【作者】 周生宝；

【导师】 王志平；

【作者基本信息】 大连海事大学 ， 应用数学， 2007， 硕士

【摘要】 对于自然界大量的复杂的系统都可以通过形形色色的网络加以描述。以Anna Nagurney教授为首的以超网络结构模型为研究中心的一批批研究者利用变分不等式研究网络的均衡模型，将交通网络均衡模型的有关原理运用到供应链超网络、知识超网络、金融超网络、人口转移超网络等多种网络中，超网络模型显示了不凡的作用。变分不等式作为变分原理的主要推广，是数学上的一个重要分支。近年来，经典的变分不等式理论已被大量地用于应用数学、优化控制理论、力学与热学、线性与非线性规划、经济与金融、交通与运输平衡等各个领域。特别是网络模型框架结合变分理论算法，使得模型解的精确程度和求解的速度有很大的改善与提高。网络广告是新生事物，最早起源于美国，作为一种新的营销手段已成为广告界的热点；但是对网络广告资源分配的认识刚开始，一些模型的建立只以点击量为目标量，没有引入现实网络广告中的转化量，这样就不能真实反映广告效果，就会造成决策者决策失误。本文通过引入点击量、转化量和用显示概率作为权值的展示量，采用超网络模型、变分不等式算法解决网络广告资源优化问题，通过理论论证和实例分析进一步说明了该模型理论的正确性与实际的可用性。更多还原

【Abstract】 A large number of complex systems in nature can be described in various networks models. Headed by Professor Anna Nagurney, the scholars concentrate their attentions to the research of super-network model, using variational inequalities to research network equilibrium model. They have applied the principles of traffic network to the supply chain supernetworks, finance supernetworks, knowledge supernetworks and so on successfully. Supernetwork model has been showing its extraordinary role. As the extension of variational theory, the variational inequality is an important branch of mathematics. In recent years, it has been used to many fields, such as applied mathematics, physics, linear and nonlinear programming problem, economics, finance, transport. Specially, the integration between the framework of supernetwork and variational inequality has improved the efficiency of solving a model, including precision and speed.Network advertisement as a new thing, it has more and more life-force and has drawn increasing concern, but researches on resource allocation are still on seedtime. Some models only use click-through as the objective reference, but lose sight of conversions. Thus these can not reflect the effect of net advertisement exactly and will result in decision-making errors for policy makers. Based on the previous researches and practices, we develop a framework, which adopts supernetwork model and variational inequality to solve the optimal resource allocation of net advertisement. This model involves not only click-through and conversions but also weighted exposures with impression probability that revises the expression. Computer simulation with a numerical example is used to validate the feasibility of the model and the algorithm.更多还原