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A convergent algorithm for solving linear programs with an additional reverse convex constraint. (English) Zbl 0596.90081
The author proposes a method of the branch and bound type for the solution of linear problems with an additional reverse convex constraint. This algorithm is inspired by that of N. V. Thoai and H. Tuy [Math. Oper. Res. 5, 556-566 (1980; Zbl 0472.90054)] for the minimization of a concave function subject to linear inequalities. It is proved that, when the method does not terminate, a sequence of points is generated, one of whose accumulation is a solution of the problem.

90C30 Nonlinear programming
49M37 Numerical methods based on nonlinear programming
65K05 Numerical mathematical programming methods
Full Text: EuDML
[1] M. Avriel, A. C. Williams: Complementary geometric programming. SIAM J. Appl. Math. /P (1970), 125-141. · Zbl 0319.90035 · doi:10.1137/0119011
[2] M. Avriel, A. C. Williams: An extension of geometric programming with applications in engineering optimization. J. Engng. Math. 5 (1971), 187-194.
[3] P. P. Bansal, S. E. Jacobsen: Characterization of local solution for a class of nonconvex programs. J. Optim. Theory Appl. 15 (1975), 127-131. · Zbl 0281.90078 · doi:10.1007/BF00933745
[4] R. J. Hillestad: Optimization problems subject to a budged constraint with economies of scale. Oper. Res. 23 (1975), 1091-1098. · Zbl 0335.90039
[5] R. J. Hillestad, S. E. Jacobsen: Linear programs with an additional reverse convex constraint. Appl. Math. Optim. 6 (1980), 257-269. · Zbl 0435.90065 · doi:10.1007/BF01442898
[6] R. J. Hillestad, S. E. Jacobsen: Reverse convex programming. Appl. Math. Optim. 6 (1980) 63-78. · Zbl 0448.90044 · doi:10.1007/BF01442883
[7] R. Meyer: The validity of a family of optimization methods. SIAM J. Control 8 (1970), 41-54. · Zbl 0194.20501 · doi:10.1137/0308003
[8] J. B. Rosen: Iterative solution of nonlinear optimal control problems. SIAM J. Control 4 (1766), 223-244. · Zbl 0229.49025 · doi:10.1137/0304021
[9] N. V. Thoai, H. Tuy: Convergent algorithms for minimizing a concave function. Math. Oper. Res. 4 (1980), 556-565. · Zbl 0472.90054 · doi:10.1287/moor.5.4.556
[10] H. Tuy: Concave programming under linear constraints. Dokl. Akad. Nauk SSSR 159 (1964), 32-35.
[11] H. Tuy: Conical algorithm for solving a class of complementarity problems. Preprint series 18 (1981), Hanoi. · Zbl 0618.90090
[12] U. Ueing: A combinatorical method to compute a global solution of certain nonconvex optimization problems. Numerical Methods for Non-Linear Optimization (F. A. Lootsma, pp. 223-230, Academic Press, New York 1972. · Zbl 0267.90088
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