Piecewise linear approximations in nonconvex nonsmooth optimization

GAUDIOSO, MANLIO;GORGONE, ENRICO;Monaco, M. F.

2009-01-01

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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.