We introduce an algorithm to minimize a function of several variables with no convexity nor smoothness assumptions. The main peculiarity of our approach is the use of an objective function model which is the difference of two piecewise affine convex functions. Bundling and trust region concepts are embedded into the algorithm. Convergence of the algorithm to a stationary point is proved and some numerical results are reported.

A DC piecewise affine model and a bundling technique in nonconvex nonsmooth minimization

FUDULI, Antonio;GAUDIOSO, Manlio;GIALLOMBARDO, Giovanni
2004

Abstract

We introduce an algorithm to minimize a function of several variables with no convexity nor smoothness assumptions. The main peculiarity of our approach is the use of an objective function model which is the difference of two piecewise affine convex functions. Bundling and trust region concepts are embedded into the algorithm. Convergence of the algorithm to a stationary point is proved and some numerical results are reported.
Nonsmooth optimization; Cutting planes; Bundle methods; DC functions
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11770/158660
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