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Nondifferentiable reverse convex programs and facetial convexity cuts via a disjunctive characterization.(English)Zbl 0626.90078

The paper considers mathematical programming problems of minimizing a linear functional subject to inequality constraints of the form \(g_ i(x)\leq 0\), where \(g_ i\) are real valued, possibly nondifferentiable, concave functions. Such constraints are called reverse convex and the corresponding programs are called reverse convex programs. By extending a work of Hillestad and Jacobsen (1980) it is shown that the closure of the convex hull of the feasible region of the problem is polyhedral. Some connections between disjunctive programs and reverse convex programs are established. It is shown how results about disjunctive programs can be applied to reverse convex programs. Finally an application to a general linear complementarity problem is examined.
Reviewer: A.Shapiro

MSC:

90C30 Nonlinear programming
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)

Cite

References:

[1]M. Avriel, ”Methods for solving signomial and reverse convex programming problems,” in: M. Avriel, M.J. Rijckaert and D.J. Wilde, eds.,Optimization and Design (Prentice-Hall, Englewood Cliffs, NJ, 1973) pp. 307–320.
[2]M. Avriel,Nonlinear Programming: Analysis and Methods (Prentice-Hall, Englewood Cliffs, NJ, 1976).
[3]M. Avriel and A.C. Williams, ”Complementary geometric programming,”SIAM Journal of Applied Mathematics 19 (1970) 125–141. ·Zbl 0319.90035 ·doi:10.1137/0119011
[4]E. Balas, ”Intersection cuts–a new type of cutting planes for integer programming,”Operations Research 19 (1971) 19–39. ·Zbl 0219.90035 ·doi:10.1287/opre.19.1.19
[5]E. Balas, ”Disjunctive programming: Cutting planes from logical conditions,” in: O.L. Mangasarian, R.R. Meyer and S.M. Robinson, eds.,Nonlinear Programming (Academic Press, New York, 1975) pp. 279–312. ·Zbl 0349.90117
[6]P.P. Bansal and S.E. Jacobsen, ”Characterization of local solutions for a class of nonconvex programs,”Journal of Optimization Theory and Application 15 (1975a) 549–564. ·Zbl 0281.90078 ·doi:10.1007/BF00933745
[7]P.P. Bansal and S.E. Jacobsen, ”An algorithm for optimizing network flow capacity under economies of scale,Journal of Optimization Theory and Application 15 (1975b) 565–586. ·Zbl 0281.90077 ·doi:10.1007/BF00933746
[8]J. Bard and J.E. Falk, ”An explicit solution to the multi-level programming problem”,Computers and Operations Research 9 (1982a) 77–100. ·doi:10.1016/0305-0548(82)90007-7
[9]J. Bard and J.E. Falk, ”A separable programming approach to the linear complementarity problem,”Computers and Operations Research 9 (1982b) 153–159. ·doi:10.1016/0305-0548(82)90014-4
[10]R.W. Cottle and G.B. Dantzig, ”Complementary pivot theory of mathematical programming,”Linear Algebra and Applications 1 (1968) 103–125. ·Zbl 0155.28403 ·doi:10.1016/0024-3795(68)90052-9
[11]R.S. Dembo, ”Solution of complementary geometric programming problems,” M.Sc. Thesis, Technion, Israel Institute of Technology, Haifa (1972).
[12]G. Gallo and A. Ulkucu, ”Bilinear programming: An exact algorithm,”Mathematical Programming 12 (1977) 173–194. ·Zbl 0363.90086 ·doi:10.1007/BF01593787
[13]F. Glover, ”Convexity cuts and cut search,”Operations Research 21 (1973) 123–124. ·Zbl 0263.90020 ·doi:10.1287/opre.21.1.123
[14]F. Glover, ”Polyhedral convexity cuts and negative edge extensions,”Zeitschrift für Operations Research 18 (1974) 181–186. ·Zbl 0288.90056 ·doi:10.1007/BF02026599
[15]S.A. Gustafson and K.O. Kortanek, ”Numerical solution of a class of semiinfinite programming problems,”Naval Research Logistics Quarterly 20 (1973) 477–504. ·Zbl 0272.90073 ·doi:10.1002/nav.3800200310
[16]R.J. Hillestad, ”Optimization problems subject to a budget constraint with economies of scale,”Operations Research 23 (1975) 1091–1098. ·Zbl 0335.90039 ·doi:10.1287/opre.23.6.1091
[17]R.J. Hillestad and S.E. Jacobsen, ”Reverse convex programming,”Applied Mathematics and Optimization 6 (1980a) 63–78. ·Zbl 0448.90044 ·doi:10.1007/BF01442883
[18]R.J. Hillestad and S.E. Jacobsen, ”Linear programs with an additional reverse convex constraint,”Applied Mathematics and Optimization 6 (1980b) 257–269. ·Zbl 0435.90065 ·doi:10.1007/BF01442898
[19]R.G. Jeroslow, ”Cutting planes for complementarity constraints,”SIAM Journal on Control and Optimization 16 (1978) 56–62. ·Zbl 0395.90076 ·doi:10.1137/0316005
[20]C.E. Lemke, ”Bimatrix equilibrium points and mathematical programming,”Management Science 11 (1965) 681–689. ·Zbl 0139.13103 ·doi:10.1287/mnsc.11.7.681
[21]M. Raghavachari, ”On the zero-one integer programming problem,”Operations Research 17 (1969) 680–685. ·Zbl 0176.49805 ·doi:10.1287/opre.17.4.680
[22]B. Ramarao and C.M. Shetty, ”Development of valid inequalities for disjunctive programming,”Naval Research Logistics Quarterly 31 (1984) 581–600. ·Zbl 0559.90088 ·doi:10.1002/nav.3800310408
[23]R.T. Rockafellar,Convex Analysis (Princeton University Press, Princeton, NJ, 1970). ·Zbl 0193.18401
[24]J.B. Rosen, ”Iterative solution of nonlinear optimal control problems,”SIAM Journal on Control 4 (1966) 223–244. ·Zbl 0229.49025 ·doi:10.1137/0304021
[25]S. Sen and H.D. Sherali, ”On the convergence of cutting plane algorithms for a class of nonconvex mathematical programs,”Mathematical Programming 31 (1985a) 42–56. ·Zbl 0562.90076 ·doi:10.1007/BF02591860
[26]S. Sen and H.D. Sherali, ”A branch and bound algorithm for extreme point mathematical programming problems,”Discrete Applied Mathematics 11 (1985b) 265–280. ·Zbl 0595.90063 ·doi:10.1016/0166-218X(85)90078-2
[27]S. Sen and H.D. Sherali, ”Facet inequalties from simple disjunctions in cutting plane theory,”Mathematical Programming 34 (1986) 72–83. ·Zbl 0582.90077 ·doi:10.1007/BF01582164
[28]S. Sen and A. Whiteson, ”A cone splitting algorithm for reverse convex programming,”Proceedings, IEEE Conference on Systems, Man and Cybernetics (Tucson, AZ, 1985) pp. 656–660.
[29]H.D. Sherali and C.M. Shetty,Optimization with Disjunctive Constraints (Springer-Verlag, Berlin-Heidelberg-New York, 1980a). ·Zbl 0437.90052
[30]H.D. Sherali and C.M. Shetty, ”Deep cuts in disjunctive programming,”Naval Research Logistics Quarterly 27 (1980b) 453–357. ·Zbl 0442.90066 ·doi:10.1002/nav.3800270310
[31]J. Stoer and C. Witzgall,Convexity and Optimization in Finite Dimensions I (Springer-Verlag, Berlin, 1970). ·Zbl 0203.52203
[32]C. Van de Panne,Methods for Linear and Quadratic Programming (North-Holland, Amsterdam, 1974). ·Zbl 0298.90039
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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