Improved Decision Rule Approximations for Multistage Robust Optimization via Copositive Programming

Published Online:https://doi.org/10.1287/opre.2018.0505

References

  • Alizadeh F, Goldfarb D (2003) Second-order cone programming. Math. Programming 95(1):3–51.CrossrefGoogle Scholar
  • Anderson BD, Moore JB (2007) Optimal Control: Linear Quadratic Methods (Courier Corporation, North Chelmsford, MA).Google Scholar
  • ApS (2016) The MOSEK optimization toolbox for MATLAB, version 8.0.0.94. Accessed October 31, 2017, http://docs.mosek.com/8.0/toolbox/index.html.Google Scholar
  • Ardestani-Jaafari A, Delage E (2021) Linearized robust counterparts of two-stage robust optimization problems with applications in operations management. INFORMS J. Comput. 33(3):1138–1161.LinkGoogle Scholar
  • Atamtürk A, Zhang M (2007) Two-stage robust network flow and design under demand uncertainty. Oper. Res. 55(4):662–673.LinkGoogle Scholar
  • Bampou D, Kuhn D (2011) Scenario-free stochastic programming with polynomial decision rules. Proc. 50th IEEE Conf. Decision Control Eur. Control Conf. (CDC-ECC) (IEEE, Piscataway, NJ), 7806–7812.Google Scholar
  • Bemporad A, Borrelli F, Morari M (2003) Min-max control of constrained uncertain discrete-time linear systems. IEEE Trans. Automatic Control 48(9):1600–1606.CrossrefGoogle Scholar
  • Ben-Tal A, Nemirovski A (1999) Robust solutions of uncertain linear programs. Oper. Res. Lett. 25(1):1–13.CrossrefGoogle Scholar
  • Ben-Tal A, Nemirovski A (2002) Robust optimization—Methodology and applications. Math. Programming 92(3):453–480.CrossrefGoogle Scholar
  • Ben-Tal A, El Ghaoui L, Nemirovski A (2009) Robust Optimization (Princeton University Press, Princeton, NJ).CrossrefGoogle Scholar
  • Ben-Tal A, El Housni O, Goyal V (2020) A tractable approach for designing piecewise affine policies in two-stage adjustable robust optimization. Math. Programming 182(1):57–102.CrossrefGoogle Scholar
  • Ben-Tal A, Margalit T, Nemirovski A (2000) Robust modeling of multi-stage portfolio problems. Frenk H, Roos K, Terlaky T, Zhang S, eds. High Performance Optimization, Applied Optimization, vol. 33 (Springer, Boston), 303–328.CrossrefGoogle Scholar
  • Ben-Tal A, Golany B, Nemirovski A, Vial JP (2005) Retailer-supplier flexible commitments contracts: A robust optimization approach. Manufacturing Service Oper. Management 7(3):248–271.LinkGoogle Scholar
  • Ben-Tal A, Goryashko A, Guslitzer E, Nemirovski A (2004) Adjustable robust solutions of uncertain linear programs. Math. Programming 99(2):351–376.CrossrefGoogle Scholar
  • Bertsimas D, de Ruiter FJ (2016) Duality in two-stage adaptive linear optimization: Faster computation and stronger bounds. INFORMS J. Comput. 28(3):500–511.LinkGoogle Scholar
  • Bertsimas D, Dunning I (2016) Multistage robust mixed-integer optimization with adaptive partitions. Oper. Res. 64(4):980–998.LinkGoogle Scholar
  • Bertsimas D, Georghiou A (2015) Design of near optimal decision rules in multistage adaptive mixed-integer optimization. Oper. Res. 63(3):610–627.LinkGoogle Scholar
  • Bertsimas D, Georghiou A (2018) Binary decision rules for multistage adaptive mixed-integer optimization. Math. Programming 167(2):395–433.CrossrefGoogle 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.CrossrefGoogle Scholar
  • Bertsimas D, Brown DB, Caramanis C (2011a) Theory and applications of robust optimization. SIAM Rev. 53(3):464–501.CrossrefGoogle Scholar
  • Bertsimas D, Goyal V, Lu BY (2015) A tight characterization of the performance of static solutions in two-stage adjustable robust linear optimization. Math. Programming 150(2):281–319.CrossrefGoogle Scholar
  • Bertsimas D, Iancu DA, Parrilo PA (2010) Optimality of affine policies in multistage robust optimization. Math. Oper. Res. 35(2):363–394.LinkGoogle 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.CrossrefGoogle Scholar
  • Bertsimas D, Litvinov E, Sun XA, Zhao J, Zheng T (2013) Adaptive robust optimization for the security constrained unit commitment problem. IEEE Trans. Power Systems 28(1):52–63.CrossrefGoogle Scholar
  • Bomze IM (2012) Copositive optimization—Recent developments and applications. Eur. J. Oper. Res. 216(3):509–520.CrossrefGoogle Scholar
  • Bomze IM, de Klerk E (2002) Solving standard quadratic optimization problems via linear, semidefinite and copositive programming. J. Global Optim. 24(2):163–185.CrossrefGoogle Scholar
  • Bomze IM, Dür M, De Klerk E, Roos C, Quist AJ, Terlaky T (2000) On copositive programming and standard quadratic optimization problems. J. Global Optim. 18(4):301–320.CrossrefGoogle Scholar
  • Burer S (2009) On the copositive representation of binary and continuous nonconvex quadratic programs. Math. Programming 120(2):479–495.CrossrefGoogle Scholar
  • Burer S (2012) Copositive programming. Anjos MF, Lasserre JB, eds. Handbook on Semidefinite, Conic and Polynomial Optimization (Springer, New York), 201–218.CrossrefGoogle Scholar
  • Burer S (2015) A gentle, geometric introduction to copositive optimization. Math. Programming 151(1):89–116.CrossrefGoogle Scholar
  • Burer S, Dong H (2012) Representing quadratically constrained quadratic programs as generalized copositive programs. Oper. Res. Lett. 40(3):203–206.CrossrefGoogle Scholar
  • Calafiore GC (2008) Multi-period portfolio optimization with linear control policies. Automatica J. IFAC 44(10):2463–2473.CrossrefGoogle Scholar
  • Chen J, Burer S (2012) Globally solving nonconvex quadratic programming problems via completely positive programming. Math. Programming Comput. 4(1):33–52.CrossrefGoogle Scholar
  • Chen X, Zhang Y (2009) Uncertain linear programs: Extended affinely adjustable robust counterparts. Oper. Res. 57(6):1469–1482.LinkGoogle Scholar
  • Chen X, Sim M, Sun P (2007) A robust optimization perspective on stochastic programming. Oper. Res. 55(6):1058–1071.LinkGoogle Scholar
  • Chen X, Sim M, Sun P, Zhang J (2008) A linear decision-based approximation approach to stochastic programming. Oper. Res. 56(2):344–357.LinkGoogle Scholar
  • Dantzig GB, Infanger G (1993) Multi-stage stochastic linear programs for portfolio optimization. Ann. Oper. Res. 45(1):59–76.CrossrefGoogle Scholar
  • de Klerk E, Pasechnik DV (2002) Approximation of the stability number of a graph via copositive programming. SIAM J. Optim. 12(4):875–892.CrossrefGoogle Scholar
  • Dür M (2010) Copositive programming—A survey. Diehl M, Glineur F, Jarlebring E, Michiels W, eds. Recent Advances in Optimization and Its Applications in Engineering (Springer, Berlin), 3–20.CrossrefGoogle Scholar
  • Eichfelder G, Jahn J (2008) Set-semidefinite optimization. J. Convex Anal. 15:767–801.Google Scholar
  • Garey MR, Johnson DS (1979) Computers and Intractability, vol. 29 (W. H. Freeman and Company, San Francisco).Google Scholar
  • Georghiou A, Tsoukalas A, Wiesemann W (2019) Robust dual dynamic programming. Oper. Res. 67(3):813–830.LinkGoogle Scholar
  • Georghiou A, Tsoukalas A, Wiesemann W (2020) A primal–dual lifting scheme for two-stage robust optimization. Oper. Res. 68(2):572–590.AbstractGoogle Scholar
  • Georghiou A, Wiesemann W, Kuhn D (2015) Generalized decision rule approximations for stochastic programming via liftings. Math. Programming 152(1–2):301–338.CrossrefGoogle Scholar
  • Goh J, Sim M (2010) Distributionally robust optimization and its tractable approximations. Oper. Res. 58(4 part 1):902–917.LinkGoogle Scholar
  • Gounaris CE, Wiesemann W, Floudas CA (2013) The robust capacitated vehicle routing problem under demand uncertainty. Oper. Res. 61(3):677–693.LinkGoogle Scholar
  • Guslitser E (2002) Uncertainty-immunized solutions in linear programming. PhD thesis, Technion–Israel Institute of Technology, Haifa.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. Proc. 50th IEEE Conf. Decision Control Eur. Control Conf. (CDC-ECC) (IEEE, Piscataway, NJ).Google Scholar
  • Hanasusanto GA, Kuhn D (2013) Robust data-driven dynamic programming. Adv. Neural Inform. Processing Systems, 827–835.Google Scholar
  • Hanasusanto GA, Kuhn D (2018) Conic programming reformulations of two-stage distributionally robust linear programs over Wasserstein balls. Oper. Res. 66(3):849–869.LinkGoogle Scholar
  • Hanasusanto GA, Kuhn D, Wallace SW, Zymler S (2015) Distributionally robust multi-item newsvendor problems with multimodal demand distributions. Math. Programming 152(1–2):1–32.CrossrefGoogle Scholar
  • Hashemi Doulabi H, Jaillet P, Pesant G, Rousseau LM (2021) Exploiting the structure of two-stage robust optimization models with exponential scenarios. INFORMS J. Comput. 33(1):143–162.LinkGoogle Scholar
  • Iancu DA, Sharma M, Sviridenko M (2013) Supermodularity and affine policies in dynamic robust optimization. Oper. Res. 61(4):941–956.LinkGoogle Scholar
  • Kong Q, Lee CY, Teo CP, Zheng Z (2013) Scheduling arrivals to a stochastic service delivery system using copositive cones. Oper. Res. 61(3):711–726.LinkGoogle 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.CrossrefGoogle Scholar
  • Lasserre JB (2009) Convexity in semialgebraic geometry and polynomial optimization. SIAM J. Optim. 19(4):1995–2014.CrossrefGoogle Scholar
  • Lofberg J (2004) YALMIP: A toolbox for modeling and optimization in MATLAB. 2004 IEEE Internat. Sympos. Comput. Aided Control Systems Design (IEEE, Piscataway, NJ), 284–289.Google Scholar
  • Martins da Silva Rocha PC (2013) Medium-term planning in deregulated energy markets with decision rules. PhD thesis, Imperial College London, London.Google Scholar
  • Mittal A, Gokalp C, Hanasusanto GA (2020) Robust quadratic programming with mixed-integer uncertainty. INFORMS J. Comput. 32(2):201–218.AbstractGoogle Scholar
  • Natarajan K, Teo CP (2017) On reduced semidefinite programs for second order moment bounds with applications. Math. Programming 161(1–2):487–518.CrossrefGoogle Scholar
  • Natarajan K, Teo CP, Zheng Z (2011) Mixed 0-1 linear programs under objective uncertainty: A completely positive representation. Oper. Res. 59(3):713–728.LinkGoogle Scholar
  • Parrilo PA (2000) Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization. PhD thesis, California Institute of Technology, Pasadena, CA.Google Scholar
  • Postek K, den Hertog D (2016) Multistage adjustable robust mixed-integer optimization via iterative splitting of the uncertainty set. INFORMS J. Comput. 28(3):553–574.LinkGoogle Scholar
  • Rocha P, Kuhn D (2012) Multistage stochastic portfolio optimisation in deregulated electricity markets using linear decision rules. Eur. J. Oper. Res. 216(2):397–408.CrossrefGoogle Scholar
  • See CT, Sim M (2010) Robust approximation to multiperiod inventory management. Oper. Res. 58(3):583–594.LinkGoogle Scholar
  • Xu G, Burer S (2018) A copositive approach for two-stage adjustable robust optimization with uncertain right-hand sides. Comput. Optim. Appl. 70(1):33–59.CrossrefGoogle Scholar
  • Zeng B, Zhao L (2013) Solving two-stage robust optimization problems using a column-and-constraint generation method. Oper. Res. Lett. 41(5):457–461.CrossrefGoogle Scholar
  • Zhen J, den Hertog D, Sim M (2018) Adjustable robust optimization via Fourier–Motzkin elimination. Oper. Res. 66(4):1086–1100.LinkGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.