Abstract
A nonconvex programming problem, which arises in the context of application of Benders' decomposition procedure to a class of network optimization problems, is considered. Conditions which are both necessary and sufficient for a local maximum are derived. The concept of a basic local maximum is introduced, and it is shown that there is a finite number of basic local maxima and at least one such local maximum is optimal.
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Soland, R. M.,An Algorithm for Separable Nonconvex Programming Problems, II, Nonconvex Constraints, Management Science, Vol. 17, pp. 759–773, 1971.
Rosen, J. B.,Iterative Solution of Nonlinear Optimal Control Problems, SIAM Journal on Control, Vol. 4, pp. 223–244, 1966.
Meyer, R.,The Validity of a Family of Optimization Methods, SIAM Journal on Control, Vol. 8, pp. 41–54, 1970.
Benders, J. F.,Partitioning Procedures for Solving Mixed-Variables Programming Problems, Numerische Mathematik, Vol. 4, pp. 238–252, 1962.
Geoffrion, A. M.,Generalized Benders Decomposition, Journal of Optimization Theory and Applications, Vol. 4, pp. 237–260, 1972.
Tucker, A. W.,Dual Systems of Homogeneous Linear Relations, Linear Inequalities and Related Systems, Edited by H. W. Kuhn and A. W. Tucker, Princeton University Press, Princeton, New Jersey, 1956.
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Communicated by C. T. Leondes
This research was supported by the National Science Foundation, Grant No. GK-32791.
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Bansal, P.P., Jacobsen, S.E. Characterization of local solutions for a class of nonconvex programs. J Optim Theory Appl 15, 549–564 (1975). https://doi.org/10.1007/BF00933745
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DOI: https://doi.org/10.1007/BF00933745