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A Feasible Directions Method for Nonsmooth Convex Optimization

Jose Herskovits(jose***at***optimize.ufrj.br)
Wilhelm Freire(wilhelmfreire***at***yahoo.com.br)
Mario Tanaka Fo.(tanaka***at***ufpa.br)

Abstract: We propose a new technique for minimization of convex functions not necessarily smooth. Our approach employs an equivalent constrained optimization problem and approximated linear programs obtained with cutting planes. At each iteration a search direction and a step length are computed. If the step length is considered ``non serious", a cutting plane is added and a new search direction is computed. This procedure is repeated until a ``serious" step is obtained. When this happens, the search direction is a feasible descent direction of the constrained equivalent problem. The search directions are computed with FDIPA, the Feasible Directions Interior Point Algorithm. We prove global convergence and solve several test problems very efficiently.

Keywords: Unconstrained convex optimization; Non-smooth optimization; Bundle methods; Interior point methods

Category 1: Convex and Nonsmooth Optimization

Category 2: Nonlinear Optimization

Citation: Herskovits,J., Freire,W.P., Tanaka T.F., A Feasible Directions Method for Nonsmooth Convex Optimization. Technical Report, Mechanical Engineering Program-COPPE/UFRJ, Rio de Janeiro, julho 2009.

Download: [PDF]

Entry Submitted: 01/08/2010
Entry Accepted: 01/09/2010
Entry Last Modified: 01/08/2010

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