Decomposition approach for solving large-scale spatially disaggregated economic equilibrium problems

References

• Adams, D., Alig, R. J., Callaway, J. M., McCarl, B. A., & Winnett, S. M. (1996). The Forest and Agricultural Sector Optimization Model (FASOM): Model Structure and Policy Applications.
   Google Scholar
• Aganagic, M., & Mokhtari, S. (1997). Security constrained economic dispatch using nonlinear Dantzig-Wolfe decomposition. IEEE Transactions on Power Systems, 12(1), 105–112. https://doi.org/10.1109/59.574929
   Web of Science ®Google Scholar
• Ahn, B.-H., & Hogan, W. W. (1982). On convergence of the PIES algorithm for computing equilibria. Operations Research, 30(2), 281–300. https://doi.org/10.1287/opre.30.2.281
   Web of Science ®Google Scholar
• Baier, S., Clements, M., Griffiths, C., Ihrig, J. (2009). Biofuels impact on crop and food prices. Retrieved from https://www.federalreserve.gov/pubs/ifdp/2009/967/ifdp967.pdf
   Google Scholar
• Bazaraa, M. S., Sherali, H. D., & Shetty, C. M. (2006). Nonlinear programming: Theory and algorithms. John Wiley and Sons.
   Google Scholar
• Bradley, S. P., Hax, A. C., & Magnanti, T. L. (1977). Applied mathematical programming. Addison-Wesley.
   Google Scholar
• Büeler, B. (1997). Solving an equilibrium model for trade of CO2 emission permits. European Journal of Operational Research, 102(2), 393–403. https://doi.org/10.1016/S0377-2217(97)00117-3
   Web of Science ®Google Scholar
• Carey, M. (1977). Integrability and mathematical programming models: A survey and a parametric approach. Econometrica, 45(8), 1957. https://doi.org/10.2307/1914120
   Web of Science ®Google Scholar
• Çelebi, E., & Fuller, J. D. (2013). Master problem approximations in Dantzig-Wolfe decomposition of variational inequality problems with applications to two energy market models. Computers & Operations Research, 40(11), 2724–2739. https://doi.org/10.1016/j.cor.2013.05.012
   Web of Science ®Google Scholar
• Chen, X., Huang, H., Khanna, M., & Önal, H. (2014). Alternative transportation fuel standards: Welfare effects and climate benefits. Journal of Environmental Economics and Management, 67(3), 241–257. https://doi.org/10.1016/j.jeem.2013.09.006
   Web of Science ®Google Scholar
• Chen, X., & Önal, H. (2012). Modeling agricultural supply response using mathematical programming and crop mixes. American Journal of Agricultural Economics, 94(3), 674–686. https://doi.org/10.1093/ajae/aar143
   Web of Science ®Google Scholar
• Chung, W., Fuller, J. D., & Wu, Y. J. (2003). A new demand-supply decomposition method for a class of economic equilibrium models. Computational Economics, 21(3), 231–243. https://doi.org/10.1023/A:1023995710308
   Google Scholar
• Chung, W., Fuller, J. D., & Wu, Y. J. (2006). A new decomposition method for multiregional economic equilibrium models. Operations Research, 54(4), 643–655. https://doi.org/10.1287/opre.1060.0274
   Web of Science ®Google Scholar
• Conejo, A. J., Castillo, E., Mínguez, R., & García-Bertrand, R. (2006). Decomposition techniques in mathematical programming: Engineering and science applications. Springer Science & Business Media.
   Google Scholar
• Dafermos, S., & Nagurney, A. (1984). A network formulation of market equilibrium problems and variational inequalities. Operations Research Letters, 3(5), 247–250. https://doi.org/10.1016/0167-6377(84)90055-5
   Web of Science ®Google Scholar
• Dantzig, G. (1963). Linear programming and extensions. Princeton University Press.
   Google Scholar
• Dantzig, G., & Thapa, M. (2003). Linear programming II: Theory and extensions. Springer.
   Google Scholar
• Devadoss, S., Westhoff, P. C., Helmar, M. D., Grundmeier, E., Skold, K. D., Meyers, W. H., & Johnson, S. R. (1989). The FAPRI Modeling System at CARD: A Documentation Summary. CARD Technical Reports.
   Google Scholar
• EIA. (2011). Annual Energy Outlook 2011:With Projections to 2035. U.S. Energy Information Administration, Office of Integrated Analysis and Forecasting, Washington, DC.
   Google Scholar
• Friesz, T. L., Tobin, R. L., Smith, T. E., & Harker, P. T. (1983). A nonlinear complementarity formulation and solution procedure for the general derived demand network equilibrium problem. Journal of Regional Science, 23(3), 337–359. https://doi.org/10.1111/j.1467-9787.1983.tb00994.x
   Web of Science ®Google Scholar
• Gabriel, S., Conejo, A., Fuller, J., Hobbs, B., & Ruiz, C. (2012). Complementarity modeling in energy markets. Springer Science and Business Media.
   Google Scholar
• Gabriel, S., Kydes, A. S., & Whitman, P. (2001). The national energy modeling system: A large-scale energy-economic equilibrium model. Operations Research, 49(1), 14–25. https://doi.org/10.1287/opre.49.1.14.11195
   Web of Science ®Google Scholar
• Gilmore, P. C., & Gomory, R. E. (1963). A Linear Programming Approach to the Cutting Stock Problem—Part II. Operations Research, 11(6), 863–888. https://doi.org/10.1287/opre.11.6.863
   Web of Science ®Google Scholar
• Grothey, A. (2001). Decomposition methods for nonlinear nonconvex optimization problems. Doctoral Dissertation, University of Edinburgh.
   Google Scholar
• Hearn, D. W., Lawphongpanich, S., & Ventura, J. (1987). Restricted simplicial decomposition: computation and extensions. In K. L. Hoffman, R. H. F. Jackson, J. Telgen (Eds.), Computation mathematical programming. Mathematical Programming Studies (vol 31). Springer. https://doi.org/10.1007/BFb0121181
   Google Scholar
• Ho, J. K., & Loute, E. (1983). Computational experience with advanced implementation of decomposition algorithms for linear programming. Mathematical Programming, 27(3), 283–290. https://doi.org/10.1007/BF02591904
   Web of Science ®Google Scholar
• Ho, J., & Loute, E. (1981). An advanced implementation of the Dantzig–Wolfe decomposition algorithm for linear. Mathematical Programming, 20(1), 303–326. https://doi.org/10.1007/BF01589355
   Web of Science ®Google Scholar
• Hurwicz, L., & Uzawa, H. (1971). On the integrability of demand functions. In J. S. Chipman, L. Hurwicz, M. K. Richter, & H. F. Sonnenschein (Eds.), Preferences, utility, and demand: A Minnesota Symposium (pp. 27–64). Harcourt Brace Jovanavich Ltd.
   Google Scholar
• Lasdon, L. S. (1970). Optimization theory for large systems. Macmillan.
   Google Scholar
• Lawphongpanich, S. (2000). Simplicial with truncated Dantzig-Wolfe decomposition for nonlinear multicommodity network flow problems with side constraints. Operations Research Letters, 26(1), 33–41. https://doi.org/10.1016/S0167-6377(99)00059-0
   Web of Science ®Google Scholar
• Ljung, B., & Selmer, J. (1979). An experimental test of the dantzig and wolfe decomposition algorithm as a planning tool in a business firm. The Scandinavian Journal of Economics, 81(3), 415–426. https://doi.org/10.2307/3439493
   Web of Science ®Google Scholar
• Luo, Z.-Q., Pang, J.-S., & Ralph, D. (1996). Mathematical programs with equilibrium constraints. Cambridge University Press.
   Google Scholar
• Mathiesen, L. (1985). Computational experience in solving equilibrium models by a sequence of linear complementarity problems. Operations Research, 33(6), 1225–1250. https://doi.org/10.1287/opre.33.6.1225
   Web of Science ®Google Scholar
• McCarl, B. A., & Spreen, T. H. (1980). Price endogenous mathematical programming as a tool for sector analysis. American Journal of Agricultural Economics, 62(1), 87–102. https://doi.org/10.2307/1239475
   Web of Science ®Google Scholar
• Murphy, F. H., Conti, J. J., Shaw, S. H., & Sanders, R. (1988). Modeling and forecasting energy markets with the intermediate future forecasting system. Operations Research, 36(3), 406–420. https://doi.org/10.1287/opre.36.3.406
   Web of Science ®Google Scholar
• Nagurney, A. (1987). Competitive equilibrium problems, variational inequalities and regional science. Journal of Regional Science, 27(4), 503–517. https://doi.org/10.1111/j.1467-9787.1987.tb01179.x
   Web of Science ®Google Scholar
• Patriksson, M. (2008). A survey on the continuous nonlinear resource allocation problem. European Journal of Operational Research, 185(1), 1–46. https://doi.org/10.1016/j.ejor.2006.12.006
   Web of Science ®Google Scholar
• Samuelson, P. A. (1950). The problem of integrability in utility theory. Economica, 17(68), 355–385. https://doi.org/10.2307/2549499
   Web of Science ®Google Scholar
• Samuelson, P. A. (1952). Spatial price equilibrium and linear programming. American Economic Review, 42(3), 283–303. https://doi.org/10.2307/1810381
   Web of Science ®Google Scholar
• Takayama, T., & Judge, G. (1971). Spatial and temporal price and allocation models. North-Holland Publishing Company.
   Google Scholar
• Takayama, T., & Judge, G. G. (1964). Equilibrium among spatially separated markets: A reformulation. Econometrica, 32(4), 510–524. https://doi.org/10.2307/1910175
   Web of Science ®Google Scholar
• Von Hohenbalken, B. (1977). Simplicial decomposition in nonlinear programming algorithms. Mathematical Programming, 13(1), 49–68. https://doi.org/10.1007/BF01584323
   Web of Science ®Google Scholar