TY  - JOUR
ID  - publications26260
UR  - http://tse-fr.eu/pub/32945
IS  - 2
A1  - Bolte, Jérôme
A1  - Hochart, Antoine
A1  - Pauwels, Edouard
Y1  - 2018///
N2  - 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.
PB  - Society for Industrial and Applied Mathematics,
JF  - SIAM Journal on Optimization
VL  - 28
SN  - 1095-7189
TI  - Qualification conditions in semi-algebraic programming
SP  - 1867
AV  - none
EP  - 1891
ER  -