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Quasi-Newton methods for constrained nonlinear systems: complexity analysis and application

Leopoldo Marini (leopoldo.marini***at***unifi.it)
Benedetta Morini (benedetta.morini***at***unifi.it)
Margherita Porcelli (margherita.porcelli***at***unifi.it)

Abstract: We address the solution of convex constrained nonlinear systems by new linesearch Quasi-Newton methods. These methods are based on a proper use of the projection map onto the constraint set and on a derivative-free and nonmonotone linesearch strategy. The convergence properties of the proposed methods are presented along with a worst-case iteration complexity bound. Several implementations of the proposed scheme are discussed and validated on bound-constrained problems including gas distribution network models. The results reported show that the new methods are very efficient and competitive with an existing affine-scaling procedure.

Keywords: nonlinear systems of equations; Quasi-Newton methods; nonmonotone derivative-free linesearch; convergence theory; complexity analysis

Category 1: Nonlinear Optimization

Category 2: Nonlinear Optimization (Nonlinear Systems and Least-Squares )


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Entry Submitted: 01/12/2017
Entry Accepted: 01/12/2017
Entry Last Modified: 10/26/2017

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