Minimizing nonconvex nonsmooth functions via cutting planes and proximity control

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

Abstract: We describe an extension of the classical cutting plane algorithm to tackle the unconstrained minimization of a nonconvex, not necessarily differentiable function of several variables. The method is based on the construction of both a lower and an upper polyhedral approximation to the objective function and it is related to the use of the concept of proximal trajectory. Convergence to a stationary point is proved for locally Lipschitz functions.

Keywords: Nonsmooth optimization, cutting planes, bundle methods, proximal trajectory

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 2: Nonlinear Optimization (Unconstrained Optimization )

Citation: SIAM Journal on Optimization, 14(3), 743-756, 2004.

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Entry Submitted: 07/19/2002
Entry Accepted: 07/19/2002
Entry Last Modified: 11/05/2004

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