Hidden Convexity in a Class of Optimization Problems with Bilinear Terms

Published Online:https://doi.org/10.1287/opre.2022.0383

References

  • Ahmadi A, Parrilo P (2013) A complete characterization of the gap between convexity and SOS-convexity. SIAM J. Optim. 23(2):811–833.CrossrefGoogle Scholar
  • Ahuja RK, Orlin JB (2001) Inverse optimization. Oper. Res. 49(5):771–783.LinkGoogle Scholar
  • Babier A, Chan TC, Lee T, Mahmood R, Terekhov D (2021) An ensemble learning framework for model fitting and evaluation in inverse linear optimization. INFORMS J. Optim. 3(2):119–138.LinkGoogle Scholar
  • Beck A, Ben-Tal A (2009) Duality in robust optimization: Primal worst equals dual best. Oper. Res. Lett. 37(1):1–6.CrossrefGoogle Scholar
  • Ben-Tal A, den Hertog D (2014) Hidden conic quadratic representation of some nonconvex quadratic optimization problems. Math. Programming 143(1–2):1–29.CrossrefGoogle Scholar
  • Ben-Tal A, Nemirovski A (2001) Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications, MOS-SIAM Series on Optimization (SIAM, Philadelphia).CrossrefGoogle Scholar
  • Ben-Tal A, Teboulle M (1996) Hidden convexity in some nonconvex quadratically constrained quadratic programming. Math. Programming 72(1):51–63.CrossrefGoogle Scholar
  • Ben-Tal A, Boyd SP, Nemirovski A (2006) Extending scope of robust optimization: Comprehensive robust counterparts of uncertain problems. Math. Programming 107(1):63–89.CrossrefGoogle Scholar
  • Ben-Tal A, Den Hertog D, Laurent M (2011) Hidden convexity in partially separable optimization. CentER Discussion Paper CDP-070, Tilburg University, Tilburg, Netherlands. Optimization Online, https://optimization-online.org/2011/06/3075/.Google Scholar
  • Ben-Tal A, den Hertog D, Vial JPH (2015) Deriving robust counterparts of nonlinear uncertain inequalities. Math. Programming 149(1–2):265–299.CrossrefGoogle Scholar
  • Ben-Tal A, El Ghaoui L, Nemirovski A (2009) Robust Optimization, Princeton Series in Applied Mathematics (Princeton University Press, Princeton, NJ).CrossrefGoogle Scholar
  • Bertsimas D, den Hertog D (2022) Robust and Adaptive Optimization (Dynamic Ideas LLC, Belmont, MA).Google Scholar
  • Bertsimas D, Brown DB, Caramanis C (2011) Theory and applications of robust optimization. SIAM Rev. 53(3):464–501.CrossrefGoogle Scholar
  • Bertsimas D, Dunning I, Lubin M (2015) Reformulation versus cutting-planes for robust optimization. Comput. Management Sci. 13(2):195–217.CrossrefGoogle Scholar
  • Bertsimas D, den Hertog D, Pauphilet J, Zhen J (2023) Robust convex optimization: A new perspective that unifies and extends. Math. Programming 200(2):877–918.CrossrefGoogle Scholar
  • Bhurjee A, Panda G (2012) Efficient solution of interval optimization problem. Math. Methods Oper. Res. 76(3):273–288. CrossrefGoogle Scholar
  • Boyd SP, Vandenberghe L (2004) Convex Optimization (Cambridge University Press, Cambridge, UK).CrossrefGoogle Scholar
  • Chan TCY, Kaw N (2020) Inverse optimization for the recovery of constraint parameters. Eur. J. Oper. Res. 282(2):415–427.CrossrefGoogle Scholar
  • Chan TCY, Mahmood R, Zhu IY (2023) Inverse optimization: Theory and applications. Oper. Res. 73(2):1046–1074.LinkGoogle Scholar
  • Chan TCY, Craig T, Lee T, Sharpe MB (2014) Generalized inverse multiobjective optimization with application to cancer therapy. Oper. Res. 62(3):680–695.LinkGoogle Scholar
  • Chen L, Chen Y, Langevin A (2021) An inverse optimization approach for a capacitated vehicle routing problem. Eur. J. Oper. Res. 295(3):1087–1098.CrossrefGoogle Scholar
  • Cooper A, Charnes W (1962) Programming with linear fractional functionals. Naval Res. Logist. Quart. 9(3):181–186.Google Scholar
  • Dantzig GB (1963) Linear Programming and Extensions (RAND Corporation, Santa Monica, CA).CrossrefGoogle Scholar
  • de Moor D, Wagenaar J, Poos R, den Hertog D, Fleuren H (2024) A robust approach to food aid supply chains. Eur. J. Oper. Res. 318(1):269–285.CrossrefGoogle Scholar
  • Duffin R, Peterson E, Zener C (1967) Geometric Programming: Theory and Application (Wiley, New York).Google Scholar
  • Dunning I (2016) JuMPeR—Robust optimization with JuMP. Retrieved January 2021, http://iainnz.github.io/JuMPeR.jl/.Google Scholar
  • Fiedler M, Nedoma J, Ramik J, Rohn J, Zimmermann K (2006) Linear Optimization Problems with Inexact Data (Springer, New York).Google Scholar
  • Gay DM (1985) Electronic mail distribution of linear programming test problems. Math. Programming Soc. COAL Newsletter 13:10–12.Google Scholar
  • Ghobadi K, Mahmoudzadeh H (2021) Inferring linear feasible regions using inverse optimization. Eur. J. Oper. Res. 290(3):829–843.CrossrefGoogle Scholar
  • Goh J, Sim M (2011) Robust optimization made easy with ROME. Oper. Res. 59(4):973–985.LinkGoogle Scholar
  • Goldfarb D, Iyengar G (2003) Robust portfolio selection problems. Math. Oper. Res. 28(1):1–38.LinkGoogle Scholar
  • Gorissen BL, Ben-Tal A, Blanc JPC, den Hertog D (2014) Deriving robust and globalized robust solutions of uncertain linear programs with general convex uncertainty sets. Oper. Res. 62(3):672–679.LinkGoogle Scholar
  • Helton JW, Nie J (2010) Semidefinite representation of convex sets. Math. Programming 122(1):21–64.CrossrefGoogle Scholar
  • Iyengar G, Kang W (2005) Inverse conic programming with applications. Oper. Res. Lett. 33(3):319–330.CrossrefGoogle Scholar
  • Jeyakumar V, Li G, Vicente-Pérez J (2015) Robust SOS-convex polynomial optimization problems: Exact SDP relaxations. Optim. Lett. 9(1):1–18.CrossrefGoogle Scholar
  • Laurent M (2009) Sums of squares, moment matrices and optimization over polynomials. Putinar M, Sullivant S, eds. Emerging Applications of Algebraic Geometry, The IMA Volumes in Mathematics and Its Applications, vol. 149 (Springer, New York).CrossrefGoogle Scholar
  • Li W, Xia M, Li H (2016) Some results on the upper bound of optimal values in interval convex quadratic programming. J. Comput. Appl. Math. 302:38–49.CrossrefGoogle Scholar
  • Löfberg J (2012) Automatic robust convex programming. Optim. Methods Software 27(1):115–129.CrossrefGoogle Scholar
  • Maros I, Mészáros C (1999) A repository of convex quadratic programming problems. Optim. Methods Software 11(1–4):671–681.CrossrefGoogle Scholar
  • Nesterov Y, Nemirovskii A (1994) Interior-Point Polynomial Algorithms in Convex Programming (SIAM, Philadelphia).CrossrefGoogle Scholar
  • Peters K, Silva S, Gonçalves R, Kavelj M, Fleuren H, den Hertog D, Ergun O, Freeman M (2021) The nutritious supply chain: Optimizing humanitarian food assistance. INFORMS J. Optim. 3(2):200–226.LinkGoogle Scholar
  • Postek K, den Hertog D, Melenberg B (2016) Computationally tractable counterparts of distributionally robust constraints on risk measures. SIAM Rev. 58(4):603–650.CrossrefGoogle Scholar
  • Rathore H, Jakhar SK (2021) Differential carbon tax policy in aviation: One stone that kills two birds? J. Cleaner Production 296:126479.CrossrefGoogle Scholar
  • Rockafellar RT (1970) Convex Analysis (Princeton University Press, Princeton, NJ).CrossrefGoogle Scholar
  • Roelofs M, Bisschop J (2015) AIMMS 4.3: The language reference. AIMMS BV, Haarlem, Netherlands. http://www.aimms.com/.Google Scholar
  • Roos E, den Hertog D, Ben-Tal A, de Ruiter F, Zhen J (2023) Approximation of hard uncertain convex inequalities. Optimization Online, https://optimization-online.org/2018/06/6679/.Google Scholar
  • Shahmoradi Z, Lee T (2022) Quantile inverse optimization: Improving stability in inverse linear programming. Oper. Res. 70(4):2538–2562.LinkGoogle Scholar
  • Siem AYD, de Klerk E, den Hertog D (2008) Discrete least-norm approximation by nonnegative (trigonometric) polynomials and rational functions. Structural Multidisciplinary Optim. 35(4):327–339.CrossrefGoogle Scholar
  • Virtanen P, Gommers R, Oliphant TE, Haberland M, Reddy T, Cournapeau D, Burovski E, et al. (2020) SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17(3):261–272.CrossrefGoogle Scholar
  • Xia Y (2020) A survey of hidden convex optimization. J. Oper. Res. Soc. China 8(1):1–28.CrossrefGoogle Scholar
  • Zhang J, Xu C (2010) Inverse optimization for linearly constrained convex separable programming problems. Eur. J. Oper. Res. 200(3):671–679.CrossrefGoogle Scholar
  • Zhang J, Zhang L (2010) An augmented Lagrangian method for a class of inverse quadratic programming problems. Appl. Math. Optim. 61(1):57–83.CrossrefGoogle 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.