution of the nonlinear complementarity problem satisfying certain regularity conditions for which the problem has a nonempty bounded solution set.