Solving Chance-Constrained Optimization Problems with Stochastic Quadratic Inequalities

References

• Achterberg T, Koch T, Martin A (2005) Branching rules revisited. OR Letters 33:42–54.Crossref, Google Scholar
• Averbakh I, Bereg S (2005) Facility location problems with uncertainty on the plane. Discrete Optim. 2(1):3–34.Crossref, Google Scholar
• Baron O, Berman O, Krass D (2008) Facility location with stochastic demand and constraints on waiting time. Manufacturing Service Oper. Management 100(3):484–505.Link, Google Scholar
• Baron O, Berman O, Krass D, Wang Q (2007) The equitable location problem on the plane. Eur. J. Oper. Res. 90:183–578.Google Scholar
• Beale EML, Forrest JJH (1976) Global optimization using special ordered sets. Math. Programming 10:52–69.Crossref, Google Scholar
• Belotti P (2009) Couenne: A user’s manual. Technical Report, Lehigh University, Bethlehem, PA.Google Scholar
• Belotti P, Lee J, Liberti L, Margot F, Wächter A (2009) Branching and bound tightening techniques for nonconvex MINLPs. Optim. Methods Software 24:597–634.Crossref, Google Scholar
• Belotti P, Kirches C, Leyffer S, Linderoth J, Luedtke J, Mahajan A (2013) Mixed-integer nonlinear optimization. Acta Numerica 22:1–131.Crossref, Google Scholar
• Benkoczi R, Bhattacharya BK, Das S, Sember J (2009) Single facility collection depots location problem in the plane. Comput. Geometry 42(5):403–418.Crossref, Google Scholar
• Beraldi P, Bruni ME (2010) An exact approach for solving integer problems under probabilistic constraints with random technology matrix. Ann. Oper. Res. 177(1):127–137.Crossref, Google Scholar
• Berman O, Krass D (2011) On n-facility median problem with facilities subject to failure facing uniform demand. Discrete Appl. Math. 159:420–432.Crossref, Google Scholar
• Bonami P, Lejeune MA (2009) An exact solution approach for portfolio optimization problems under stochastic and integer constraints. Oper. Res. 57(3):650–670.Link, Google Scholar
• Boros E, Hammer PL, Ibaraki T, Kogan A (1997) Logical analysis of numerical data. Math. Programming 79(1–3):163–190.Crossref, Google Scholar
• Carbone R (1974) Public facilities location under stochastic demand. INFOR 12(3):261–270.Google Scholar
• COIN-OR. (2016) Computational infrastructure for operations research project. http://www.coin-or.org/.Google Scholar
• Couenne (2016a) https://projects.coin-or.org/svn/Couenne/stable/0.4, revision 1068.Google Scholar
• Couenne (2016b) https://projects.coin-or.org/svn/Couenne/trunk, revision 1070.Google Scholar
• Crama Y, Hammer PL (2011) Boolean Functions—Theory, Algorithms, and Applications (Cambridge University Press, Cambridge, UK).Crossref, Google Scholar
• Dentcheva D, Prékopa A, Ruszczyński A (2001) Concavity and efficient points of discrete distributions in probabilistic programming. Math. Programming 47(3):1997–2009.Google Scholar
• Enns EA, Mounzer JJ, Brandeau ML (2012) Optimal link removal for epidemic mitigation: A two-way partitioning approach. Math. Biosciences 235:138–147.Crossref, Google Scholar
• Farahani RZ, Hekmatfar M (2009) Facility Location: Concepts, Models, Algorithms and Case Studies (Springer, Berlin).Crossref, Google Scholar
• FMWebStoch (2016) http://wpweb2.tepper.cmu.edu/fmargot/stoch.html.Google Scholar
• Geletu A, Kloeppel M, Zhang H, Li P (2013) Advances and applications of chance-constrained approaches to systems optimization under uncertainty. Internat. J. Systems Sci. 44:1209–1232.Crossref, Google Scholar
• Goldberg N, Leyffer S, Safro I (2015) Optimal response to epidemics and cyber attacks in networks. Naval Res. Logist. 66(2):145–158.Google Scholar
• Grossmann I (2002) Review of nonlinear mixed-integer and disjunctive programming techniques. Optim. Engrg. 3:227–252.Crossref, Google Scholar
• Günlük D, Lee J, Weismantel R (2007) MINLP strengthening for separable convex quadratic transportation-cost UFL. IBM Res. Report 1–16.Google Scholar
• Henrion R, Möller A (2012) A gradient formula for linear chance constraints under Gaussian distribution. Math. Oper. Res. 37:475–488.Link, Google Scholar
• Henrion R, Strugarek C (2008) Convexity of chance constraints with independent random variables. Comput. Optim. Appl. 41(2):263–276.Crossref, Google Scholar
• Hong X, Lejeune MA, Noyan N (2015) Stochastic network design for disaster preparedness. IIE Trans. 47:1–29.Crossref, Google Scholar
• Horst R, Tuy H (1996) Global Optimization: Deterministic Approaches (Springer, Berlin).Crossref, Google Scholar
• Kataoka S (1963) A stochastic programming model. Econometrica 31(1–2):181–196.Crossref, Google Scholar
• Kogan A, Lejeune MA (2014) Threshold Boolean form for joint probabilistic constraints with random technology matrix. Math. Programming 147:391–427.Crossref, Google Scholar
• Küçükyavuz S (2012) On mixing sets arising in probabilistic programming. Math. Programming 132:31–56.Crossref, Google Scholar
• Laporte G, Louveaux FV, van Hamme L (1994) Exact solution to a location problem with stochastic demands. Transportation Sci. 28(2):95–103.Link, Google Scholar
• Larson RC, Sadiq G (1983) Facility locations with the Manhattan metric in the presence of barriers to travel. Oper. Res. 31(4):652–669.Link, Google Scholar
• Lasry A, Sansom SL, Hicks KA, Uzunangelov V (2011) A model for allocating CDC’s HIV prevention resources in the United States. Health Care Management Sci. 14:115–124.Crossref, Google Scholar
• Latorre G, Cruz RD, Areiza JM, Villegas A (2003) Classification of publications and models on transmission expansion planning. IEEE Trans. Power Systems 18(2):938–946.Crossref, Google Scholar
• Lejeune MA (2012a) Pattern-based modeling and solution of probabilistically constrained optimization problems. Oper. Res. 60(6):1356–1372.Link, Google Scholar
• Lejeune MA (2012b) Pattern definition of the p-efficiency concept. Ann. Oper. Res. 200(1):23–36.Crossref, Google Scholar
• Lejeune MA, Margot F (2014) Solving chance-constrained optimization problems with stochastic quadratic inequalities. Tepper Working Paper 2014-E8, Carnegie Mellon University, Pittsburgh, http://wpweb2.tepper.cmu.edu/fmargot/.Google Scholar
• Lejeune MA, Shen S (2016) Multi-objective probabilistically constrained programming with variable risk: New models and applications. Eur. J. Oper. Res. 252(2):522–539.Crossref, Google Scholar
• Li X, Tomasgard A, Barton PI (2012) Decomposition strategy for the stochastic pooling problem. J. Global Optim. 54:765–790.Crossref, Google Scholar
• Liberti L (2006) Writing global optimization software. Liberti L, Maculan N, eds. Global Optimization: From Theory to Implementation (Springer, Berlin), 211–262.Crossref, Google Scholar
• LINDO (2016) Solver Suite. Lindo Systems, Inc. Chicago, http://www.lindo.com/.Google Scholar
• McCormick GP (1976) Computability of global solutions to factorable nonconvex programs: Part I. Convex underestimating problems. Math. Programming 10:147–175.Crossref, Google Scholar
• Murray W, Shanbhag UV (2006) A local relaxation approach for the siting of electrical substations. Comput. Optim. Appl. 33:7–49.Crossref, Google Scholar
• Perron S, Hansen P, Le Digabel S, Mladenovic N (2010) Exact and heuristic solutions of the global supply chain problem with transfer pricing. Eur. J. Oper. Res. 202:864–879.Crossref, Google Scholar
• Prékopa A (1974) Programming under probabilistic constraints with a random technology matrix. Mathematische Operationsforschung und Statistik 5(2):109–116.Crossref, Google Scholar
• Prékopa A (2003) Probabilistic programming. Ruszczyński A, Shapiro A, eds. Stochastic Programming. Handbook in Operations Research and Management Science, Vol. 10 (Elsevier Science, Amsterdam), 267–351.Crossref, Google Scholar
• Rawls CG, Turnquist MA (2010) Pre-positioning of emergency supplies for disaster response. Transportation Res. Part B 44:521–534.Crossref, Google Scholar
• Ray J, Boggs PT, Gay DM, Lemaster MN, Ehlen ME (2009) Risk-based decision making for staggered bioterrorist attacks: Resource allocation and risk reduction in reload scenarios. Sandia Report 2009–6008:1–61.Crossref, Google Scholar
• Ruszczyński A (2002) Probabilistic programming with discrete distribution and precedence constrained knapsack polyhedra. Math. Programming 93(2):195–215.Crossref, Google Scholar
• Sahinidis NV (1996) Baron: A general purpose global optimization software package. J. Global Optim. 8:201–205.Crossref, Google Scholar
• Sen S (1992) Relaxations for probabilistically constrained programs with discrete random variables. Oper. Res. Lett. 11:81–86.Crossref, Google Scholar
• Tanner MW, Ntaimo L (2010) IIS branch-and-cut for joint chance-constrained stochastic programs and application to optimal vaccine allocation. Eur. J. Oper. Res. 207(1):290–296.Crossref, Google Scholar
• Tawarmalani M, Sahinidis NV (2002) Convexification and global optimization in continuous and mixed-integer nonlinear programming: Theory, algorithms, software and applications. Nonconvex Optimization and Its Applications 65 (Kluwer Academic Publishers, Dordrecht, Netherlands).Crossref, Google Scholar
• Tawarmalani M, Sahinidis NV (2004) Global optimization of mixed-integer nonlinear programs: A theoretical and computational study. Math. Programming 99:563–591.Crossref, Google Scholar
• van Ackooij W, Henrion R (2014) Gradient formulae for nonlinear probabilistic constraints with Gaussian and Gaussian-like distributions. SIAM J. Optim. 24:1864–1889.Crossref, Google Scholar
• van Ackooij W, Henrion R, Möller A, Zorgati R (2011) On joint probabilistic constraints with Gaussian coefficient matrix. Oper. Res. Lett. 39(2):99–102.Crossref, Google Scholar
• van de Panne C, Popp W (1963) Minimum cost cattle feed under probabilistic constraints. Management Sci. 9(3):405–430.Link, Google Scholar
• Ventura JA (1991) Computational development of a Lagrangian dual approach for quadratic networks. Networks 21:469–485.Crossref, Google Scholar