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Qualification conditions in semi-algebraic programming

Bolte, Jérôme and Hochart, Antoine and Pauwels, Edouard Qualification conditions in semi-algebraic programming. (2018) SIAM Journal on Optimization, 28 (2). 1867-1891. ISSN 1052-6234

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Official URL: https://doi.org/10.1137/16M1133889


For an arbitrary finite family of semi-algebraic/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 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 semi-algebraic/definable problem. Applications to sequential quadratic programming methods and sum of squares relaxation are provided.

Item Type:Article
Additional Information:SIAM: Society for Industrial and Applied Mathematics https://epubs.siam.org/doi/10.1137/16M1133889
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Other partners > Toulouse School of Economics - TSE (FRANCE)
Laboratory name:
USAF: United States Air Force : Air Force Office of Scientific Research and Air Force Material Command (USA) - FMJH : Fondation Mathématique Jacques Hadamard (Orsay, France)
Deposited On:11 Oct 2019 08:02

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