共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, we propose a feasible smooth method based on Barzilai–Borwein (BB) for stochastic linear complementarity problem.
It is based on the expected residual minimization (ERM) formulation for the stochastic linear complementarity problem. Numerical
experiments show that the method is efficient. 相似文献
2.
3.
考虑一类随机互线性补问题的求解方法,目的是通过定义NCP函数来使正则化期望残差最小化.通过拟蒙洛包洛方法产生一系列观察值并且证得离散近似问题最小值解的聚点就是相应随机线性互补问题的期望残差最小值ERM,同时得到利用ERM到解为有界的充分条件.进一步证明ERM法能够得到具有稳定性和最小灵敏度的稳健解. 相似文献
4.
Chao Zhang 《Operations Research Letters》2011,39(1):78-82
In this paper we show the solvability of the expected residual minimization (ERM) formulation for the general stochastic linear complementarity problem (SLCP) under mild assumptions. The properties of the ERM formulation are dependent on the choice of NCP functions. We focus on the ERM formulations defined by the “min” NCP function and the penalized FB function, both of which are nonconvex programs on the nonnegative orthant. 相似文献
5.
We consider the expected residual minimization (ERM) formulation of stochastic linear complementarity problem (SLCP). By employing the Barzilai–Borwein (BB) stepsize and active set strategy, we present a BB type method for solving the ERM problem. The global convergence of the proposed method is proved under mild conditions. Preliminary numerical results show that the method is promising. 相似文献
6.
This paper considers a class of stochastic second-order-cone complementarity problems (SSOCCP), which are generalizations of the noticeable stochastic complementarity problems and can be regarded as the Karush–Kuhn–Tucker conditions of some stochastic second-order-cone programming problems. Due to the existence of random variables, the SSOCCP may not have a common solution for almost every realization . In this paper, motivated by the works on stochastic complementarity problems, we present a deterministic formulation called the expected residual minimization formulation for SSOCCP. We present an approximation method based on the Monte Carlo approximation techniques and investigate some properties related to existence of solutions of the ERM formulation. Furthermore, we experiment some practical applications, which include a stochastic natural gas transmission problem and a stochastic optimal power flow problem in radial network. 相似文献
7.
Stochastic Nonlinear Complementarity Problem and?Applications to?Traffic Equilibrium under?Uncertainty 总被引:1,自引:0,他引:1
The expected residual minimization (ERM) formulation for the stochastic nonlinear complementarity problem (SNCP) is studied
in this paper. We show that the involved function is a stochastic R
0 function if and only if the objective function in the ERM formulation is coercive under a mild assumption. Moreover, we model
the traffic equilibrium problem (TEP) under uncertainty as SNCP and show that the objective function in the ERM formulation
is a stochastic R
0 function. Numerical experiments show that the ERM-SNCP model for TEP under uncertainty has various desirable properties.
This work was partially supported by a Grant-in-Aid from the Japan Society for the Promotion of Science. The authors thank
Professor Guihua Lin for pointing out an error in Proposition 2.1 on an earlier version of this paper. The authors are also
grateful to the referees for their insightful comments. 相似文献
8.
We consider the stochastic linear complementarity problem (SLCP) involving a random matrix whose expectation matrix is positive semi-definite. We show that the expected residual minimization (ERM) formulation of this problem has a nonempty and bounded solution set if the expected value (EV) formulation, which reduces to the LCP with the positive semi-definite expectation matrix, has a nonempty and bounded solution set. We give a new error bound for the monotone LCP and use it to show that solutions of the ERM formulation are robust in the sense that they may have a minimum sensitivity with respect to random parameter variations in SLCP. Numerical examples including a stochastic traffic equilibrium problem are given to illustrate the characteristics of the solutions. 相似文献
9.
Bidushi Chakraborty Sudarshan Nanda Mahendra Prasad Biswal 《Mediterranean Journal of Mathematics》2005,2(3):291-299
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. 相似文献
10.
11.
12.
On the extended linear complementarity problem 总被引:8,自引:0,他引:8
M. Seetharama Gowda 《Mathematical Programming》1996,72(1):33-50
For the extended linear complementarity problem (Mangasarian and Pang, 1995), we introduce and characterize column-sufficiency,
row-sufficiency andP-properties. These properties are then specialized to the vertical, horizontal and mixed linear complementarity problems.
This paper is dedicated to Professor Olvi L. Mangasarian on the occasion of his 60th birthday. 相似文献
13.
The generalized linear complementarity problem revisited 总被引:5,自引:0,他引:5
Given a vertical block matrixA, we consider in this paper the generalized linear complementarity problem VLCP(q, A) introduced by Cottle and Dantzig. We formulate this problem as a linear complementarity problem with a square matrixM, a formulation which is different from a similar formulation given earlier by Lemke. Our formulation helps in extending many
well-known results in linear complementarity to the generalized linear complementarity problem. We also show that the class
of vertical block matrices which Cottle and Dantzig's algorithm can process is the same as the class of equivalent square
matrices which Lemke's algorithm can process. We also present some degree-theoretic results on a vertical block matrix. 相似文献
14.
Sándor Zoltán Németh Lianghai Xiao 《Journal of Optimization Theory and Applications》2018,176(2):269-288
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. 相似文献
15.
Michael V. Solodov 《Computational Optimization and Applications》1999,13(1-3):187-200
We consider the extended linear complementarity problem (XLCP) introduced by Mangasarian and Pang [22], of which the horizontal and vertical linear complementarity problems are two special cases. We give some new sufficient conditions for every stationary point of the natural bilinear program associated with XLCP to be a solution of XLCP. We further propose some unconstrained and bound constrained reformulations for XLCP, and study the properties of their stationary points under assumptions similar to those for the bilinear program. 相似文献
16.
Zhensheng Yu Yangchen Liu Xinyue Gan 《Numerical Functional Analysis & Optimization》2017,38(11):1458-1472
This paper presents a nonmonotone inexact Newton-type method for the extended linear complementarity problem (ELCP). We first reformulate the optimization system of the ELCP problem into a system of smoothed equations. Then we solve this system by a nonmonotone inexact Newton-type algorithm. The global convergence is obtained and numerical tests for some classes of ELCP include linear complementarity, horizontal linear complementarity, and generalized linear complementarity problems are also given to show the e?ciency of the proposed algorithm. 相似文献
17.
In this paper we consider a two-person zero-sum discounted stochastic game with ARAT structure and formulate the problem of
computing a pair of pure optimal stationary strategies and the corresponding value vector of such a game as a vertical linear
complementarity problem. We show that Cottle-Dantzig’s algorithm (a generalization of Lemke’s algorithm) can solve this problem
under a mild assumption.
Received July 8, 1998 / Revised version received April 16, 1999? Published online September 15, 1999 相似文献
18.
基于凝聚函数,提出一个求解垂直线性互补问题的光滑Newton法.该算法具有以下优点:(i)每次迭代仅需解一个线性系统和实施一次线性搜索;(ⅱ)算法对垂直分块P0矩阵的线性互补问题有定义且迭代序列的每个聚点都是它的解.而且,对垂直分块P0+R0矩阵的线性互补问题,算法产生的迭代序列有界且其任一聚点都是它的解;(ⅲ)在无严格互补条件下证得算法即具有全局线性收敛性又具有局部二次收敛性.许多已存在的求解此问题的光滑Newton法都不具有性质(ⅲ). 相似文献
19.
A family of complementarity problems is defined as extensions of the well-known linear complementarity problem (LCP). These are:
A number of well-known mathematical programming problems [namely, quadratic programming (convex, nonconvex, pseudoconvex, nonconvex), linear variational inequalities, bilinear programming, game theory, zero-one integer programming, fixed-charge problem, absolute value programming, variable separable programming] are reformulated as members of this family of four complementarity problems. A brief discussion of the main algorithms for these four problems is presented, together with some computational experience. 相似文献
(i) | second linear complementarity problem (SLCP), which is an LCP extended by introducing further equality restrictions and unrestricted variables; |
(ii) | minimum linear complementarity problem (MLCP), which is an LCP with additional variables not required to be complementary and with a linear objective function which is to be minimized; |
(iii) | second minimum linear complementarity problem (SMLCP), which is an MLCP, but the nonnegative restriction on one of each pair of complementary variables is relaxed so that it is allowed to be unrestricted in value. |
20.
In this article, we revisit the concept of principal pivot transform and its generalization in the context of vertical linear
complementarity problem. We study solution set and solution rays of a vertical linear complementarity problem. Finally we
present an application of generalized principal pivot transform in game theory. 相似文献