Characterization of local solutions for a class of nonconvex programs

  • P. P. Bansal
  • S. E. Jacobsen
Contributed Papers

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.

Key Words

Nonconvex programming mathematical programming operations research sufficiency conditions necessary conditions 

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References

  1. 1.
    Soland, R. M.,An Algorithm for Separable Nonconvex Programming Problems, II, Nonconvex Constraints, Management Science, Vol. 17, pp. 759–773, 1971.Google Scholar
  2. 2.
    Rosen, J. B.,Iterative Solution of Nonlinear Optimal Control Problems, SIAM Journal on Control, Vol. 4, pp. 223–244, 1966.Google Scholar
  3. 3.
    Meyer, R.,The Validity of a Family of Optimization Methods, SIAM Journal on Control, Vol. 8, pp. 41–54, 1970.Google Scholar
  4. 4.
    Benders, J. F.,Partitioning Procedures for Solving Mixed-Variables Programming Problems, Numerische Mathematik, Vol. 4, pp. 238–252, 1962.Google Scholar
  5. 5.
    Geoffrion, A. M.,Generalized Benders Decomposition, Journal of Optimization Theory and Applications, Vol. 4, pp. 237–260, 1972.Google Scholar
  6. 6.
    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.Google Scholar

Copyright information

© Plenum Publishing Corporation 1975

Authors and Affiliations

  • P. P. Bansal
    • 1
  • S. E. Jacobsen
    • 1
  1. 1.Engineering Systems DepartmentUniversity of CaliforniaLos Angeles

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