Efficient Scenario Generation for Heavy-Tailed Chance Constrained Optimization

References

• Ahmed S, Shapiro A (2008) Solving chance-constrained stochastic programs via sampling and integer programming. Chen Z-L, Raghavan S, eds. State-of-the-Art Decision-Making Tools in the Information-Intensive Age (INFORMS), 261–269.Link, Google Scholar
• Alsenwi M, Pandey SR, Tun YK, Kim KT, Hong CS (2019) A chance constrained based formulation for dynamic multiplexing of eMBB-URLLC traffics in 5G new radio. Proc. Internat. Conf. on Information Networking (IEEE, New York), 108–113.Google Scholar
• Andrieu L, Henrion R, Römisch W (2010) A model for dynamic chance constraints in hydro power reservoir management. Eur. J. Oper. Res. 207(2):579–589.Google Scholar
• Barrera J, Homem-de Mello T, Moreno E, Pagnoncelli BK, Canessa G (2016) Chance-constrained problems and rare events: An importance sampling approach. Math. Programming 157(1):153–189.Google Scholar
• Ben-Tal A, Nemirovski A (2000) Robust solutions of linear programming problems contaminated with uncertain data. Math. Programming 88(3):411–424.Google Scholar
• Ben-Tal A, Nemirovski A (2002) Robust optimization: Methodology and applications. Math. Programming 92(3):453–480.Google Scholar
• Bertsimas D, Sim M (2004) The price of robustness. Oper. Res. 52(1):35–53.Link, Google Scholar
• Blanchet J, Liu J (2010) Efficient importance sampling in ruin problems for multidimensional regularly varying random walks. J. Appl. Probability 47(2):301–322.Google Scholar
• Bonami P, Lejeune MA (2009) An exact solution approach for portfolio optimization problems under stochastic and integer constraints. Oper. Res. 57(3):650–670.Link, Google Scholar
• Boyd S, Vandenberghe L (2004) Convex Optimization (Cambridge University Press, Cambridge, UK).Google Scholar
• Calafiore G, Campi MC (2005) Uncertain convex programs: Randomized solutions and confidence levels. Math. Programming 102(1):25–46.Google Scholar
• Calafiore G, Campi MC (2006) The scenario approach to robust control design. IEEE Trans. Automated Control 51(5):742–753.Google Scholar
• Charnes A, Cooper WW, Symonds GH (1958) Cost horizons and certainty equivalents: An approach to stochastic programming of heating oil. Management Sci. 4(3):235–263.Link, Google Scholar
• Chen B, Blanchet J, Rhee CH, Zwart B (2019) Efficient rare-event simulation for multiple jump events in regularly varying random walks and compound Poisson processes. Math. Oper. Res. 44(3):919–942.Link, Google Scholar
• Chen W, Sim M, Sun J, Teo CP (2010) From CVaR to uncertainty set: Implications in joint chance-constrained optimization. Oper. Res. 58(2):470–485.Link, Google Scholar
• Diamond S, Boyd S (2016) CVXPY: A Python-embedded modeling language for convex optimization. J. Machine Learn. Res. 17(83):1–5.Google Scholar
• Eisenberg L, Noe TH (2001) Systemic risk in financial systems. Management Sci. 47(2):236–249.Link, Google Scholar
• Embrechts P, Klüppelberg C, Mikosch T (2013) Modelling Extremal Events: For Insurance and Finance, vol. 33 (Springer Science & Business Media, Boston).Google Scholar
• Frank B (2008) Municipal bond fairness act. 110th Congress, 2d Session, House of Representatives, Report, 110–835.Google Scholar
• Gudmundsson T, Hult H (2014) Markov chain Monte Carlo for computing rare-event probabilities for a heavy-tailed random walk. J. Appl. Probability 51(2):359–376.Google Scholar
• Hillier FS (1967) Chance-constrained programming with 0-1 or bounded continuous decision variables. Management Sci. 14(1):34–57.Link, Google Scholar
• Hong LJ, Huang Z, Lam H (2021) Learning-based robust optimization: Procedures and statistical guarantees. Management Sci. 67(6):3447–3467.Link, Google Scholar
• Hong LJ, Yang Y, Zhang L (2011) Sequential convex approximations to joint chance constrained programs: A Monte Carlo approach. Oper. Res. 59(3):617–630.Link, Google Scholar
• Kley O, Klüppelberg C, Reinert G (2016) Risk in a large claims insurance market with bipartite graph structure. Oper. Res. 64(5):1159–1176.Link, Google Scholar
• Küçükyavuz S (2012) On mixing sets arising in chance-constrained programming. Math. Programming 132(1–2):31–56.Google Scholar
• Lagoa CM, Li X, Sznaier M (2005) Probabilistically constrained linear programs and risk-adjusted controller design. SIAM J. Optim. 15(3):938–951.Google Scholar
• Lejeune MA, Margot F (2016) Solving chance-constrained optimization problems with stochastic quadratic inequalities. Oper. Res. 64(4):939–957.Link, Google Scholar
• Luedtke J (2014) A branch-and-cut decomposition algorithm for solving chance-constrained mathematical programs with finite support. Math. Programming 146(1–2):219–244.Google Scholar
• Luedtke J, Ahmed S (2008) A sample approximation approach for optimization with probabilistic constraints. SIAM J. Optim. 19(2):674–699.Google Scholar
• Luedtke J, Ahmed S, Nemhauser GL (2010) An integer programming approach for linear programs with probabilistic constraints. Math. Programming 122(2):247–272.Google Scholar
• McGill R, Tukey JW, Larsen WA (1978) Variations of box plots. Amer. Statist. 32(1):12–16.Google Scholar
• MOSEK ApS (2020) MOSEK fusion API for Python. Retrieved September 10, 2020, https://docs.mosek.com/9.2/pythonfusion.pdf.Google Scholar
• Nemirovski A, Shapiro A (2006a) Convex approximations of chance constrained programs. SIAM J. Optim. 17(4):969–996.Google Scholar
• Nemirovski A, Shapiro A (2006b) Scenario approximations of chance constraints. Probabilistic and Randomized Methods for Design Under Uncertainty (Springer, Berlin), 3–47.Google Scholar
• Peña-Ordieres A, Luedtke JR, Wächter A (2020) Solving chance-constrained problems via a smooth sample-based nonlinear approximation. SIAM J. Optim. 30(3):2221–2250.Google Scholar
• Prekopa A (1970) On probabilistic constrained programming. William Kuhn H, ed. Proc. Princeton Sympos. on Math. Programming, vol. 113 (Princeton University Press, Princeton), 138.Google Scholar
• Prékopa A (2003) Probabilistic programming. Handbook Oper. Res. Management Sci. 10:267–351.Google Scholar
• Resnick SI (2013) Extreme Values, Regular Variation and Point Processes (Springer, Berlin).Google Scholar
• Seppälä Y (1971) Constructing sets of uniformly tighter linear approximations for a chance constraint. Management Sci. 17(11):736–749.Link, Google Scholar
• Tong S, Subramanyam A, Rao V (2022) Optimization under rare chance constraints. SIAM J. Optim. 32(2):930–958.Google Scholar
• Wierman A, Zwart B (2012) Is tail-optimal scheduling possible? Oper. Res. 60(5):1249–1257.Link, Google Scholar
• Zhang M, Küçükyavuz S, Goel S (2014) A branch-and-cut method for dynamic decision making under joint chance constraints. Management Sci. 60(5):1317–1333.Link, Google Scholar