Qualification Conditions In Semialgebraic Programming
Bolte
J
author
Hochart
A
author
Pauwels
E
author
2018
English
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.
constraint qualification
Mangasarian-Fromovitz
Arrow-Hurwicz-Uzawa
Lagrange multipliers
optimality conditions
tame programming
WOS:000436991600036
exported from refbase (show.php?record=882), last updated on Tue, 07 Aug 2018 20:10:07 -0400
text
files/882_Bolte_etal2018.pdf
10.1137/16M1133889
Bolte_etal2018
Siam Journal On Optimization
SIAM J. Optim.
2018
Siam Publications
continuing
periodical
academic journal
28
2
1867
1891
1052-6234