## Une méthode de quasi-Newton réduite en optimisation sous contraintes avec priorité à la restauration. (A reduced quasi-Newton method in constrained optimization with priority to the restoration).(French)Zbl 0599.90112

Analysis and optimization of systems, Proc. 7th int. Conf., Antibes/France 1986, Lect. Notes Control Inf. Sci. 83, 40-53 (1986).
[For the entire collection see Zbl 0587.00029.]
To minimize a function on $${\mathcal R}^ n$$ with m nonlinear equality constraints, we propose an algorithm with the following features: each iteration is formed of two steps of restoration of the constraints and one step of minimization of the function, the constraints are linearized once per iteration; a matrix of order n-m (approximation of the reduced Hessian of the Lagrangian) is updated but not at each iteration (a criterion is proposed); the method is global with priority to the restoration and generates a Q-superlinearly converging sequence of points.

### MSC:

 90C30 Nonlinear programming 65K05 Numerical mathematical programming methods

Zbl 0587.00029