Convex Maximization via Adjustable Robust Optimization

Published Online:https://doi.org/10.1287/ijoc.2021.1134

References

  • Andrianova AA, Korepanova AA, Halilova IF (2016) One algorithm for branch and bound method for solving concave optimization problem. IOP Conference Ser. Materials Sci. Engrg. 158:012005.CrossrefGoogle Scholar
  • Ardestani-Jaafari A, Delage E (2016) Robust optimization of sums of piecewise linear functions with application to inventory problems. Oper. Res. 64(2):474–494.LinkGoogle Scholar
  • Audet C, Hansen P, Savard G (2005) Essays and Surveys in Global Optimization (Springer, Boston).CrossrefGoogle Scholar
  • Benson HP (1995) Concave minimization: theory, applications and algorithms. Horst R, Pardalos PM, eds. Handbook of Global Optimization (Springer, Boston), 43–148.CrossrefGoogle Scholar
  • Bienstock D, Özbay N (2008) Computing robust basestock levels. Discrete Optim. 5(2):389–414.CrossrefGoogle Scholar
  • Boyd S, Mattingley J (2007) Branch and bound methods. Accessed July 1, 2020, https://stanford.edu/class/ee364b/lectures/bb_notes.pdf.Google Scholar
  • Boyd S, Vandenberghe L (2004) Convex Optimization (Cambridge University Press, Cambridge, UK).CrossrefGoogle Scholar
  • Byrd RH, Nocedal J, Waltz RA (2006) Knitro: An integrated package for nonlinear optimization. Di Pillo G, Roma M, eds. Large-Scale Nonlinear Optimization (Springer, Boston), 35–59.CrossrefGoogle Scholar
  • Goemans MX, Williamson DP (1994).879-approximation algorithms for MAX CUT and MAX 2SAT. Leighton FT, Goodrich M, eds. Proc. 26th Annual ACM Sympos. Theory Comput. (Association for Computing Machinery, New York), 422–431.Google Scholar
  • Gurobi Optimization L (2018) Gurobi optimizer reference manual. Accessed July 1, 2020, http://www.gurobi.com.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. 50th IEEE Conf. Decision Control Eur. Control Conf. (IEEE), 7386–7391.Google Scholar
  • Horst R, Thoai NV (1999) DC programming: Overview. J. Optim. Theory Appl. 103(1):1–43.CrossrefGoogle Scholar
  • Horst R, Phong TQ, Thoai NV, de Vries J (1991) On solving a DC programming problem by a sequence of linear programs. J. Global Optim. 1(2):183–203.CrossrefGoogle Scholar
  • IBM ILOG CPLEX (2014) V12.6: User’s Manual for CPLEX. Accessed July 1, 2020, https://www.ibm.com/support/knowledgecenter/SSSA5P_12.6.2/ilog.odms.studio.help/pdf/usrcplex.pdf.Google Scholar
  • Le Thi HA, Pham Dinh T (2018) DC programming and DCA: Thirty years of developments. Math. Programming 169(1):5–68.CrossrefGoogle Scholar
  • Lipp T, Boyd S (2016) Variations and extension of the convex–concave procedure. Optim. Engrg. 17(2):263–287.CrossrefGoogle Scholar
  • Löfberg J (2004) YALMIP: A toolbox for modeling and optimization in MATLAB. IEEE Internat. Conf. Robotics Automation (IEEE), 284–289.Google Scholar
  • Löfberg J (2016) YALMIP tutorial: Nonlinear operators—Integer models. Accessed July 1, 2020, https://yalmip.github.io/tutorial/nonlinearoperators mixedinteger/.Google Scholar
  • Mangasarian OL (1996) Machine Learning via Polyhedral Concave Minimization (Physica-Verlag HD, Heidelberg, Germany).CrossrefGoogle Scholar
  • Mangasarian OL (2015) Unsupervised classification via convex absolute value inequalities. Optim. 64(1):81–86.CrossrefGoogle Scholar
  • MATLAB (2018) Version 9.5.0 (R2018b) (The MathWorks Inc., Natick, MA).Google Scholar
  • MOSEK ApS (2019) The MOSEK optimization toolbox for MATLAB manual. Version 9.0. Accessed July 1, 2020, http://docs.mosek.com/9.0/toolbox/index.html.Google Scholar
  • Nemhauser GL, Wolsey LA (1988) Integer and Combinatorial Optimization (Wiley-Interscience, New York).CrossrefGoogle Scholar
  • Pardalos PM, Rosen JB (1986) Methods for global concave minimization: A bibliographic survey. SIAM Rev. 28(3):367–379.CrossrefGoogle Scholar
  • Pardalos PM, Schnitger G (1988) Checking local optimality in constrained quadratic programming is NP-hard. Oper. Res. Lett. 7(1):33–35.CrossrefGoogle Scholar
  • Rebennack S, Nahapetyan A, Pardalos PM (2009) Bilinear modeling solution approach for fixed charge network flow problems. Optim. Lett. 3(3):347–355.CrossrefGoogle Scholar
  • Rockafellar RT (1970) Convex Analysis, Princeton Mathematical Series (Princeton University Press, Princeton, NJ).Google Scholar
  • Selvi A, Den Hertog D, Wiesemann W (2020) A reformulation-linearization technique for optimization over simplices. Preprint 8098: Optimization Online. http://www.optimization-online.org/DB_HTML/2020/11/8098.html.Google Scholar
  • Sherali HD, Adams WP (2013) A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems, vol. 31 (Springer, Boston).Google Scholar
  • Sherali HD, Fraticelli BM (2002) Enhancing RLT relaxations via a new class of semidefinite cuts. J. Global Optim. 22(1–4):233–261.CrossrefGoogle Scholar
  • Tuy H (1964) Concave programming under linear constraints. Soviet Mathematics Doklady 5:1437–1440.Google Scholar
  • Tuy H (1986) A General Deterministic Approach to Global Optimization via DC Programming. North-Holland Mathematics Studies, vol. 129 (Elsevier, Amsterdam), 273–303.Google Scholar
  • Tuy H, Horst R (1988) Convergence and restart in branch-and-bound algorithms for global optimization. Application to concave minimization and DC optimization problems. Math. Programming 41(1–3):161–183.CrossrefGoogle Scholar
  • Wächter A, Biegler LT (2006) On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Programming 106(1):25–57.CrossrefGoogle Scholar
  • Yanikoğlu İ, Gorissen BL, den Hertog D (2019) A survey of adjustable robust optimization. Eur. J. Oper. Res. 277(3):799–813.CrossrefGoogle Scholar
  • Zass R, Shashua A (2007) Nonnegative sparse PCA. Schölkopf B, Platt JC, Hoffman T, eds. Adv. Neural Inform. Processing Systems, vol. 19 (MIT Press, Cambridge, MA), 1561–1568.CrossrefGoogle Scholar
  • Zhen J, De Ruiter F, Den Hertog D (2017) Robust optimization for models with uncertain SOC and SDP constraints. Preprint 6371: Optimization Online. http://www.optimization-online.org/DB_HTML/2017/12/6371.html.Google Scholar
  • Zhen J, Den Hertog D, Sim M (2018) Adjustable robust optimization via Fourier–Motzkin Elimination. Oper. Res. 66(4):1086–1100.LinkGoogle Scholar
  • Zwart PB (1974) Global maximization of a convex function with linear inequality constraints. Oper. Res. 22(3):602–609.LinkGoogle Scholar
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