A predictor corrector method for the computation of boundary points of a multi-objective optimization problem

Recently, a gradient based method has been proposed which allows to steer a given candidate solution of a multi-objective optimization problem (MOP) F : Q ⊂ ℝⁿ → ℝ^k in any direction α ∈ ℝ^k defined in objective space. Since in the context of optimization improvements are sought, α is typically a descent direction, and the resulting curve of improving solutions steers in case the objectives are bounded below toward a boundary solution, i.e., a point x* whose image F(x*) is at the boundary of F(Q). The efficient computation of such points is of particular interest both for descent methods (i.e., to find solutions of the MOP) or for methods that move along the solution set of a MOP. Here we present a predictor corrector algorithm for the computation of such points that increases the performance of the above mentioned steering method.