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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(Document in English)
PDF (Publisher's version) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader 442kB |
Official URL: https://doi.org/10.1137/16M1133889
Abstract
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 |
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Additional Information: | SIAM: Society for Industrial and Applied Mathematics https://epubs.siam.org/doi/10.1137/16M1133889 |
Audience (journal): | International peer-reviewed journal |
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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) |
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Funders: | USAF: United States Air Force : Air Force Office of Scientific Research and Air Force Material Command (USA) - FMJH : Fondation Mathématique Jacques Hadamard (Orsay, France) |
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Deposited On: | 11 Oct 2019 08:02 |
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