A variant of the CESTAC method and its application to constrained optimization

The Vignes-La Porte CESTAC method enables the computer, when solving a problem in floating-point arithmetics (e.g., a system of equations), to construct 95% confidence intervals for the accuracy of the solution. In iterative methods, this involves the Optimal Stopping Criterion, which may be too costly or impossible to achieve. Here we present a variant which permits the use of classical stopping criteria. This variant is applied to the Generalized Reduced Gradient (GRG) method for nonlinear constrained optimization problems. Numerical experiments are presented.