In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field...

This paper addresses the robust counterparts of optimization problems containing sums of maxima of linear functions and proposes several reformulations. These problems include many practical problems, e.g. problems with sums of absolute values, and arise when taking the robust counterpart of a...

In many fields, we come across problems where we want to optimize several conflicting objectives simultaneously. To find a good solution for such multi-objective optimization problems, an approximation of the Pareto set is often generated. In this paper, we consider the approximation of Pareto...