Multi-objective optimization with convex quadratic cost functions: A multi-parametric programming approach

• Formulation of the multi-objective optimization problem as a multi-parametric QCQP.
• Derivation of suitable affine overestimators with a guaranteed bound of suboptimality.
• Solution of the resulting mp-QP problem with state-of-the-art solvers, thus obtaining the Pareto front explicitly.
• Numerical examples highlight the capabilities of this approach.

In this note we present an approximate algorithm for the explicit calculation of the Pareto front for multi-objective optimization problems featuring convex quadratic cost functions and linear constraints based on multi-parametric programming and employing a set of suitable overestimators with tunable suboptimality. A numerical example as well as a small computational study highlight the features of the novel algorithm.