A subgradient supported ellipsoid method for convex multiobjective optimization problems

Multi-objective optimization is a computational technique used to find the best solution for a problem with multiple conflicting objectives. A set of solutions that represents a trade-off between the competing objectives, known as the Pareto front or Pareto set. A common method for solving multi-objective optimization problems is the scalarization method, which converts multi objectives into a single objective. However, the scalarization may not cover the entire pareto front in complex multi-objective optimization problems. In this paper, an ellipsoid algorithm is proposed to overcome the disadvantages of the scalarization method. An ellipsoid algorithm does not combine objectives into single objective. Rather, it directly explore the solution space, aiming to find solutions that are not restricted by the limitations of scalarization. The proposed algorithm mainly targets the multi-objective optimization problems with linear constraints. Also, the convergence rate and the numerical examples justify the effectiveness of the proposed ellipsoid method.