M.Sc. in Applied Mathematics, 2019; currently PhD student in the Data Science and Engineering group at Paderborn University, Germany.
We present the key ideas for finding first-order critical points of multi-objective optimization problems with nonlinear objectives and constraints. A gradient-based trust-region algorithm is modified to employ local, derivative-free surrogate models instead, and a so-called Filter ensures convergence towards feasibility. We show results of a prototype implementation in Julia, relying heavily on JuMP and suitable LP or QP solvers, that confirm the use of surrogates to reduce function calls.