Multistage Adjustable Robust Mixed-Integer Optimization via Iterative Splitting of the Uncertainty Set

References

• Beck A, Ben-Tal A (2009) Duality in robust optimization: Primal worst equals dual best. Oper. Res. Lett. 37(1):1–6.Crossref, Google Scholar
• Ben-Tal A, Den Hertog D, Vial J-Ph (2014) Deriving robust counterparts of nonlinear uncertain inequalities. Math. Programming 149(1–2):265–299.Crossref, Google Scholar
• Ben-Tal A, El Ghaoui L, Nemirovski A (2009) Robust Optimization (Princeton University Press, Princeton, NJ).Crossref, Google Scholar
• Ben-Tal A, Goryashko A, Guslitzer E, Nemirovski A (2004) Adjustable robust solutions of uncertain linear programs. Math. Programming 99(2):351–376.Crossref, Google Scholar
• Bertsimas D, Caramanis C (2007) Adaptability via sampling. 46th IEEE Conf. Decision Control, New Orleans, 4717–4722.Crossref, Google Scholar
• Bertsimas D, Caramanis C (2010) Finite adaptability in multistage linear optimization. IEEE Trans. Automatic Control 55(12):2751–2766.Crossref, Google Scholar
• Bertsimas D, Georghiou A (2014) Binary decision rules for multistage adaptive mixed-integer optimization. Accessed July 22, 2015, http://www.optimization-online.org/DB_FILE/2014/08/4510.pdf.Google Scholar
• Bertsimas D, Georghiou A (2015) Design of near optimal decision rules in multistage adaptive mixed-integer optimization. Oper. Res. 63(3):610–627.Link, Google 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.Link, Google Scholar
• Bertsimas D, Goyal V, Lu BY (2014) A tight characterization of the performance of static solutions in two-stage adjustable robust linear optimization. Math. Programming 150(2):281–319.Crossref, Google Scholar
• Bertsimas D, Goyal V, Sun XA (2011a) A geometric characterization of the power of finite adaptability in multistage stochastic and adaptive optimization. Math. Oper. Res. 36(1):24–54.Link, Google Scholar
• Bertsimas D, Iancu DA, Parrilo PA (2010) Optimality of affine policies in multistage robust optimization. Math. Oper. Res. 35(2):363–394.Link, Google Scholar
• Bertsimas D, Iancu DA, Parrilo PA (2011b) A hierarchy of near-optimal policies for multistage adaptive optimization. IEEE Trans. Automatic Control 56(12):2809–2824.Crossref, Google Scholar
• Birge JR, Louveaux F (2011) Introduction to Stochastic Programming (Springer Science & Business Media, New York).Crossref, Google Scholar
• Birge JR, Wets RJ-B (1986) Designing approximation schemes for stochastic optimization problems, in particular for stochastic programs with recourse. Prékopa A, Wets RJ-B, eds. Stochastic Programming 84 Part I, Mathematical Programming Studies, Vol. 27 (Springer, Berlin), 54–102.Crossref, Google Scholar
• Boyd S, Vandenberghe L (2004) Convex Optimization (Cambridge University Press, Cambridge, UK).Crossref, Google Scholar
• Chen X, Zhang Y (2009) Uncertain linear programs: Extended affinely adjustable robust counterparts. Oper. Res. 57(6):1469–1482.Link, Google Scholar
• Chen X, Sim M, Sun P (2007) A robust optimization perspective on stochastic programming. Oper. Res. 55(6):1058–1071.Link, Google Scholar
• Frauendorfer K, Kall P (1988) A solution method for SLP recourse problems with arbitrary multivariate distributions—The independent case. Problems Control Inform. Theory 17:177–205.Google Scholar
• Gorissen BL, Blanc H, den Hertog D, Ben-Tal A (2014) Technical note—Deriving robust and globalized robust solutions of uncertain linear programs with general convex uncertainty sets. Oper. Res. 62(3):672–679.Link, Google Scholar
• Goyal V, Lu BY (2014) On the adaptivity gap in two-stage robust linear optimization under uncertain constraints. Accessed July 22, 2015, http://www.optimization-online.org/DB_FILE/2014/12/4706.pdf.Google Scholar
• Grant M, Boyd S (2014) CVX: Matlab software for disciplined convex programming, version 2.0 beta. Accessed July 22, 2015, http://cvxr.com/cvx.Google Scholar
• Gurobi Optimization, Inc. (2014) Gurobi Optimizer Reference Manual. Accessed July 22, 2015, http://www.gurobi.com.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. IEEE Conf. Decision Control Euro. Control Conf., Orlando, FL.Crossref, Google Scholar
• Hanasusanto GA, Kuhn D, Wiesemann W (2015) K-adaptability in two-stage robust binary programming. Oper. Res. 63(4):877–891.Link, Google 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.Crossref, Google Scholar
• Shapiro A, Dentcheva D, Ruszczyński A (2014) Lectures on Stochastic Programming: Modeling and Theory, Vol. 16 (SIAM, Philadelphia).Crossref, Google Scholar
• Vayanos P, Kuhn D, Rustem B (2011) Decision rules for information discovery in multi-stage stochastic programming. 50th IEEE Conf. Decision Control Euro. Control Conf. (CDC-ECC), Orlando, FL, 7368–7373.Crossref, Google Scholar