Abstract
A constraintg(x)⩾0 is said to be a reverse convex constraint if the functiong is continuous and strictly quasi-convex. The feasible regions for linear programs with an additional reverse convex constraint are generally non-convex and disconnected. It is shown that the convex hull of the feasible region is a convex polytope and, as a result, there is an optimal solution on an edge of the polytope defined by only the linear constraints. The only possible edges which can contain such an optimal solution are characterized in relation to the best feasible vertex of the polytope defined by only the linear constraints. This characterization then provides a finite algorithm for finding a globally optimal solution.
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Communicated by J. Stoer
Research supported by NSF Grant ENG76-12250 and ONR Contract N00014-78-C-0428.
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Hillestad, R.J., Jacobsen, S.E. Linear programs with an additional reverse convex constraint. Appl Math Optim 6, 257–269 (1980). https://doi.org/10.1007/BF01442898
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DOI: https://doi.org/10.1007/BF01442898