Abstract
This paper introduces lower subgradients as a generalization of subgradients. The properties and characterization of boundedly lower subdifferentiable functions are explored. A cutting plane algorithm is introduced for the minimization of a boundedly lower subdifferentiable function subject to linear constraints. Its convergence is proven and the relation is discussed with the well-known Kelley method for convex programming problems. As an example of application, the minimization of the maximum of a finite number of concave-convex composite functions is outlined.
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Communicated by O. L. Mangasarian
The author thanks the referees for several constructive remarks.
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Plastria, F. Lower subdifferentiable functions and their minimization by cutting planes. J Optim Theory Appl 46, 37–53 (1985). https://doi.org/10.1007/BF00938758
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DOI: https://doi.org/10.1007/BF00938758