Title: Trust-regions, filter and non-monotonicity in nonlinear optimization Philippe Toint Univ. Namur, Belgium email: philippe.toint@fundp.ac.be Nick Gould, Caroline Sainvitu and Philippe Toint Abstract: The talk will consider several variants of the trust-region algorithm and its filter variants, both for constrained and unconstrained optimization problem, putting emphasis on how non-monotonicity can be included in these variants. Convergence theory will be outlined and numerical experiments discussed for the nonlinear feasibility problem and the unconstrained case.