Robust Pareto solutions for convex quadratic multiobjective optimization problems under data uncertainty

In this paper, we consider a convex quadratic multiobjective optimization problem, where both the objective and constraint functions involve data uncertainty. We employ a deterministic approach to examine robust optimality conditions and find robust (weak) Pareto solutions of the underlying uncertain multiobjective problem. We first present new necessary and sufficient conditions in terms of linear matrix inequalities for robust (weak) Pareto optimality of the multiobjective optimization problem. We then show that the obtained optimality conditions can be alternatively checked via other verifiable criteria including a robust Karush-Kuhn-Tucker condition. Moreover, we establish that a (scalar) relaxation problem of a robust weighted-sum optimization program of the multiobjective problem can be solved by using a semidefinite programming (SDP) problem. This provides us with a way to numerically calculate a robust (weak) Pareto solution of the uncertain multiobjective problem as an SDP problem that can be implemented using, e.g., MATLAB.

Automated summary

This paper investigates a convex quadratic multiobjective optimization problem with data uncertainty, finding robust (weak) Pareto solutions using linear matrix inequalities. It also demonstrates that the obtained optimality conditions can be verified via a robust Karush-Kuhn-Tucker condition. Additionally, a relaxation problem of a robust weighted-sum optimization program can be solved as a semidefinite programming (SDP) problem.