Multi-objective convex polynomial optimization and semidefinite programming relaxations

This paper aims to find efficient solutions a multi-objective optimization problem (MP) with convex polynomial data. To this end, hybrid method, which allows us transform into scalar \(({\mathrm{P}}_{z})\) and does not destroy the properties of convexity, is considered. First, we show an existence result for under some mild assumption. Then, \((P_{z})\), establish two kinds representations non-negativity polynomials over semi-algebraic sets, propose finite convergence results Lasserre-type hierarchy semidefinite programming relaxations suitable assumptions. Finally, that finding can be achieved successfully by solving hierarchies checking flat truncation condition.