Effective Budget of Uncertainty for Classes of Robust Optimization

References

• Alizadeh F, Goldfarb D (2003) Second-order cone programming. Math. Programming 95(1):3–51.Google Scholar
• Ang M, Lim YF, Sim M (2012) Robust storage assignment in unit-load warehouses. Management Sci. 58(11):2114–2130.Link, Google Scholar
• Ansaripour A, Trafalis TB (2013) A robust multicriteria optimization model for city logistic terminal locations. Krishnamurthy A, Chan WKV, eds. IIE Annual Conf. Proc. (Institute of Industrial and Systems Engineers, Norcross, GA), 3161–3169.Google 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.Link, Google Scholar
• Atamtürk A, Zhang M (2007) Two-stage robust network flow and design under demand uncertainty. Oper. Res. 55(4):662–673.Link, Google Scholar
• Ben-Tal A, Nemirovski A (1998) Robust convex optimization. Math. Oper. Res. 23(4):769–805.Link, Google Scholar
• Ben-Tal A, Nemirovski A (2002) Robust optimization–methodology and applications. Math. Programming 92(3):453–480.Google Scholar
• Ben-Tal A, El Ghaoui L, Nemirovski A (2009) Robust Optimization, Vol. 28 (Princeton University Press, Princeton, NJ).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.Google Scholar
• Bertsekas DP, Bertsekas DP, Bertsekas DP, Bertsekas DP (1995) Dynamic Programming and Optimal Control, Vol. 1 (Athena Scientific, Belmont, MA).Google Scholar
• Bertsimas D, Caramanis C (2010) Finite adaptability in multistage linear optimization. IEEE Trans. Automatic Control 55(12):2751–2766.Google 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.Google Scholar
• Bertsimas D, Sim M (2003) Robust discrete optimization and network flows. Math. Programming 98(1–3):49–71.Google Scholar
• Bertsimas D, Sim M (2004) The price of robustness. Oper. Res. 52(1):35–53.Link, Google Scholar
• Bertsimas D, Thiele A (2006) A robust optimization approach to inventory theory. Oper. Res. 54(1):150–168.Link, Google Scholar
• Bertsimas D, Brown DB, Caramanis C (2011) Theory and applications of robust optimization. SIAM Rev. 53(3):464–501.Google Scholar
• Billinton R, Bollinger KE (1968) Transmission system reliability evaluation using Markov processes. IEEE Trans. Power Apparatus Systems PAS-87(2):538–547.Google Scholar
• Chan TC, Mar PA (2017) Stability and continuity in robust optimization. SIAM J. Optim. 27(2):817–841.Google Scholar
• Chan TC, Mahmoudzadeh H, Purdie TG (2014) A robust-CVaR optimization approach with application to breast cancer therapy. Eur. J. Oper. Res. 238(3):876–885.Google Scholar
• Chatterjee T, Chowdhury R (2017) Improved sparse approximation models for stochastic computations. Samui P, Sekhar S, Balas VE, eds. Handbook of Neural Computation (Elsevier, London), 201–223.Google Scholar
• Crespi GP, Kuroiwa D, Rocca M (2017) Quasiconvexity of set-valued maps assures well-posedness of robust vector optimization. Ann. Oper. Res. 251(1–2):89–104.Google Scholar
• Crespi GP, Kuroiwa D, Rocca M (2018) Robust optimization: Sensitivity to uncertainty in scalar and vector cases, with applications. Oper. Res. Perspect. 5(3):113–119.Google Scholar
• Dehghani Filabadi M (2019) Robust optimization for SCED in AC-HVDC power systems. Master’s thesis, University of Waterloo, Waterloo, ON, Canada.Google Scholar
• Delage E, Iancu DA (2015) Robust multistage decision making. Aleman DM, Thiele AC, eds. The Operations Research Revolution (INFORMS, Catonsville, MD), 20–46.Link, Google Scholar
• Delage E, Ye Y (2010) Distributionally robust optimization under moment uncertainty with application to data-driven problems. Oper. Res. 58(3):595–612.Link, Google Scholar
• El Ghaoui L, Lebret H (1997) Robust solutions to least-squares problems with uncertain data. SIAM J. Matrix Anal. Appl. 18(4):1035–1064.Google Scholar
• Ermoliev YM, Wets RJ-B, eds. (1988) Numerical Techniques for Stochastic Optimization (Springer-Verlag, Berlin).Google Scholar
• Fathabad AM, Cheng J, Pan K, Qiu F (2020) Data-driven planning for renewable distributed generation integration. IEEE Trans. Power Systems 35(6):4357–4368.Google Scholar
• Frank S, Rebennack S (2016) An introduction to optimal power flow: Theory, formulation, and examples. IIE Trans. 48(12):1172–1197.Google Scholar
• Gabrel V, Murat C, Thiele A (2014) Recent advances in robust optimization: An overview. Eur. J. Oper. Res. 235(3):471–483.Google Scholar
• Grigg C, Wong P, Albrecht P, Allan R, Bhavaraju M, Billinton R, Chen Q, et al. (1999) The IEEE Reliability Test System-1996. A report prepared by the Reliability Test System Task Force of the Application of Probability Methods Subcommittee. IEEE Trans. Power Systems 14(3):1010–1020.Google Scholar
• Gupta V (2019) Near-optimal Bayesian ambiguity sets for distributionally robust optimization. Management Sci. 65(9):4242–4260.Link, Google Scholar
• Hassanzadeh F, Nemati H, Sun M (2014) Robust optimization for interactive multiobjective programming with imprecise information applied to R&D project portfolio selection. Eur. J. Oper. Res. 238(1):41–53.Google Scholar
• Horn RA (1990) The Hadamard product. Johnson CJ, ed. Matrix Theory Appl., Proc. Sympos. Appl. Math., Vol. 40 (American Mathematical Society, Providence, RI), 87–169.Google Scholar
• Iancu DA, Sharma M, Sviridenko M (2013) Supermodularity and affine policies in dynamic robust optimization. Oper. Res. 61(4):941–956.Link, Google Scholar
• Ide J, Köbis E, Kuroiwa D, Schöbel A, Tammer C (2014) The relationship between multi-objective robustness concepts and set-valued optimization. Fixed Point Theory and Applications 1:1–20.Google Scholar
• Imholz M, Faes M, Vandepitte D, Moens D (2020) Robust uncertainty quantification in structural dynamics under scarse experimental modal data: A Bayesian-interval approach. J. Sound Vibration 467(February):114983.Google Scholar
• Kurtz J (2018) Robust combinatorial optimization under budgeted–ellipsoidal uncertainty. EURO J. Comput. Optim. 6(4):315–337.Google Scholar
• Li Z, Wu W, Shahidehpour M, Zhang B (2016) Adaptive robust tie-line scheduling considering wind power uncertainty for interconnected power systems. IEEE Trans. Power Systems 31(4):2701–2713.Google Scholar
• Li Z, Wu W, Zhang B, Wang B (2015) Robust look-ahead power dispatch with adjustable conservativeness accommodating significant wind power integration. IEEE Trans. Sustainable Energy 6(3):781–790.Google Scholar
• Lopez A, Roberts B, Heimiller D, Blair N, Porro G (2012) U.S. renewable energy technical potentials: A GIS-based analysis. Technical Report NREL/TP-6A20-51946, National Renewable Energy Laboratory, Washington, DC.Google 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.Google Scholar
• Mahmoudzadeh H, Shalamzari AM, Abouee-Mehrizi H (2020) Robust multi-class multi-period patient scheduling with wait time targets. Oper. Res. Health Care 25(June):100254.Google Scholar
• Minoux M (2008) Robust linear programming with right-hand-side uncertainty, duality and applications. Floudas CA, Pardalos PM, eds. Encyclopedia of Optimization, 2nd ed. (Springer, New York), 3317–3327.Google Scholar
• Minoux M (2012) Two-stage robust LP with ellipsoidal right-hand side uncertainty is NP-hard. Optim. Lett. 6(7):1463–1475.Google Scholar
• Niazi Shahraki N (2020) A robust optimization approach for advance scheduling in healthcare systems with demand uncertainty: Policy insights. Master’s thesis, University of Waterloo, Waterloo, ON, Canada.Google Scholar
• Ouorou A (2016) Robust models for linear programming with uncertain right hand side. Networks 68(3):200–211.Google Scholar
• Schneider J, Kirkpatrick S (2007) Stochastic Optimization (Springer Science & Business Media, New York).Google Scholar
• Sebah P, Gourdon X (2002) Introduction to the gamma function. Amer. J. Sci. Res. 2–18.Google Scholar
• Smith RC (2013) Uncertainty Quantification: Theory, Implementation, and Applications, Computational Science and Engineering, Vol. 12 (SIAM, Philadelphia).Google Scholar
• Soyster AL (1973) Convex programming with set-inclusive constraints and applications to inexact linear programming. Oper. Res. 21(5):1154–1157.Link, Google Scholar
• Washington Data Library (2019) Renewable Energy Analysis Lab—Library. https://www2.ee.washington.edu/research/real/library.html.Google Scholar
• Wilson J (2010) Volume of n-dimensional ellipsoid. Sci. Acta Xaveriana. 1(1):101–106.Google Scholar
• Wu W, Chen J, Zhang B, Sun H (2014) A robust wind power optimization method for look-ahead power dispatch. IEEE Trans. Sustainable Energy 5(2):507–515.Google Scholar