Annick Sartenaer

Learn More
A class of trust region based algorithms is presented for the solution of nonlinear optimization problems with a convex feasible set. At variance with previously published analysis of this type, the theory presented allows for the use of general norms. Furthermore, the proposed algorithms do not require the explicit computation of the projected gradient,(More)
We consider the global and local convergence properties of a class of augmented Lagrangian methods for solving nonlinear programming problems. In these methods, linear and more general constraints are handled in different ways. The general constraints are combined with the objective function in an augmented Lagrangian. The iteration consists of solving a(More)
Abstract. A class of trust-region methods is presented for solving unconstrained nonlinear and possibly nonconvex discretized optimization problems, like those arising in systems governed by partial differential equations. The algorithms in this class make use of the discretization level as a mean of speeding up the computation of the step. This use is(More)
This work is concerned with the development and study of a class of limited memory preconditioners for the solution of sequences of linear systems. To this aim, we consider linear systems with the same symmetric positive definite matrix and multiple right-hand sides available in sequence. We first propose a general class of preconditioners, called Limited(More)
It is well known that the norm of the gradient may be unreliable as a stopping test in unconstrained optimization and that it often exhibits oscillations in the course of the optimization In this paper we present results describing the properties of the gradient norm for the steepest descent method applied to quadratic objective functions We also make some(More)
This paper presents an analysis of the involvement of the penalty parameter in exact penalty function methods that yields modiications to the standard outer loop which decreases the penalty parameter (typically dividing it by a constant). The procedure presented is based on the simple idea of making explicit the dependence of the penalty function upon the(More)
We consider an implementation of the recursive multilevel trust-region algorithm proposed by Gratton, Sartenaer and Toint (2004), and provide significant numerical experience on multilevel test problems. A suitable choice of the algorithm’s parameters is identified on these problems, yielding a very satisfactory compromise between reliability and(More)
We consider the local convergence properties of the class of augmented Lagrangian methods for solving nonlinear programming problems whose global convergence properties are analyzed by Conn et al. (1993a). In these methods, linear constraints are treated separately from more general constraints. These latter constraints are combined with the objective(More)