RT Journal Article
SR 00
ID 10.1137/16M1133889
A1 Bolte, Jérôme
A1 Hochart, Antoine
A1 Pauwels, Edouard
T1 Qualification conditions in semi-algebraic programming
JF SIAM Journal on Optimization
YR 2018
FD 2018
VO 28
IS 2
SP 1867
OP 1891
AB 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,
SN 1095-7189
LK https://publications.ut-capitole.fr/id/eprint/26260/
UL http://tse-fr.eu/pub/32945