@article{publications26260,
          volume = {28},
          number = {2},
          author = {J{\'e}r{\^o}me Bolte and Antoine Hochart and Edouard Pauwels},
           title = {Qualification conditions in semi-algebraic programming},
       publisher = {Society for Industrial and Applied Mathematics,},
         journal = {SIAM Journal on Optimization},
           pages = {1867--1891},
            year = {2018},
             url = {https://publications.ut-capitole.fr/id/eprint/26260/},
        abstract = {For an arbitrary finite family of semialgebraic/definable functions, we consider the corresponding inequality constraint set and we study qualification conditions for perturbations of this set. In particular we prove that all positive diagonal perturbations, save perhaps a finite number of them, ensure that any point within the feasible set satisfies the Mangasarian--Fromovitz constraint qualification. Using the Milnor--Thom theorem, we provide a bound for the number of singular perturbations when the constraints are polynomial functions. Examples show that the order of magnitude of our exponential bound is relevant. Our perturbation approach provides a simple protocol to build sequences of ?regular? problems approximating an arbitrary semialgebraic/definable problem. Applications to sequential quadratic programming methods and sum of squares relaxation are provided.}
}