Quasi-Newton updates with weighted secant equations

Serge Gratton (1, 2) , Vincent Malmedy (3) , Philippe Toint (4)

1 IRIT-APO - Algorithmes Parallèles et Optimisation
2 Toulouse INP - Institut National Polytechnique (Toulouse)
3 LMS Samtech - Siemens (UNITED KINGDOM)
4 NaXys - Namur Center for Complex Systems [Namur]

We provide a formula for variational quasi-Newton updates with multiple weighted secant equations. The derivation of the formula leads to a Sylvester equation in the correction matrix. Examples are given.

Mots clés: Nonlinear optimization; Quasi-Newton formulae; Secant equations

Domaines: Arithmétique des ordinateurs

Serge Gratton, Vincent Malmedy, Philippe Toint. Quasi-Newton updates with weighted secant equations. Optimization Methods and Software, 2015, 30 (4), pp.748-755. ⟨10.1080/10556788.2014.971025⟩. ⟨hal-02147968⟩