Abstract
In this paper we introduce a modification of the basic cutting plane approach for the minimization of convex nondifferentiable functions which allows dynamic management of the “bundle” of information.
At each iteration, a new affine piece is considered in the approximation of the objective function and all the points obtained during previous iterations are opportunely modified using a line-search type strategy.
The proposed scheme appears particularly suitable for parallel execution since independent line search need to be executed at each iteration.
The convergence of the approach is proved, under simple assumptions on the step size on the modification procedure that will prevent instability.
The work of the second author is partially supported by the Fondo Ricerca di Ateneo, Università di Camerino.
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References
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© 1998 Kluwer Academic Publishers, Boston
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Capalbo, V., De Leone, R., Gaudioso, M. (1998). The Cobweb Method for Minimizing Convex Functions. In: De Leone, R., Murli, A., Pardalos, P.M., Toraldo, G. (eds) High Performance Algorithms and Software in Nonlinear Optimization. Applied Optimization, vol 24. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3279-4_7
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DOI: https://doi.org/10.1007/978-1-4613-3279-4_7
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