A bundle-Newton method for nonsmooth unconstrained minimization | Zendy

Ladislav Lukšan | Zendy; Jan Vlček | Zendy

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A bundle-Newton method for nonsmooth unconstrained minimization

Author(s) -

Ladislav Lukšan,

Jan Vlček

Publication year - 1998

Publication title -

mathematical programming

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.358

H-Index - 131

eISSN - 1436-4646

pISSN - 0025-5610

DOI - 10.1007/bf02680566

Subject(s) - mathematics , minification , convergence (economics) , differentiable function , quadratic equation , newton's method , local convergence , stationary point , numerical analysis , regular polygon , mathematical optimization , iterative method , mathematical analysis , nonlinear system , geometry , physics , quantum mechanics , economics , economic growth

An algorithm based on a combination of the polyhedral and quadratic approximation is given for finding stationary points for unconstrained minimization problems with locally Lips-chitz problem functions that are not necessarily convex or differentiable. Global convergence of the algorithm is established. Under additional assumptions, it is shown that the algorithm generates Newton iterations and that the convergence is superlinear. Some encouraging numerical experience is reported.

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