Research Of The Network Advertisement Super-network Model Based On The Variational Inequalities

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.