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Author  |
Bolte, J.; Hochart, A.; Pauwels, E. |

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Title |
Qualification Conditions In Semialgebraic Programming |
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Year |
2018 |
Publication |
Siam Journal On Optimization |
Abbreviated Journal |
SIAM J. Optim. |
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Volume |
28 |
Issue |
2 |
Pages |
1867-1891 |
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Keywords |
constraint qualification; Mangasarian-Fromovitz; Arrow-Hurwicz-Uzawa; Lagrange multipliers; optimality conditions; tame programming |
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Abstract |
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. |
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Address |
[Bolte, Jerome] Univ Toulouse 1 Capitole, Toulouse Sch Econ, Toulouse, France, Email: jerome.bolte@tse-fr.eu; |
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Publisher |
Siam Publications |
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Language |
English |
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ISSN |
1052-6234 |
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Notes |
WOS:000436991600036 |
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Call Number |
UAI @ eduardo.moreno @ |
Serial |
882 |
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