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

Antonio Fuduli (antonio.fuduliunical.it)
Manlio Gaudioso (gaudiosodeis.unical.it)
Giovanni Giallombardo (giallodeis.unical.it)

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 the 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.

Keywords: Nonsmooth optimization, cutting planes, bundle methods, DC functions

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 2: Nonlinear Optimization (Unconstrained Optimization )

Citation: Optimization Methods and Software, 18(1), 89-102, 2004.

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Entry Submitted: 12/27/2002
Entry Accepted: 01/03/2003
Entry Last Modified: 11/05/2004

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