A Primal–Dual Lifting Scheme for Two-Stage Robust Optimization

Published Online:https://doi.org/10.1287/opre.2019.1873

References

  • An Y, Zeng B, Zhang Y, Zhao L (2014) Reliable p-median facility location problem: Two-stage robust models and algorithms. Transportation Res. Part B: Methodological 64:54–72.CrossrefGoogle Scholar
  • Anderson BDO, Moore JB (1990) Optimal Control: Linear Quadratic Methods (Prentice-Hall, Inc., Upper Saddle River, NJ).Google Scholar
  • Angulo G, Ahmed S, Dey SS, Kaibel V (2015) Forbidden vertices. Math. Oper. Res. 40(2):350–360.LinkGoogle Scholar
  • Ardestani-Jaafari A, Delage E (2016) Robust optimization of sums of piecewise linear functions with application to inventory problems. Oper. Res. 64(2):474–494.LinkGoogle Scholar
  • Atamtürk A, Zhang M (2007) Two-stage robust network flow and design under demand uncertainty. Oper. Res. 55(4):662–673.LinkGoogle Scholar
  • Ayoub J, Poss M (2016) Decomposition for adjustable robust linear optimization subject to uncertainty polytope. Comput. Management Sci. 13(2):219–239.CrossrefGoogle Scholar
  • Ben-Tal A, Goryashko A, Guslitzer E, Nemirovski A (2004) Adjustable robust solutions of uncertain linear programs. Math. Programming 99(2):351–376.CrossrefGoogle Scholar
  • Bertsimas D, Caramanis C (2010) Finite adaptibility in multistage linear optimization. IEEE Trans. Automatic Control 55(12):2751–2766.CrossrefGoogle Scholar
  • Bertsimas D, de Ruiter FJCT (2016) Duality in two-stage adaptive linear optimization: Faster computation and stronger bounds. INFORMS J. Comput. 28(3):500–511.LinkGoogle Scholar
  • Bertsimas D, Dunning I (2016) Multistage robust mixed-integer optimization with adaptive partitions. Oper. Res. 64(4):980–998.LinkGoogle Scholar
  • Bertsimas D, Georghiou A (2015) Design of near optimal decision rules in multistage adaptive mixed-integer optimization. Oper. Res. 63(3):610–627.LinkGoogle Scholar
  • Bertsimas D, Goyal V (2010) On the power of robust solutions in two-stage stochastic and adaptive optimization problems. Math. Oper. Res. 35(2):284–305.LinkGoogle Scholar
  • Bertsimas D, Goyal V (2012) On the power and limitations of affine policies in two-stage adaptive optimization. Math. Programming 134(2):491–531.CrossrefGoogle Scholar
  • Bertsimas D, Brown DB, Caramanis C (2011a) Theory and applications of robust optimization. SIAM Rev. 53(3):464–501.CrossrefGoogle Scholar
  • Bertsimas D, Goyal V, Sun XA (2011b) A geometric characterization of the power of finite adaptability in multistage stochastic and adaptive optimization. Math. Oper. Res. 36(1):24–54.LinkGoogle Scholar
  • Bertsimas D, Iancu DA, Parrilo PA (2010) Optimality of affine policies in multi-stage robust optimization. Math. Oper. Res. 35(2):363–394.LinkGoogle Scholar
  • Bertsimas D, Iancu DA, Parrilo PA (2011c) A hierarchy of near-optimal policies for multistage adaptive optimization. IEEE Trans. Automatic Control 56(12):2809–2824.CrossrefGoogle Scholar
  • Bertsimas D, Litvinov E, Sun XA, Zhao J, Zheng T (2013) Adaptive robust optimization for the security constrained unit commitment problem. IEEE Trans. Power Systems 28(1):52–63.CrossrefGoogle Scholar
  • Buchta C, Müller J, Tichy RF (1985) Stochastical approximation of convex bodies. Math. Ann. 271(2):225–235.CrossrefGoogle Scholar
  • Büeler B, Enge A, Fukuda K (2000) Exact volume computation for polytopes: A practical study. Kalai G, Ziegler GM, eds. Polytopes—Combinatorics and Computation (Birkhäuser, Basel, Switzerland), 131–154.CrossrefGoogle Scholar
  • Chen X, Zhang Y (2009) Uncertain linear programs: Extended affinely adjustable robust counterparts. Oper. Res. 57(6):1469–1482.LinkGoogle Scholar
  • Chen X, Sim M, Sun P, Zhang J (2008) A linear decision-based approximation approach to stochastic programming. Oper. Res. 56(2):344–357.LinkGoogle Scholar
  • Delage E, Iancu DA (2015) Robust multistage decision making. Aleman DM, Thiele AC, eds. The Operations Research Revolution: Tutorials in Operations Research (INFORMS, Catonsville, MD), 20–46.LinkGoogle Scholar
  • Gabrel V, Murat C, Thiele A (2014) Recent advances in robust optimization: An overview. Eur. J. Oper. Res. 235(3):471–483.CrossrefGoogle Scholar
  • Gal T (1993) Degeneracy graphs: Theory and application an updated survey. Ann. Oper. Res. 46(1):81–105.CrossrefGoogle Scholar
  • Georghiou A, Tsoukalas A, Wiesemann W (2019) Robust dual dynamic programming. Oper. Res. 67(3):599–904.LinkGoogle Scholar
  • Georghiou A, Wiesemann W, Kuhn D (2015) Generalized decision rule approximations for stochastic programming via liftings. Math. Programming 152(1):301–338.CrossrefGoogle Scholar
  • Goh J, Sim M (2010) Distributionally robust optimization and its tractable approximations. Oper. Res. 58(4):902–917.LinkGoogle Scholar
  • Gorissen BL, den Hertog D (2013) Robust counterparts of inequalities containing sums of maxima of linear functions. Eur. J. Oper. Res. 227(1):30–43.CrossrefGoogle Scholar
  • Gorissen BL, Yanıkoğlu İ, den Hertog D (2015) A practical guide to robust optimization. Omega 53:124–137.CrossrefGoogle Scholar
  • Gounaris CE, Wiesemann W, Floudas CA (2013) The robust capacitated vehicle routing problem under demand uncertainty. Oper. Res. 61(3):677–693.LinkGoogle Scholar
  • Guslitser E (2002) Uncertainty-immunized solutions in linear programming. Unpublished master’s thesis, Technion, Haifa, Israel.Google Scholar
  • Hadjiyiannis MJ, Goulart PJ, Kuhn D (2011) A scenario approach for estimating the suboptimality of linear decision rules in two-stage robust optimization. Proc. 50th IEEE Conf. Decision Control Eur. Control Conf. (IEEE, Piscataway, NJ), 7386–7391.Google Scholar
  • Hanasusanto GA, Kuhn D (2018) Conic programming reformulations of two-Stage distributionally robust linear programs over Wasserstein balls. Oper. Res. 66(3):849–869.LinkGoogle Scholar
  • Hanasusanto GA, Kuhn D, Wiesemann W (2015) K-adaptability in two-stage robust binary programming. Oper. Res. 63(4):877–891.LinkGoogle Scholar
  • Henk M (2012) Löwner–John ellipsoids. Documenta Mathematica—Extra Volume: Optimization Stories (Deutschen Mathematiker-Vereinigung, Berlin), 95–106.Google Scholar
  • Jiang R, Zhang M, Li G, Guan Y (2014) Two-stage network constrained robust unit commitment problem. Eur. J. Oper. Res. 234(3):751–762.CrossrefGoogle Scholar
  • Kuhn D, Wiesemann W, Georghiou A (2011) Primal and dual linear decision rules in stochastic and robust optimization. Math. Programming 130(1):177–209.CrossrefGoogle Scholar
  • Lappas NH, Gounaris CE (2016) Multi-stage adjustable robust optimization for process scheduling under uncertainty. AIChE J. 62(5):1646–1667.CrossrefGoogle Scholar
  • Liebchen C, Lübbecke M, Möhring RH, Stiller S. (2009) The concept of recoverable robustness, linear programming recovery, and railway applications. Ahuja RK, Möhring RH, Zaroliagis CD, eds. Robust and Online Large-Scale Optimization: Models and Techniques for Transportation Systems (Springer, Berlin, Heidelberg), 1–27.CrossrefGoogle Scholar
  • Lorca A, Sun XA (2015) Adaptive robust optimization with dynamic uncertainty sets for multi-period economic dispatch under significant wind. IEEE Trans. Power Systems 30(4):1702–1713.CrossrefGoogle Scholar
  • Lorca A, Sun XA (2017) Multistage robust unit commitment with dynamic uncertainty sets and energy storage. IEEE Trans. Power Systems 32(3):1678–1688.CrossrefGoogle Scholar
  • Postek K, den Hertog D (2016) Multistage adjustable robust mixed-integer optimization via iterative splitting of the uncertainty set. INFORMS J. Comput. 28(3):553–574.LinkGoogle Scholar
  • Ruiz C, Conejo AJ (2015) Robust transmission expansion planning. Eur. J. Oper. Res. 242(2):390–401.CrossrefGoogle Scholar
  • Seidel R (2004) Convex hull computations. Toth CD, O’Rourke J, Goodman JE, eds. Handbook of Discrete and Computational Geometry (Chapman and Hall, Boca Raton, FL), 494–512.CrossrefGoogle Scholar
  • Song Y, Luedtke J (2015) An adaptive partition-based approach for solving two-stage stochastic programs with fixed recourse. SIAM J. Optim. 25(3):1344–1367.CrossrefGoogle Scholar
  • Subramanyam A, Gounaris C, Wiesemann W (2017a) K-adaptability in two-stage mixed-integer robust optimization. Accessed January 22, 2020, http://www.optimization-online.org/DB_FILE/2017/06/6093.pdf.Google Scholar
  • Subramanyam A, Mufalli F, Pinto JM, Gounaris CE (2017b) Robust multi-period vehicle routing under customer order uncertainty. Accessed January 22, 2020, http://www.optimization-online.org/DB_HTML/2017/04/5947.html.Google Scholar
  • Thiele A, Terry T, Epelman M (2010) Robust linear optimization with recourse. Technical report, Lehigh University, Bethlehem, PA, and University of Michigan, Ann Arbor.Google Scholar
  • Vayanos P, Kuhn D, Rustem B (2011) Decision rules for information discovery in multi-stage stochastic programming. Proc. 50th IEEE Conf. Decision Control Eur. Control Conf. (IEEE, Piscataway, NJ), 7368–7373.Google Scholar
  • Warrington J, Goulart P, Mariéthoz S, Morari M (2013) Policy-based reserves for power systems. IEEE Trans. Power Systems 28(4):4427–4437.CrossrefGoogle Scholar
  • Wiesemann W, Kuhn D, Rustem B (2012) Robust resource allocations in temporal networks. Math. Programming 135(1–2):437–471.CrossrefGoogle Scholar
  • Xu G, Burer S (2018) A copositive approach for two-stagae adjustable robust optimization with uncertain right-hand sides. Comput. Optim. Appl. 70(1):33–59.Google Scholar
  • Yanıkoğlu İ, Gorissen BL, den Hertog D (2019) Adjustable robust optimization—a survey and tutorial. Eur. J. Oper. Res. 277(3):799–813.Google Scholar
  • Zeng B, Zhao L (2013) Solving two-stage robust optimization problems using a column-and-constraint generation method. Oper. Res. Lett. 41(5):457–461.CrossrefGoogle Scholar
  • Zhao C, Wang J, Watson J-P, Guan Y (2013) Multi-stage robust unit commitment considering wind and demand response uncertainties. IEEE Trans. Power Systems 28(3):2708–2717.CrossrefGoogle Scholar
  • Zhen J, den Hertog D, Sim M (2018) Adjustable robust optimization via Fourier-Motzkin elimination. Oper. Res. 66(4):1086–1100.LinkGoogle Scholar
  • Ziegler GM. (2000) Lectures on 0/1-polytopes. Kalai G, Ziegler GM, eds. Polytopes—Combinatorics and Computation (Birkhäuser, Basel, Switzerland), 1–41.CrossrefGoogle Scholar
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