A Practicable Robust Counterpart Formulation for Decomposable Functions: A Network Congestion Case Study
Published Online:16 Feb 2018https://doi.org/10.1287/opre.2017.1679
References
- (2013) A robust optimization approach for energy-aware routing in MPLS networks. Proc. Internat. Conf. Comput., Networking Comm., ICNC (IEEE Computer Society, Washington, DC), 567–572.Google Scholar
- (2014) On the energy cost of robustness and resiliency in IP networks. Comput. Networks 75, Part A:239–259.Crossref, Google Scholar
- (2012) Oblivious OSPF routing with weight optimization under polyhedral demand uncertainty. Networks 60(2):132–139.Google Scholar
- (2007) Provisioning virtual private networks under traffic uncertainty. Networks 49(1):100–115.Crossref, Google Scholar
- (2014) The value of flexibility in robust location-transportation problem. Cahier du GERAD G-2014-83.Google Scholar
- (2016) Robust optimization of sums of piecewise linear functions with application to inventory problems. Oper. Res. 64(2):474–494.Link, Google Scholar
- (2005) Routing of uncertain traffic demands. Optim. Engrg. 6(3):283–313.Crossref, Google Scholar
- (2011) Immunizing conic quadratic optimization problems against implementation errors. Technical report, CentER Discussion Paper Series 2012-053.Google Scholar
- (1998) Robust convex optimization. Math. Oper. Res. 23(4):769–805.Link, Google Scholar
- (1999) Robust solutions of uncertain linear programs. Oper. Res. Lett. 25(1):1–13.Crossref, Google Scholar
- (2000) Robust solutions of linear programming problems contaminated with uncertain data. Math. Programming 88(3):411–424.Crossref, Google Scholar
- (2002) Robust optimization—Methodology and applications. Math. Programming 92(3):453–480.Crossref, Google Scholar
- (2003) On approximate robust counterparts of uncertain semidefinite and conic quadratic programs. Sachs EW, Tichatschke R, eds. System Modeling and Optimization XX (Springer, New York), 1–22.Crossref, Google Scholar
- (2012) Deriving robust counterparts of nonlinear uncertain inequalities. Technical report, CentER Discussion Paper Series 2012-053.Google Scholar
- (1998) Robust semidefinite programming. Handbook on Semidefinite Programming, Vol. 27 (Springer, New York),.Google Scholar
- (2009) Robust Optimization (Princeton University Press, Princeton, NJ).Crossref, Google Scholar
- (2009) Constructing uncertainty sets for robust linear optimization. Oper. Res. 57(6):1483–1495.Link, Google Scholar
- (2003) Robust discrete optimization and network flows. Math. Programming 98(1):49–71.Crossref, Google Scholar
- (2004) The price of robustness. Oper. Res. 52(1):35–53.Link, Google Scholar
- (2011) Theory and applications of robust optimization. SIAM Rev. 53(3):464–501.Crossref, Google Scholar
- (2014) Data-driven robust optimization. Preprint arXiv:1401.0212.Google Scholar
- (2010) Robust optimization for unconstrained simulation-based problems. Oper. Res. 58(1):161–178.Link, Google Scholar
- (2008) The exact feasibility of randomized solutions of uncertain convex programs. SIAM J. Optim. 19(3):1211–1230.Crossref, Google Scholar
- (2013) Robust redundancy elimination for energy-aware routing. Proc. IEEE Internat. Conf. Green Comput. Comm. IEEE Internet of Things and IEEE Cyber, Physical Soc. Comput. (IEEE, Piscataway, NJ), 179–186.Google Scholar
- (1955) Linear programming under uncertainty. Management Sci. 1(3–4):197–206.Link, Google Scholar
- (1997) Robust solutions to least-squares problems with uncertain data. SIAM J. Matrix Anal. Appl. 18(4):1035–1064.Crossref, Google Scholar
- (2004) Increasing Internet capacity using local search. Comput. Optim. Appl. 29(1):13–48.Crossref, Google Scholar
- (2014) Recent advances in robust optimization: An overview. Eur. J. Oper. Res. 235(3):471–483.Crossref, Google Scholar
- (1996) Optimizing routing in packet-switched networks with non-Poisson offered traffic. Telecomm. Systems-Modeling, Anal., Design and Management 5(2):323–340.Crossref, Google Scholar
- (2013) Robust counterparts of inequalities containing sums of maxima of linear functions. Eur. J. Oper. Res. 227(1):30–43.Crossref, Google Scholar
- (1981) The ellipsoid method and its consequences in combinatorial optimization. Combinatorica 1(2):169–197.Crossref, Google Scholar
- (2013) Robust delay-constrained routing in telecommunications. Ann. Oper. Res. 206(1):163–181.Crossref, Google Scholar
- (2001) Fundamentals of Convex Analysis, Grundlehren Text, ed. (Springer, Berlin).Crossref, Google Scholar
- (2008) Tractable approximate robust geometric programming. Optim. Engrg. 9(2)95–118.Crossref, Google Scholar
- (2014) Pareto efficiency in robust optimization. Management Sci. 60(1):130–147.Link, Google Scholar
- (2005) Quantile Regression (Cambridge University Press, New York).Crossref, Google Scholar
- (2011) Interval uncertainty-based robust optimization for convex and non-convex quadratic programs with applications in network infrastructure planning. Networks and Spatial Econom. 11(1):159–191.Crossref, Google Scholar
- (2015) Appointment scheduling with limited distributional information. Management Sci. 61(2):316–334.Link, Google Scholar
- (2013) The robust network loading problem with dynamic routing. Computational Optim. Appl. 54(3):619–643.Crossref, Google Scholar
- (2005) Optimizing IP networks for uncertain demands using outbound traffic constraints. Proc. 2nd INOC, 695–701.Google Scholar
- (2010) Sndlib 1.0 survivable network design library. Networks 55(3):276–286.Google Scholar
- (2011) Affine decision rules for tractable approximations to robust capacity planning in telecommunications. Network Optimization (Springer, Berlin), 277–282.Crossref, Google Scholar
- (2013) Tractable approximations to a robust capacity assignment model in telecommunications under demand uncertainty. Comput. Oper. Res. 40(1):318–327.Crossref, Google Scholar
- (2002) A typology for multi-technology, multi-service broadband network synthesis. Telecomm. Systems 19(1):39–73.Crossref, Google Scholar
- (2013) Affine recourse for the robust network design problem: Between static and dynamic routing. Networks 61(2):180–198.Crossref, Google Scholar
- (2009) Energy profile aware routing. IEEE Internat. Conf. Comm. Workshops (IEEE, Piscataway, NJ), 1–5.Google Scholar
- (1997) Convex Analysis (Princeton University Press, Princeton, NJ).Google Scholar
- (2009) On reliability, performance and Internet power consumption. Proc. 7th Internat. Worshop Design Reliable Comm. Networks, DRCN ’09 (IEEE, Piscataway, NJ), 259–264.Google Scholar
- (2003) Estimating the moments of a random vector with applications. Siemons J, ed. Proc. GRETSI 2003 Conf., 47–52.Google Scholar
- (1973) Technical note—Convex programming with set-inclusive constraints and applications to inexact linear programming. Oper. Res. 21(5):1154–1157.Link, Google Scholar
- (2010) A relaxation algorithm with a probabilistic guarantee for robust deviation optimization. Comput. Optim. Appl. 47(1):1–31.Crossref, Google Scholar
- (2002) Capacity planning for carrier-scale IP networks. BT Tech. J. 20(3):116–123.Crossref, Google Scholar
- (2013) Solving two-stage robust optimization problems using a column-and-constraint generation method. Oper. Res. Lett. 41(5):457–461.Crossref, Google Scholar

