Intersection Disjunctions for Reverse Convex Sets

References

• [1] Balas E (1971) Intersection cuts—A new type of cutting planes for integer programming. Oper. Res. 19(1):19–39.Link, Google Scholar
• [2] Balas E (1972) Integer programming and convex analysis: intersection cuts from outer polars. Math. Programming 2(1):330–382.Crossref, Google Scholar
• [3] Balas E (1979) Disjunctive programming. Ann. Discrete Math. 5:3–51.Crossref, Google Scholar
• [4] Balas E (1998) Disjunctive programming: Properties of the convex hull of feasible points. Discrete Appl. Math. 89(1–3):3–44.Crossref, Google Scholar
• [5] Balas E, Margot F (2013) Generalized intersection cuts and a new cut generating paradigm. Math. Programming 137(1-2):19–35.Crossref, Google Scholar
• [6] Bansal PP, Jacobsen SE (1975) An algorithm for optimizing network flow capacity under economies of scale. J. Optim. Theory Appl. 15(5):565–586.Crossref, Google Scholar
• [7] Bansal PP, Jacobsen SE (1975) Characterization of local solutions for a class of nonconvex programs. J. Optim. Theory Appl. 15(5):549–564.Crossref, Google Scholar
• [8] Basu A, Cornuéjols G, Zambelli G (2011) Convex sets and minimal sublinear functions. J. Convex Anal. 18(2):427–432.Google Scholar
• [9] Basu A, Conforti M, Cornuéjols G, Zambelli G (2010) Minimal inequalities for an infinite relaxation of integer programs. SIAM J. Discrete Math. 24(1):158–168. Crossref, Google Scholar
• [10] Ben Saad S, Jacobsen SE (1990) A level set algorithm for a class of reverse convex programs. Ann. Oper. Res. 25(1):19–42.Crossref, Google Scholar
• [11] BenSaad S, Jacobsen SE (1994) Comments on a reverse convex programming algorithm. J. Global Optim. 5(1):95–96.Crossref, Google Scholar
• [12] Bienstock D, Chen C, Muñoz G (2020) Outer-product-free sets for polynomial optimization and oracle-based cuts. Math. Programming 183(1):105–148.Crossref, Google Scholar
• [13] Conforti M, Cornuéjols G, Zambelli G (2014) Integer Programming (Springer, Berlin).Crossref, Google Scholar
• [14] Conforti M, Cornuéjols G, Daniilidis A, Lemaréchal C, Malick J (2014) Cut-generating functions and -free sets. Math. Oper. Res. 40(2):276–301.Link, Google Scholar
• [15] Cornuéjols G, Li Y (2001) Elementary closures for integer programs. Oper. Res. Lett. 28(1):1–8.Crossref, Google Scholar
• [16] Dey SS, Wolsey LA (2010) Constrained infinite group relaxations of MIPs. SIAM J. Optim. 20(6):2890–2912.Crossref, Google Scholar
• [17] Farkas J (1902) Theorie der einfachen Ungleichungen. J. Reine Angew Math. 124:1–27.Google Scholar
• [18] Fischetti M, Ljubić I, Monaci M, Sinnl M (2016) Intersection cuts for bilevel optimization. 18th Internat. Conf. Integer Programming Combinatorial Optim. (Springer, Berlin), 77–88.Crossref, Google Scholar
• [19] Fukasawa R, Günlük O (2011) Strengthening lattice-free cuts using non-negativity. Discrete Optim. 8(2):229–245.Crossref, Google Scholar
• [20] Fülöp J (1990) A finite cutting plane method for solving linear programs with an additional reverse convex constraint. Eur. J. Oper. Res. 44(3):395–409.Crossref, Google Scholar
• [21] Glover F (1974) Polyhedral convexity cuts and negative edge extensions. J. Oper. Res. 18(5):181–186.Google Scholar
• [22] Grötschel M, Lovász L, Schrijver A (1981) The ellipsoid method and its consequences in combinatorial optimization. Combinatorica 1(2):169–197.Crossref, Google Scholar
• [23] Grötschel M, Lovász L, Schrijver A (2012) Geometric Algorithms and Combinatorial Optimization, vol. 2 (Springer, Berlin).Google Scholar
• [24] Günlük O, Pochet Y (2001) Mixing mixed-integer inequalities. Math. Programming 90(3):429–457.Crossref, Google Scholar
• [25] Gurlitz TR (1985) Algorithms for reverse convex programs (non-convex, cutting planes). PhD thesis, University of California, Los Angeles.Google Scholar
• [26] Gurlitz TR, Jacobsen SE (1991) On the use of cuts in reverse convex programs. J. Optim. Theory Appl. 68(2):257–274.Crossref, Google Scholar
• [27] Hartman P (1959) On functions representable as a difference of convex functions. Pacific J. Math. 9(3):707–713.Crossref, Google Scholar
• [28] Hillestad RJ (1975) Optimization problems subject to a budget constraint with economies of scale. Oper. Res. 23(6):1091–1098.Link, Google Scholar
• [29] Hillestad RJ, Jacobsen SE (1980) Linear programs with an additional reverse convex constraint. Appl. Math. Optim. 6(1):257–269.Crossref, Google Scholar
• [30] Hillestad RJ, Jacobsen SE (1980) Reverse convex programming. Appl. Math. Optim. 6(1):63–78.Crossref, Google Scholar
• [31] Horst R (1988) Deterministic global optimization with partition sets whose feasibility is not known: Application to concave minimization, reverse convex constraints, DC-programming, and Lipschitzian optimization. J. Optim. Theory Appl. 58(1):11–37.Crossref, Google Scholar
• [32] Horst R, Phong TQ, Thoai NV (1990) On solving general reverse convex programming problems by a sequence of linear programs and line searches. Ann. Oper. Res. 25(1):1–17.Crossref, Google Scholar
• [33] Luedtke J, Ahmed S (2008) A sample approximation approach for optimization with probabilistic constraints. SIAM J. Optim. 19(2):674–699.Crossref, Google Scholar
• [34] Martin RK (1991) Using separation algorithms to generate mixed integer model reformulations. Oper. Res. Lett. 10(3):119–128.Crossref, Google Scholar
• [35] Matsui T (1996) NP-hardness of linear multiplicative programming and related problems. J. Global Optim. 9(2):113–119.Crossref, Google Scholar
• [36] Miller AJ, Wolsey LA (2003) Tight formulations for some simple mixed integer programs and convex objective integer programs. Math. Programming 98(1-3):73–88.Crossref, Google Scholar
• [37] Muu LD (1985) A convergent algorithm for solving linear programs with an additional reverse convex constraint. Kybernetika (Prague) 21(6):428–435.Google Scholar
• [38] Nemhauser GL, Wolsey LA (1990) A recursive procedure to generate all cuts for 0–1 mixed integer programs. Math. Programming 46(1-3):379–390.Crossref, Google Scholar
• [39] Orlin JB (2009) A faster strongly polynomial time algorithm for submodular function minimization. Math. Programming 118(2):237–251.Crossref, Google Scholar
• [40] Saxena A, Bonami P, Lee J (2010) Convex relaxations of non-convex mixed integer quadratically constrained programs: Extended formulations. Math. Programming 124(1-2):383–411.Crossref, Google Scholar
• [41] Saxena A, Bonami P, Lee J (2011) Convex relaxations of non-convex mixed integer quadratically constrained programs: Projected formulations. Math. Programming 130(2):359–413.Crossref, Google Scholar
• [42] Sen S, Sherali HD (1987) Nondifferentiable reverse convex programs and facetial convexity cuts via a disjunctive characterization. Math. Programming 37(2):169–183.Crossref, Google Scholar
• [43] Thuong NV, Tuy H (1984) A finite algorithm for solving linear programs with an additional reverse convex constraint. Demyanov VF, Pallaschke D, eds. Nondifferentiable Optimization: Motivations and Applications (Springer, Berlin), 291–302.Google Scholar
• [44] Tuy H (1964) Concave programming under linear constraints. Doklady Akademii Nauk 5:1437–1440.Google Scholar
• [45] Tuy H (1986) A general deterministic approach to global optimization via d.c. programming. North-Holland Math. Stud. 129:273–303.Crossref, Google Scholar
• [46] Tuy H (1987) Convex programs with an additional reverse convex constraint. J. Optim. Theory Appl. 52(3):463–486.Crossref, Google Scholar
• [47] Ueing U (1972) A combinatorial method to compute a global solution of certain non-convex optimization problems. Lootsma FA, ed. Numerical Methods for Non-Linear Optimization (Academic Press, New York), 223–230.Google Scholar