Qualification conditions in semi-algebraic programming

Bolte, Jérôme, Hochart, Antoine and Pauwels, Edouard (2018) Qualification conditions in semi-algebraic programming. SIAM Journal on Optimization, 28 (2). pp. 1867-1891.

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Official URL: http://tse-fr.eu/pub/32945


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.

Item Type: Article
Language: English
Date: 2018
Refereed: Yes
Divisions: TSE-R (Toulouse)
Site: UT1
Date Deposited: 18 Sep 2018 10:38
Last Modified: 15 Jul 2019 09:37
OAI ID: oai:tse-fr.eu:32945
URI: http://publications.ut-capitole.fr/id/eprint/26260

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