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Author Bolte, J.; Hochart, A.; Pauwels, E. pdf  doi
  Title Qualification Conditions In Semialgebraic Programming Type
  Year 2018 Publication Siam Journal On Optimization Abbreviated Journal SIAM J. Optim.  
  Volume 28 Issue 2 Pages 1867-1891  
  Keywords constraint qualification; Mangasarian-Fromovitz; Arrow-Hurwicz-Uzawa; Lagrange multipliers; optimality conditions; tame programming  
  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.  
  Address [Bolte, Jerome] Univ Toulouse 1 Capitole, Toulouse Sch Econ, Toulouse, France, Email:;  
  Corporate Author Thesis  
  Publisher Siam Publications Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1052-6234 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000436991600036 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 882  
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