We present a bundle type method for minimizing nonconvex nondifferentiable functions of several variables. The algorithm is based on the construction of both a lower and an upper polyhedral approximation of the objective function. In particular, at each iteration, a search direction is computed by solving a quadratic program aiming at maximizing the difference between the lower and the upper model. A proximal approach is used to guarantee convergence to a stationary point under the hypothesis of weak semismoothness. © 2009 Springer-Verlag.

Piecewise linear approximations in nonconvex nonsmooth optimization

GAUDIOSO, MANLIO;GORGONE, ENRICO;
2009

Abstract

We present a bundle type method for minimizing nonconvex nondifferentiable functions of several variables. The algorithm is based on the construction of both a lower and an upper polyhedral approximation of the objective function. In particular, at each iteration, a search direction is computed by solving a quadratic program aiming at maximizing the difference between the lower and the upper model. A proximal approach is used to guarantee convergence to a stationary point under the hypothesis of weak semismoothness. © 2009 Springer-Verlag.
Applied Mathematics; Computational Mathematics
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11584/212584
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