Robust Mixed 0-1 Programming and Submodularity

References

• Atamtürk A (2006) Strong formulations of robust mixed 0–1 programming. Math. Programming 108(2):235–250.Google Scholar
• Atamtürk A, Bhardwaj A (2018) Network design with probabilistic capacities. Networks 71(1):16–30.Google Scholar
• Atamtürk A, Narayanan V (2008) Polymatroids and mean-risk minimization in discrete optimization. Oper. Res. Lett. 36(5):618–622.Google Scholar
• Baumann F, Berckey S, Buchheim C (2013) Exact algorithms for combinatorial optimization problems with submodular objective functions. Jünger M, Reinelt G, eds. Facets of Combinatorial Optimization (Springer, Berlin), 271–294.Google Scholar
• Ben-Tal A, Nemirovski A (1999) Robust solutions of uncertain linear programs. Oper. Res. Lett. 25(1):1–13.Google Scholar
• Ben-Tal A, El Ghaoui L, Nemirovski A (2009) Robust Optimization (Princeton University Press, Princeton, NJ).Google Scholar
• Bertsimas D, Sim M (2003) Robust discrete optimization and network flows. Math. Programming 98(1):49–71.Google Scholar
• Bertsimas D, Sim M (2004) The price of robustness. Oper. Res. 52(1):35–53.Link, Google Scholar
• Bertsimas D, Brown DB, Caramanis C (2011) Theory and applications of robust optimization. SIAM Rev. 53(3):464–501.Google Scholar
• Birge JR, Louveaux F (2011) Introduction to Stochastic Programming (Springer, New York).Google Scholar
• Dantzig GB (1955) Linear programming under uncertainty. Management Sci. 1(3–4):197–206.Link, Google Scholar
• Edmonds J (1970) Submodular functions, matroids, and certain polyhedra. Guy R, Hanani H, Sauer N, Schönheim J, eds. Combinatorial Structures and Their Applications (Gordon and Breach, New York), 69–87.Google Scholar
• Fischetti M, Monaci M (2012) Cutting plane vs. compact formulations for uncertain (integer) linear programs. Math. Programming Comput. 4(3):239–273.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
• Grötschel M, Lovász L, Schrijver A (1981) The ellipsoid method and its consequences in combinatorial optimization. Combinatorica 1(2):169–197.Google Scholar
• Joung S, Park S (2018) Lifting and separation of robust cover inequalities. Networks 72(2):272–305.Google Scholar
• Kall P, Wallace SW (1994) Stochastic Programming (John Wiley & Sons, Chichester, UK).Google Scholar
• Klopfenstein O, Nace D (2012) Cover inequalities for robust knapsack sets—Application to the robust bandwidth packing problem. Networks 59(1):59–72.Google Scholar
• Kutschka M (2013) Robustness concepts for knapsack and network design problems under data uncertainty. Unpublished doctoral thesis, Rheinisch-Westfälische Technische Hochschule Aachen University, Aachen, Germany.Google Scholar
• Lee C, Lee K, Park K, Park S (2012) Technical note: Branch-and-price-and-cut approach to the robust network design problem without flow bifurcations. Oper. Res. 60(3):604–610.Link, Google Scholar
• Lee T, Kwon C (2014) A short note on the robust combinatorial optimization problems with cardinality constrained uncertainty. 4OR 12(4):373–378.Google Scholar
• Marchand H, Wolsey LA (1999) The 0-1 knapsack problem with a single continuous variable. Math. Programming 85(1):15–33.Google Scholar
• Miller AJ, Nemhauser GL, Savelsbergh MW (2000) On the capacitated lot-sizing and continuous 0–1 knapsack polyhedra. Eur. J. Oper. Res. 125(2):298–315.Google Scholar
• Monaci M, Pferschy U, Serafini P (2013) Exact solution of the robust knapsack problem. Comput. Oper. Res. 40(11):2625–2631.Google Scholar
• Pisinger D (2005) Where are the hard knapsack problems? Comput. Oper. Res. 32(9):2271–2284.Google Scholar
• Richard JP, de Farias IR Jr, Nemhauser GL (2003a) Lifted inequalities for 0-1 mixed integer programming: Basic theory and algorithms. Math. Programming 98(1):89–113.Google Scholar
• Richard JP, de Farias IR Jr, Nemhauser GL (2003b) Lifted inequalities for 0-1 mixed integer programming: Superlinear lifting. Math. Programming 98(1):115–143.Google Scholar
• Schrijver A (2003) Combinatorial Optimization: Polyhedra and Efficiency, vol. 24 (Springer, Berlin).Google Scholar
• Shapiro A, Dentcheva D, Ruszczyński A (2009) Lectures on Stochastic Programming: Modeling and Theory (Society for Industrial and Applied Mathematics, Philadelphia).Google Scholar
• Soyster AL (1973) Technical note: Convex programming with set-inclusive constraints and applications to inexact linear programming. Oper. Res. 21(5):1154–1157.Link, Google Scholar