A trust-region LP-Newton method for constrained nonsmooth equations under Hölder metric subregularity

Letícia Becher (), Damián Fernández () and Alberto Ramos ()
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Letícia Becher: Federal University of Paraná
Damián Fernández: CIEM-CONICET, FAMAF-Universidad Nacional de Córdoba
Alberto Ramos: Universidad de Tarapacá

Computational Optimization and Applications, 2023, vol. 86, issue 2, No 9, 743 pages

Abstract: Abstract We describe and analyze a globally convergent algorithm to find a possible nonisolated zero of a piecewise smooth mapping over a polyhedral set. Such formulation includes Karush–Kuhn–Tucker systems, variational inequalities problems, and generalized Nash equilibrium problems. Our algorithm is based on a modification of the fast locally convergent Linear Programming (LP)-Newton method with a trust-region strategy for globalization that makes use of the natural merit function. The transition between global and local convergence occurs naturally under mild assumption. Our local convergence analysis of the method is performed under a Hölder metric subregularity condition of the mapping defining the possibly nonsmooth equation and the Hölder continuity of the derivative of the selection mapping. We present numerical results that show the feasibility of the approach.

Keywords: Nonlinear equations; Newton method; Global convergence; Superlinear convergence; LP-Newton method; 90C33; 90C30; 49M15; 65K05 (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10589-023-00498-9

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