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81.
Alysson M. Costa Jean-François Cordeau Bernard Gendron 《Computational Optimization and Applications》2009,42(3):371-392
Solving multicommodity capacitated network design problems is a hard task that requires the use of several strategies like
relaxing some constraints and strengthening the model with valid inequalities. In this paper, we compare three sets of inequalities
that have been widely used in this context: Benders, metric and cutset inequalities. We show that Benders inequalities associated
to extreme rays are metric inequalities. We also show how to strengthen Benders inequalities associated to non-extreme rays
to obtain metric inequalities. We show that cutset inequalities are Benders inequalities, but not necessarily metric inequalities.
We give a necessary and sufficient condition for a cutset inequality to be a metric inequality. Computational experiments
show the effectiveness of strengthening Benders and cutset inequalities to obtain metric inequalities. 相似文献
82.
针对基于网络的凸多面体不确定离散时间马尔可夫跳变系统,研究其鲁棒无源控制问题.在网络诱导时滞是时变且有界的情况下,基于李雅普诺夫稳定性理论,通过构造参数依赖的随机李雅普诺夫泛函和运用广义系统变换,提出了不依赖模态的无源控制器存在的时滞依赖充分条件.所设计的鲁棒无源控制器保证了相应的闭环系统是鲁棒随机稳定且具有指定耗散率.将鲁棒无源控制器设计问题转化为一组线性矩阵不等式的可解性问题.仿真算例证明了本文方法的有效性. 相似文献
83.
M. Sababheh 《Linear and Multilinear Algebra》2019,67(5):953-964
The main aim of this article is to present inequalities for the numerical radius of commutators of positive matrices. Some of these inequalities are analogues of known inequalities for unitarily invariant norms. In particular, variants, but weaker forms, of the well-known Heinz inequality and its generalizations are extended to the context of numerical radius. 相似文献
84.
This paper deals with a hierarchical control problem for the Kuramoto–Sivashinsky equation following a Stackelberg–Nash strategy. We assume that there is a main control, called the leader, and two secondary controls, called the followers. The leader tries to drive the solution to a prescribed target and the followers intend to be a Nash equilibrium for given functionals. It is known that this problem is equivalent to a null controllability result for an optimality system consisting of three non-linear equations. One of the novelties is a new Carleman estimate for a fourth-order equation with right-hand sides in Sobolev spaces of negative order, which allows to relax some geometric conditions for the observation sets for the followers. 相似文献
85.
Messaoud Boulbrachene 《Mathematical Methods in the Applied Sciences》2019,42(16):5305-5316
In this paper, we extend the approach developed by the author for the standard finite element method in the L∞‐norm of the noncoercive variational inequalities (VI) (Numer Funct Anal Optim.2015;36:1107‐1121.) to impulse control quasi‐variational inequality (QVI). We derive the optimal error estimate, combining the so‐called Bensoussan‐Lions Algorithm and the concept of subsolutions for VIs. 相似文献
86.
Liya Liu Xiaolong Qin Jen‐Chih Yao 《Mathematical Methods in the Applied Sciences》2019,42(18):7367-7380
The purpose of this paper is to introduce a hybrid descent algorithm for finding a common point in fixed‐point sets of quasi‐nonexpansive mappings and solution sets of variational inequality problems. In the framework of Hilbert spaces, the strong convergence of the hybrid descent algorithm is established. Numerical experiments for the bandwidth allocation, which demonstrate the effectiveness, performance, and convergence of the proposed algorithm, are provided. 相似文献
87.
88.
本文研究了机场任务指派问题,该问题是指将具有特殊属性的任务指派给有限数量的班次。由于机场任务和班次属性的多样性,机场任务指派问题是一个复杂的组合优化问题,属于NP-完全问题。本文以任务完成产生的效益总和最大化为目标建立数学优化模型,提出有效不等式,应用CPLEX软件对实际数据进行求解,结果表明,CPLEX可以在较短时间内对一定规模的算例求得最优解。同时对影响目标函数的四个因素:任务数量、班次数量、班次工作时长和任务属性分别进行分析,通过实际算例测试对比,得出具有指导意义的结论,即根据机场特征分别调整四个因素不仅能够提高机场资源的有效利用率,而且能够提高机场的运行效率和服务水平。 相似文献
89.
In this paper, we present a smoothing Newton-like method for solving non-linear systems of equalities and inequalities. By using the so-called max function, we transfer the inequalities into a system of semismooth equalities. Then a smoothing Newton-like method is proposed for solving the reformulated system, which only needs to solve one system of linear equations and to perform one line search at each iteration. The global and local quadratic convergence are studied under appropriate assumptions. Numerical examples show that the new approach is effective. 相似文献
90.
We show that a Lagrangian submanifold of a complex space form attaining equality in the inequality obtained by Oprea in [8],
must be totally geodesic.
相似文献