We address the solution of convex-constrained nonlinear systems of equations where the Jacobian matrix is unavailable or its computation/storage is burdensome. In order to efficiently solve such problems, we propose a new class of algorithms which are ``derivative-free'' both in the computation of the search direction and in the selection of the steplength. Search directions comprise the residuals and Quasi-Newton directions while the steplength is determined by using a new linesearch strategy based on a nonmonotone approximate norm descent property of the merit function. We provide a theoretical analysis of the proposed algorithm and we discuss several conditions ensuring convergence to a solution of the constrained nonlinear system. Finally, we illustrate its numerical behaviour also in comparison with existing approaches.

Approximate norm descent methods for constrained nonlinear systems / Morini, Benedetta; Porcelli, Margherita; Toint Philippe, L.. - In: MATHEMATICS OF COMPUTATION. - ISSN 1088-6842. - STAMPA. - 87:(2018), pp. 1327-1351. [10.1090/mcom/3251]

Approximate norm descent methods for constrained nonlinear systems

MORINI, BENEDETTA
;
PORCELLI, MARGHERITA;
2018

Abstract

We address the solution of convex-constrained nonlinear systems of equations where the Jacobian matrix is unavailable or its computation/storage is burdensome. In order to efficiently solve such problems, we propose a new class of algorithms which are ``derivative-free'' both in the computation of the search direction and in the selection of the steplength. Search directions comprise the residuals and Quasi-Newton directions while the steplength is determined by using a new linesearch strategy based on a nonmonotone approximate norm descent property of the merit function. We provide a theoretical analysis of the proposed algorithm and we discuss several conditions ensuring convergence to a solution of the constrained nonlinear system. Finally, we illustrate its numerical behaviour also in comparison with existing approaches.
2018
87
1327
1351
Morini, Benedetta; Porcelli, Margherita; Toint Philippe, L.
File in questo prodotto:
File Dimensione Formato  
mcom3251_AM.pdf

accesso aperto

Tipologia: Versione finale referata (Postprint, Accepted manuscript)
Licenza: Creative commons
Dimensione 468.51 kB
Formato Adobe PDF
468.51 kB Adobe PDF

I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1079577
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 18
  • ???jsp.display-item.citation.isi??? 16
social impact