2013
DOI: 10.1007/s10107-013-0680-x
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Optimality conditions and finite convergence of Lasserre’s hierarchy

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Cited by 233 publications
(229 citation statements)
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“…In addition, as recently proved by Nie [7] and Marshall [8], finite convergence is generic for POPs on compact basic semi-algebraic sets.…”
Section: Introductionmentioning
confidence: 55%
“…In addition, as recently proved by Nie [7] and Marshall [8], finite convergence is generic for POPs on compact basic semi-algebraic sets.…”
Section: Introductionmentioning
confidence: 55%
“…This is in contrast with the semidefinite relaxations (1.3) for which finite convergence takes place for convex problems where ∇ 2 f (x * ) is positive definite at every minimizer x * ∈ K (see de Klerk and Laurent [6,Corollary 3.3]) and occurs at the first relaxation for SOS-convex 1 problems [11,Theorem 3.3]. In fact, as demonstrated in recent works of Marshall [14] and Nie [15], finite convergence is generic (even for non convex problems).…”
mentioning
confidence: 71%
“…And in contrast to LP-relaxations, there is no obstruction to exactness (i.e., finite convergence). In fact, it is quite the opposite since as demonstrated recently in Nie [15], finite convergence is generic!…”
Section: On the Hierarchy Of Semidefinite Relaxationsmentioning
confidence: 95%
“…In fact, by results from Marshall [13] and more recently Nie [14], membership in Q(g) is also generic for polynomials that are only nonnegative on K. And so Putinar's Positivstellensatz is particularly useful to certify and enforce that a polynomial is nonnegative on K, and in particular the polynomial x → f (x) − f (y) for the inverse optimization problem associated with a feasible solution y ∈ K.…”
Section: Introductionmentioning
confidence: 99%