Lower subdifferentiable functions and their minimization by cutting planes |
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Authors: | F Plastria |
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Institution: | (1) Centrum voor Statistiek en Operationeel Onderzoek, Vrije Universiteit Brussel, Brussels, Belgium |
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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.The author thanks the referees for several constructive remarks. |
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Keywords: | Lower subgradients boundedly lower subdifferentiable functions quasiconvex functions Lipschitz functions cutting plane algorithm |
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