基于变分不等式的网络广告超网络模型研究
|
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。
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.
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。
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.
引文
[1] Mokhtarian P L. A Synthetic Approach to Estimating the Impacts of Telecommuting on Travel. Urban Studies, 1998, 35: 215-241.
[2] Schneider M. Access and Land Development, in Urban Development Models, Highway Research Board Special Report 97, 1968: 164-177.
[3] Dafermos S. A Multicriterion Route-Mode Choice Traffic Equilibrium Model. Lefschetz Center for Dynamical Systems, Brown University, Providence, Rhode Island. 1981.
[4] Nagurney A, Dong J, and Mokhtarian P L. Integrated Multicriteria Network Equilibrium Models for Commuting Versus Telecommuting. Isenberg School of Management, University of Massachusetts, Amherst, Massachusetts, 2000.
[5] Nagurney A, Dong J, and Mokhtarian P L. Teleshopping Versus Shopping: A Multicriteria Network Equilibrium Framework. Mathematical and Computer Modelling 2001: 783-798.
[6]Mokhtarian P L.Salomon I. Emerging Travel Patterns: Do Telecommunications Make a Difference?, in In Perpetual Motion: travel Behavior Research Opportunities and Application Chellenges, H S Mahmassani, editor, 2002: 143-181.
[7] Nagurney A, and Dong J, Supernetworks: Decision-Making for the Information Age, Edward Elgar Publishers, Cheltenham, England, in press. 2002: 41-77.
[8] Nagurney A, Loo J, Dong J, et al. Supply Chain Networks and Electronic Commerce: A Theoretical Perspective. Netnomics, 2002(4): 187-220.
[9] Nagurney A, Ke K, Cruz J, et al. A Multilevel Network Perspective (Logistical /Informational/Financial). Environment & Planning B, 2002, 29:795-818.
[10] Langheinrich Mt Nakamura At Abe T K Nt et al. Unintrusive customization techniques for web advertising. Computer Networks, 1999, 31(11—16): 1259—1272.
[11]Abe N. Nakamura A . Learning to optimally schedule internet banner advertisements. Proc of the 16th Int Conf on Machine Learning. Bled, Slovenia. 1999:12-22.
[12] Zhao L, A Nagurney. A network modeling approach for Internet advertising. Netnomics, 2005(3):181-200.
[13] Wardrop J G. Some Theoretical Aspects of Road Traffic Research. Proceedings of the Institute of Civil Engineers, 1952: II, 325-378.
[14] Dafermos S. The Traffic Assignment Problem for Multimodal Networks. Transportation Science, 1972(6): 73-87.
[15] Sheffi Y. Transportation Network Equilibrium with Discrete Choice Models.-Ph.D. thesis. Civil Engineering Department, Massachusetts Institute of Technology, Cambridge, Massachusetts. 1978.
[16] Sheffi Y, Daganzo C F. Computation of Equilibrium Over Transportation Networks: The Case of Disaggregate Demand Models. Transportation Science, 1980(14): 155-173.
[17] Dafermos S. Traffic equilibrium and Variational inequalities. Transportation Science, 1980(14): 42-54.
[18] Bar-Gera H. Origin-Based Algorithms for Transportation Network Modeling. National Institute of Statistical Sciences, Technical Report # 103, Research Triangle Park, North Carolina, 1999.
[19] Wu J H, Florian M, and He S G. EMME/2 Implementation of the SCAG-Ⅱ Model: Data Structure, System Analysis and Computation. Submitted to the Southern California Association of Governments, INRO Solutions Internal Report, Montreal, Quebec, Canada. 2000.
[20] Abello J, Pardalos P M, and Resende M G C. On Maximum Clique Problems in Very Large Graphs in External Memory Algorithms. AMS Series on Discrete Mathematics and Theoretical Computer Science, 1999, 50: 119-130.
[21] Nagurney A. Navigating the Network Economy. OR/MS Today. Lionheart Publishing Company, Atlanta, Georgia, 2000: 74-75.
[22] David Kinderlehrer. Variational inequalities and free boundary problems. Bull. Amer. Math. Soc. 1978, 84(1), 7-26.
[23] 郭友中，刘君兰译．变分不等方程及其应用．北京：1991．
[24] 单洪忠．迭代法求解变分不等式问题．北京服装学院学报(自然科学)，2000，20(1)：82-85．
[25] KORPELEVICH E N. The Extragradient Method for Finding Saddle Points and Other Problems. Matecon, 1976(12): 747-756.
[26] Han D R. A New Hybrid Generalized Proximal Point Algo2rithm for Variational Inequality Problems. Journal of Global Optimization, 2003, 26: 125-128.
[27] 王传伟．一个求解变分不等式问题的投影算法．重庆师范大学学报(自然科学)．2005，22(1)：6-11．
[28] 江莉，吕玉华．一般强单调交分不等式的改进投影算法．青岛科技大学学报． 2006，27(2)：179-181．
[29] 李郑国，王猛，曾华军译．支持向量积．北京：电子工业出版社，2004：1-24．
[30] Bertsekas D P, Tsitsiklis J N. Parallel and distributed computation. Prentice-Hall. Englewood Cliffs, New Jersey, 1992.
[31] 胡忠青．国内网络广告发展前景管窥．特区经济．2004年11月26日：115-116．
[32] 阿建卓．网络广告问题探析．廊坊师范学院学报．2007，23(3)：29-31．
[33] 张志华．王莉．网络环境下广告资源优化决策模型．鞍山科技大学学报，2006(5)：510-515．
[34] 邓文峰，周朝民．浅析网络广告效果评价．上海管理科学，2005(4)：13-15．
[35] 美国网络广告调查公司Adknowledge在“2000年第三季度网络广告调查报告”，2000．
[36] Young—Hoon Park, Peter S. Fader. Modeling browsing behavior at multiple websites. Marketing Science, 2004, 23(3): 280—303.
[37] Chattcrjec D L. Hoffman. modeling the clickstream, in applications for Webbased advertising efforts. Marketing Science, 2003, 22(4): 520—541.
[38] 梅仕鹏，蒋海波．网络广告效果评价指标的评析与构建．江苏商论．2003(12)．
[39] Anna Nagurney, June Dong. Super-networks: Decision-Making for the Information Age, Appendix B Variational Inequaliteies. 2002, 299-304.
[2] Schneider M. Access and Land Development, in Urban Development Models, Highway Research Board Special Report 97, 1968: 164-177.
[3] Dafermos S. A Multicriterion Route-Mode Choice Traffic Equilibrium Model. Lefschetz Center for Dynamical Systems, Brown University, Providence, Rhode Island. 1981.
[4] Nagurney A, Dong J, and Mokhtarian P L. Integrated Multicriteria Network Equilibrium Models for Commuting Versus Telecommuting. Isenberg School of Management, University of Massachusetts, Amherst, Massachusetts, 2000.
[5] Nagurney A, Dong J, and Mokhtarian P L. Teleshopping Versus Shopping: A Multicriteria Network Equilibrium Framework. Mathematical and Computer Modelling 2001: 783-798.
[6]Mokhtarian P L.Salomon I. Emerging Travel Patterns: Do Telecommunications Make a Difference?, in In Perpetual Motion: travel Behavior Research Opportunities and Application Chellenges, H S Mahmassani, editor, 2002: 143-181.
[7] Nagurney A, and Dong J, Supernetworks: Decision-Making for the Information Age, Edward Elgar Publishers, Cheltenham, England, in press. 2002: 41-77.
[8] Nagurney A, Loo J, Dong J, et al. Supply Chain Networks and Electronic Commerce: A Theoretical Perspective. Netnomics, 2002(4): 187-220.
[9] Nagurney A, Ke K, Cruz J, et al. A Multilevel Network Perspective (Logistical /Informational/Financial). Environment & Planning B, 2002, 29:795-818.
[10] Langheinrich Mt Nakamura At Abe T K Nt et al. Unintrusive customization techniques for web advertising. Computer Networks, 1999, 31(11—16): 1259—1272.
[11]Abe N. Nakamura A . Learning to optimally schedule internet banner advertisements. Proc of the 16th Int Conf on Machine Learning. Bled, Slovenia. 1999:12-22.
[12] Zhao L, A Nagurney. A network modeling approach for Internet advertising. Netnomics, 2005(3):181-200.
[13] Wardrop J G. Some Theoretical Aspects of Road Traffic Research. Proceedings of the Institute of Civil Engineers, 1952: II, 325-378.
[14] Dafermos S. The Traffic Assignment Problem for Multimodal Networks. Transportation Science, 1972(6): 73-87.
[15] Sheffi Y. Transportation Network Equilibrium with Discrete Choice Models.-Ph.D. thesis. Civil Engineering Department, Massachusetts Institute of Technology, Cambridge, Massachusetts. 1978.
[16] Sheffi Y, Daganzo C F. Computation of Equilibrium Over Transportation Networks: The Case of Disaggregate Demand Models. Transportation Science, 1980(14): 155-173.
[17] Dafermos S. Traffic equilibrium and Variational inequalities. Transportation Science, 1980(14): 42-54.
[18] Bar-Gera H. Origin-Based Algorithms for Transportation Network Modeling. National Institute of Statistical Sciences, Technical Report # 103, Research Triangle Park, North Carolina, 1999.
[19] Wu J H, Florian M, and He S G. EMME/2 Implementation of the SCAG-Ⅱ Model: Data Structure, System Analysis and Computation. Submitted to the Southern California Association of Governments, INRO Solutions Internal Report, Montreal, Quebec, Canada. 2000.
[20] Abello J, Pardalos P M, and Resende M G C. On Maximum Clique Problems in Very Large Graphs in External Memory Algorithms. AMS Series on Discrete Mathematics and Theoretical Computer Science, 1999, 50: 119-130.
[21] Nagurney A. Navigating the Network Economy. OR/MS Today. Lionheart Publishing Company, Atlanta, Georgia, 2000: 74-75.
[22] David Kinderlehrer. Variational inequalities and free boundary problems. Bull. Amer. Math. Soc. 1978, 84(1), 7-26.
[23] 郭友中，刘君兰译．变分不等方程及其应用．北京：1991．
[24] 单洪忠．迭代法求解变分不等式问题．北京服装学院学报(自然科学)，2000，20(1)：82-85．
[25] KORPELEVICH E N. The Extragradient Method for Finding Saddle Points and Other Problems. Matecon, 1976(12): 747-756.
[26] Han D R. A New Hybrid Generalized Proximal Point Algo2rithm for Variational Inequality Problems. Journal of Global Optimization, 2003, 26: 125-128.
[27] 王传伟．一个求解变分不等式问题的投影算法．重庆师范大学学报(自然科学)．2005，22(1)：6-11．
[28] 江莉，吕玉华．一般强单调交分不等式的改进投影算法．青岛科技大学学报． 2006，27(2)：179-181．
[29] 李郑国，王猛，曾华军译．支持向量积．北京：电子工业出版社，2004：1-24．
[30] Bertsekas D P, Tsitsiklis J N. Parallel and distributed computation. Prentice-Hall. Englewood Cliffs, New Jersey, 1992.
[31] 胡忠青．国内网络广告发展前景管窥．特区经济．2004年11月26日：115-116．
[32] 阿建卓．网络广告问题探析．廊坊师范学院学报．2007，23(3)：29-31．
[33] 张志华．王莉．网络环境下广告资源优化决策模型．鞍山科技大学学报，2006(5)：510-515．
[34] 邓文峰，周朝民．浅析网络广告效果评价．上海管理科学，2005(4)：13-15．
[35] 美国网络广告调查公司Adknowledge在“2000年第三季度网络广告调查报告”，2000．
[36] Young—Hoon Park, Peter S. Fader. Modeling browsing behavior at multiple websites. Marketing Science, 2004, 23(3): 280—303.
[37] Chattcrjec D L. Hoffman. modeling the clickstream, in applications for Webbased advertising efforts. Marketing Science, 2003, 22(4): 520—541.
[38] 梅仕鹏，蒋海波．网络广告效果评价指标的评析与构建．江苏商论．2003(12)．
[39] Anna Nagurney, June Dong. Super-networks: Decision-Making for the Information Age, Appendix B Variational Inequaliteies. 2002, 299-304.