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

Leopoldo Marini (), Benedetta Morini () and Margherita Porcelli ()
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Leopoldo Marini: Università di Firenze
Benedetta Morini: Università di Firenze
Margherita Porcelli: Università di Firenze

Computational Optimization and Applications, 2018, vol. 71, issue 1, No 7, 147-170

Abstract: Abstract We address the solution of constrained nonlinear systems by new linesearch quasi-Newton methods. These methods are based on a proper use of the projection map onto the convex 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 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10589-018-9980-7

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