Résumé
In order to obtain reliable deterministic global optima, all the computed bounds have to be certified in a way that no numerical error due to floating-point operations can discard a feasible solution. Interval arithmetic Branch and Bound algorithms which are developed since the 1980th possess this property of reliability. However, some new accelerating techniques, such as convex relaxation, could improve the convergence of those reliable global optimization algorithms while keeping the property of reliability. In this work, we show that a floating-point solution obtained by solving a relaxed convex program can be corrected in order to certify that this new lower bound is lower than the real global optimum.