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The geometry of nondegeneracy conditions in completely integrable systems. preprint math.DG/0403412
 Math. Ann
, 2004
"... Nondegeneracy conditions need to be imposed in K.A.M. theorems to insure that the set of diophantine tori has a large measure. Although they are usually expressed in action coordinates, it is possible to give a geometrical formulation using the notion of regular completely integrable systems defined ..."
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Cited by 3 (1 self)
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Nondegeneracy conditions need to be imposed in K.A.M. theorems to insure that the set of diophantine tori has a large measure. Although they are usually expressed in action coordinates, it is possible to give a geometrical formulation using the notion of regular completely integrable systems
Complementarity and Nondegeneracy in Semidefinite Programming
, 1995
"... Primal and dual nondegeneracy conditions are defined for semidefinite programming. Given the existence of primal and dual solutions, it is shown that primal nondegeneracy implies a unique dual solution and that dual nondegeneracy implies a unique primal solution. The converses hold if strict complem ..."
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Cited by 111 (9 self)
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Primal and dual nondegeneracy conditions are defined for semidefinite programming. Given the existence of primal and dual solutions, it is shown that primal nondegeneracy implies a unique dual solution and that dual nondegeneracy implies a unique primal solution. The converses hold if strict
On nondegeneracy of curves
 Algebra & Number Theory
, 2009
"... Abstract. We study the conditions under which an algebraic curve can be modelled by a Laurent polynomial that is nondegenerate with respect to its Newton polytope. We prove that every curve of genus g ≤ 4 over an algebraically closed field is nondegenerate in the above sense. More generally, let M ..."
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Cited by 8 (7 self)
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Abstract. We study the conditions under which an algebraic curve can be modelled by a Laurent polynomial that is nondegenerate with respect to its Newton polytope. We prove that every curve of genus g ≤ 4 over an algebraically closed field is nondegenerate in the above sense. More generally, let M
Nondegeneracy of Polyhedra and Linear Programs
, 1995
"... This paper deals with nondegeneracy of polyhedra and linear programming (LP) problems. We allow for the possibility that the polyhedra and the feasible polyhedra of the LP problems under consideration be nonpointed. (A polyhedron is pointed if it has a vertex.) With respect to a given polyhedron, w ..."
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Cited by 1 (1 self)
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this terminology since the term dual nondegeneracy is already used to refer to a related but different type of nondegeneracy.) We show two main results about constant cost nondegeneracy of an LP problem. The first one shows that constant cost nondegeneracy of an LP problem is equivalent to the condition
Nondegeneracy Criteria for 3D Grid Formulas for a Cell Volume
"... Nondegeneracy criteria for threedimensional grid cells are found for hexahedral cells which are given by eight corner points and generated by the trilinear map from a unit cube to a region defined by these points. The criteria include both nondegeneracy conditions and a special numerical algorithm ..."
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Nondegeneracy criteria for threedimensional grid cells are found for hexahedral cells which are given by eight corner points and generated by the trilinear map from a unit cube to a region defined by these points. The criteria include both nondegeneracy conditions and a special numerical algorithm
PBW Bases, Non–Degeneracy Conditions and Applications
 Proceedings of the ICRA X conference. Volume 45., AMS. Fields Institute Communications
, 2005
"... Abstract. We establish an explicit criteria (the vanishing of non–degeneracy conditions) for certain noncommutative algebras to have Poincaré–Birkhoff– Witt basis. We study theoretical properties of such G–algebras, concluding they are in some sense ”close to commutative”. We use the non–degenerac ..."
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Cited by 6 (3 self)
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Abstract. We establish an explicit criteria (the vanishing of non–degeneracy conditions) for certain noncommutative algebras to have Poincaré–Birkhoff– Witt basis. We study theoretical properties of such G–algebras, concluding they are in some sense ”close to commutative”. We use the non–degeneracy
Nondegeneracy of Pollard Rho Collisions
, 2008
"... The Pollard ρ algorithm is a widely used algorithm for solving discrete logarithms on general cyclic groups, including elliptic curves. Recently the first nontrivial runtime estimates were provided for it, culminating in a sharp O ( √ n) bound for the collision time on a cyclic group of order n [4] ..."
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Cited by 2 (0 self)
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]. In this paper we show that for n satisfying a mild arithmetic condition, the collisions guaranteed by these results are nondegenerate with high probability: that is, the Pollard ρ algorithm successfully finds the discrete logarithm.
Positive semidefinite matrix completions on chordal graphs and the constraint nondegeneracy in semidefinite programming
, 2008
"... LetG = (V,E) be a graph. In matrix completion theory, it is known that the following two conditions are equivalent: (i) G is a chordal graph; (ii) Every Gpartial positive semidefinite matrix has a positive semidefinite matrix completion. In this paper, we relate these two conditions to constraint n ..."
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nondegeneracy condition in semidefinite programming and prove that they are each equivalent to (iii) For any Gpartial positive definite matrix that has a positive semidefinite completion, constraint nondegeneracy is satisfied at each of its positive semidefinite matrix completions.
Constraint nondegeneracy, strong regularity, and nonsingularity in semidefinite programming
 SIAM Journal on optimization
, 2009
"... Abstract It is known that the KarushKuhnTucker (KKT) conditions of semidefinite programming can be reformulated as a nonsmooth system via the metric projector over the cone of symmetric and positive semidefinite matrices. We show in this paper that the primal and dual constraint nondegeneracies, ..."
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Cited by 18 (6 self)
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Abstract It is known that the KarushKuhnTucker (KKT) conditions of semidefinite programming can be reformulated as a nonsmooth system via the metric projector over the cone of symmetric and positive semidefinite matrices. We show in this paper that the primal and dual constraint nondegeneracies
Remarks On Nondegeneracy In Mixed SemidefiniteQuadratic Programming
, 1998
"... We consider the definitions of nondegeneracy and strict complementarity given in [5] for semidefinite programming (SDP) and their obvious extensions to mixed semidefinitequadratic programming (SDQP). We show that a solution to SDQP satisfies strict complementarity and primal and dual nondegeneracy ..."
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Cited by 2 (0 self)
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nondegeneracy if and only if the Jacobian of the Newton system determined by the optimality conditions is nonsingular at the solution.
Results 1  10
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302