A parametric programming approach to bilevel optimisation with lower-level variables in the upper level

References

• Avis, D. (2000). lrs: A revised implementation of the reverse search vertex enumeration algorithm. DMV Seminar, 29, 177–198.
   Google Scholar
• Avis, D., & Fukuda, K. (1996). Reverse search for enumeration. Discrete Applied Mathematics, 65(1–3), 21–46. doi:10.1016/0166-218X(95)00026-N
   Web of Science ®Google Scholar
• Bard, J. (1998). Practical bilevel optimization: applications and algorithms. Boston, MA: Kluwer Academic Press.
   Google Scholar
• Baringo, L., & Conejo, A. J. (2011). Wind power investment within a market environment. Applied Energy, 88(9), 3239–3247. doi:10.1016/j.apenergy.2011.03.023
   Web of Science ®Google Scholar
• Baringo, L., & Conejo, A. J. (2013). Correlated wind-power production and electric load scenarios for investment decisions. Applied Energy, 101, 475–482. doi:10.1016/j.apenergy.2012.06.002
   Web of Science ®Google Scholar
• Ben-Ayed, O., & Blair, C. E. (1990). Computational difficulties of bilevel linear programming. Operations Research, 38(3), 556–560. doi:10.1287/opre.38.3.556
   Web of Science ®Google Scholar
• Berkelaar, M. (2015). lpsolve: Interface to ‘lp_solve’ v. 5.5 to solve linear/integer programs [Computer software manual]. Retrieved from https://cran.r-project.org/package=lpSolve.
   Google Scholar
• Bertsimas, D. P., & Tsitsiklis, J. N. (1997). Introduction to Linear Optimization, Belmont, MA: Athena Scientific.
   Google Scholar
• Bialas, W. F., & Karwan, M. H. (1984). Two-level linear programming. Management Science, 30(8), 1004–1020. doi:10.1287/mnsc.30.8.1004
   Web of Science ®Google Scholar
• Chen, Y., Hobbs, B. F., Leyffer, S., & Munson, T. S. (2006). Leader-follower equilibria for electric power and NOx allowances markets. Computational Management Science, 3(4), 307–330. doi:10.1007/s10287-006-0020-1
   Google Scholar
• Colson, B., Marcotte, P., & Savard, G. (2005). Bilevel programming: A survey. 4OR, 3(2), 87–107. doi:10.1007/s10288-005-0071-0
   Google Scholar
• Colson, B., Marcotte, P., & Savard, G. (2007). An overview of bilevel optimization. Annals of Operations Research, 153(1), 235–256. doi:10.1007/s10479-007-0176-2
   Web of Science ®Google Scholar
• Conejo, A. J., Baringo, L., Kazempour, S. J., & Siddiqui, A. S. (2016). Investment in electricity generation and transmission. Heidelberg, Germany: Springer.
   Google Scholar
• Danish District Heating Association, & Danish Energy Association. (2016). Indspil til strategi for fremtidens kraftvarme (Tech. Rep.). Frederiksberg, Denmark: Danish Energy Association.
   Google Scholar
• Dempe, S. (2018). Bilevel optimization: theory, algorithms and applications (preprint 2018-11, http://tu-freiburg.de/fakult1).
   Google Scholar
• Dempe, S., Kalashnikov, V., Pérez-Valdés, G. A., & Kalashnykova, N. (2015). Bilevel programming problems. New York: Springer.
   Google Scholar
• Dua, V., Bozinis, N. A., & Pistikopoulos, E. N. (2002). A multiparametric programming approach for mixed-integer quadratic engineering problems. Computers and Chemical Engineering, 26(4–5), 715–733. doi:10.1016/S0098-1354(01)00797-9
   Web of Science ®Google Scholar
• Ehrenmann, A., & Smeers, Y. (2011). Generation capacity expansion in a risky environment: A stochastic equilibrium analysis. Operations Research, 59(6), 1332–1346. doi:10.1287/opre.1110.0992
   Web of Science ®Google Scholar
• Faísca, N. P., Dua, V., Rustem, B., Saraiva, P. M., & Pistikopoulos, E. N. (2007). Parametric global optimisation for bilevel programming. Journal of Global Optimization, 38(4), 609–623. doi:10.1007/s10898-006-9100-6
   Web of Science ®Google Scholar
• Fortuny-Amat, J., & McCarl, B. (1981). A representation and economic interpretation of a two-level programming problem. Journal of the Operational Research Society, 32(9), 783–792. doi:10.1057/jors.1981.156
   Web of Science ®Google Scholar
• Gabriel, S. A., Conejo, A. J., Fuller, J. D., Hobbs, B. F., & Ruiz, C. (2013). Complementarity Modeling in Energy Markets. New York: Springer.
   Google Scholar
• Gabriel, S. A., García-Bertrand, R., Sahakij, P., & Conejo, A. J. (2006). A practical approach to approximate bilinear functions in mathematical programming problems by using Schur’s decomposition and SOS type 2 variables. Journal of the Operational Research Society, 57(8), 995–1004. doi:10.1057/palgrave.jors.2602052
   Web of Science ®Google Scholar
• Gabriel, S. A., & Leuthold, F. U. (2010). Solving discretely-constrained MPEC problems with applications in electric power markets. Energy Economics, 32(1), 3–14.
   Web of Science ®Google Scholar
• Gal, T. (1995). Postoptimal analyses, parametric programming, and related topics. New York: Walter de Gruyter.
   Google Scholar
• GAMS. (2017). General algebraic modeling system. Retrieved from gams.com/.
   Google Scholar
• Garcés, L. P., Conejo, A. J., García-Bertrand, R., & Romero, R. (2009). A bilevel approach to transmission expansion planning within a market environment. IEEE Transactions on Power Systems, 24(3), 1513–1522. doi:10.1109/TPWRS.2009.2021230
   Web of Science ®Google Scholar
• Han, J., Liu, G., & Wang, S. (2000). A new descent algorithm for solving quadratic bilevel programming problems. Acta Mathematicae Applicatae Sinica, 16(3), 235–244.
   Google Scholar
• Hobbs, B. F., Metzler, C. B., & Pang, J.-S. (2000). Strategic gaming analysis for electric power systems: An MPEC approach. IEEE Transactions on Power Systems, 15(2), 638–645.
   Web of Science ®Google Scholar
• Joskow, P., & Tirole, J. (2005). Merchant transmission investment. Journal of Industrial Economics, 53(2), 233–264. doi:10.1111/j.0022-1821.2005.00253.x
   Web of Science ®Google Scholar
• Kazempour, S. J., & Conejo, A. J. (2012). Strategic generation investment under uncertainty via Benders decomposition. IEEE Transactions on Power Systems, 27(1), 424–432. doi:10.1109/TPWRS.2011.2159251
   Web of Science ®Google Scholar
• Kazempour, S. J., Conejo, A. J., & Ruiz, C. (2011). Strategic generation investment using a complementarity approach. IEEE Transactions on Power Systems, 26(2), 940–948. doi:10.1109/TPWRS.2010.2069573
   Web of Science ®Google Scholar
• Khanabadi, M., & Ghasemi, H. (2011). Transmission congestion management through optimal transmission switching. IEEE Power and Energy Society General Meeting, 1–5. IEEE.
   Google Scholar
• Koschker, S., & Möst, D. (2016). Perfect competition vs. strategic behaviour models to derive electricity prices and the influence of renewables on market power. Or Spectrum, 38(3), 661–686. doi:10.1007/s00291-015-0415-x
   Web of Science ®Google Scholar
• Liu, Y.-H., & Spencer, T. H. (1995). Solving a bilevel linear program when the inner decision maker controls few variables. European Journal of Operational Research, 81(3), 644–651. doi:10.1016/0377-2217(94)00005-W
   Web of Science ®Google Scholar
• Luo, Z.-Q., Pang, J.-S., & Ralph, D. (1996). Mathematical programs with equilibrium constraints. Cambridge: Cambridge University Press.
   Google Scholar
• Manas, M., & Nedoma, J. (1968). Finding all vertices of a convex polyhedron. Numerische Mathematik, 12, 226–229. doi:10.1007/BF02162916
   Web of Science ®Google Scholar
• Mirrlees, J. A. (1999). The theory of moral hazard and unobservable behaviour: Part i. The Review of Economic Studies, 66(1), 3–21. doi:10.1111/1467-937X.00075
   Web of Science ®Google Scholar
• Nord Pool AS. (2017). Nord Pool. Retrieved from nordpoolspot.com/.
   Google Scholar
• Outrata, J. V. (1988). A note on the usage of nondifferentiable exact penalties in some special optimization problems. Kybernetika, 24(4), 251–258.
   Web of Science ®Google Scholar
• Pineda, S., Bylling, H. C., & Morales, J. M. (2017). Efficiently solving linear bilevel programming problems using off-the-shelf optimization software. Optimization and Engineering, 19, 187–211
   Web of Science ®Google Scholar
• Ren, A., & Wang, Y. (2015). An interval approach based on expectation optimization for fuzzy random bilevel linear programming problems. Journal of the Operational Research Society, 66(12), 2075–2085.
   Google Scholar
• Robere, R. (2015). vertexenum: Vertex Enumeration of Polytopes [Computer software manual]. Retrieved from https://cran.r-project.org/package=vertexenum.
   Google Scholar
• Ruiz, C., & Conejo, A. J. (2009). Pool strategy of a producer with endogenous formation of locational marginal prices. IEEE Transactions on Power Systems, 24(4), 1855–1866. doi:10.1109/TPWRS.2009.2030378
   Web of Science ®Google Scholar
• Saharidis, G. K. D., Conejo, A. J., & Kozanidis, G. (2013). Exact solution methodologies for linear and (mixed) integer bilevel programming. In Metaheuristics for bi-level optimization (vol. 482, pp. 221–245). New York: Springer.
   Google Scholar
• Scheel, H., & Scholtes, S. (2000). Mathematical programs with complementarity constraints: Stationarity, optimality, and sensitivity. Mathematics of Operations Research, 25(1), 1–22. doi:10.1287/moor.25.1.1.15213
   Web of Science ®Google Scholar
• Shi, C., Lu, J., & Zhang, G. (2005). An extended Kuhn-Tucker approach for linear bilevel programming. Applied Mathematics and Computation, 162(1), 51–63. doi:10.1016/j.amc.2003.12.089
   Web of Science ®Google Scholar
• Shih, H.-S., Cheng, C.-B., Wen, U.-P., Huang, Y.-C., & Peng, M.-Y. (2012). Determining a subsidy rate for taiwan's recycling glass industry: An application of bi-level programming. Journal of the Operational Research Society, 63(1), 28–37. doi:10.1057/jors.2011.13
   Web of Science ®Google Scholar
• Siddiqui, S., & Gabriel, S. A. (2013). An SOS1-based approach for solving MPECs with a natural gas market application. Networks and Spatial Economics, 13(2), 205–227. doi:10.1007/s11067-012-9178-y
   Web of Science ®Google Scholar
• Sorokin, A., Rebennak, S., Pardalos, P. M., & Iliadis, N. A. (2012). Handbook of networks on power systems. New York: Springer.
   Google Scholar
• Stackelberg, H. V. (1934). Market structure and equilibrium. New York: Springer.
   Google Scholar
• Stoft, S. (2002). Power system economics. Journal of Energy Literature, 8, 94–99.
   Google Scholar
• Vicente, L. N., & Calamai, P. H. (1994). Bilevel and multilevel programming: A bibliography review. Journal of Global Optimization, 5(3), 291–306. doi:10.1007/BF01096458
   Web of Science ®Google Scholar