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Local zeta functions for curves, nondegeneracy conditions and Newton polygons
 Trans. Amer. Math. Soc
"... Abstract. This paper is dedicated to the description of the poles of the Igusa local zeta functions Z(s, f, v) when f(x, y) satisfies a new non degeneracy condition, that we have called arithmetic non degeneracy. More precisely, we attach to each polynomial f(x, y), a collection of convex sets ΓA {} ..."
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Cited by 6 (4 self)
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Abstract. This paper is dedicated to the description of the poles of the Igusa local zeta functions Z(s, f, v) when f(x, y) satisfies a new non degeneracy condition, that we have called arithmetic non degeneracy. More precisely, we attach to each polynomial f(x, y), a collection of convex sets ΓA
Nondegeneracy Concepts for Zeros of Piecewise Smooth Functions
, 1996
"... A zero of a piecewise smooth function f is said to be nondegenerate if the function is Fr'echet differentiable at that point. Using this concept, we describe the usual nondegeneracy notions in the settings of nonlinear (vertical, horizontal, mixed) complementarity problems and the variational i ..."
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Cited by 1 (0 self)
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A zero of a piecewise smooth function f is said to be nondegenerate if the function is Fr'echet differentiable at that point. Using this concept, we describe the usual nondegeneracy notions in the settings of nonlinear (vertical, horizontal, mixed) complementarity problems and the variational
Improvements to Platt’s SMO Algorithm for SVM Classifier Design
, 2001
"... This article points out an important source of inefficiency in Platt’s sequential minimal optimization (SMO) algorithm that is caused by the use of a single threshold value. Using clues from the KKT conditions for the dual problem, two threshold parameters are employed to derive modifications of SMO ..."
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Cited by 271 (11 self)
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This article points out an important source of inefficiency in Platt’s sequential minimal optimization (SMO) algorithm that is caused by the use of a single threshold value. Using clues from the KKT conditions for the dual problem, two threshold parameters are employed to derive modifications
Dual methods for nonconvex spectrum optimization of multicarrier systems
 IEEE TRANS. COMMUN
, 2006
"... The design and optimization of multicarrier communications systems often involve a maximization of the total throughput subject to system resource constraints. The optimization problem is numerically difficult to solve when the problem does not have a convexity structure. This paper makes progress ..."
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Cited by 202 (7 self)
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toward solving optimization problems of this type by showing that under a certain condition called the timesharing condition, the duality gap of the optimization problem is always zero, regardless of the convexity of the objective function. Further, we show that the timesharing condition is satisfied
Nondegeneracy of the discriminant
, 2014
"... To Professor Arkadiusz P loski on his 65th birthday Let (`, f): (C2, 0) − → (C2, 0) be the germ of a holomorphic mapping such that ` = 0 is a smooth curve and f = 0 has an isolated singularity at 0 ∈ C2. We assume that ` = 0 is not a branch of f = 0. The direct image of the critical locus of this ..."
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To Professor Arkadiusz P loski on his 65th birthday Let (`, f): (C2, 0) − → (C2, 0) be the germ of a holomorphic mapping such that ` = 0 is a smooth curve and f = 0 has an isolated singularity at 0 ∈ C2. We assume that ` = 0 is not a branch of f = 0. The direct image of the critical locus of this mapping is called the discriminant curve. In this paper we study the pairs (`, f) for which the discriminant curve is nondegenerate in the Kouchnirenko sense. 1
1Nondegeneracy and Inexactness of Semidefinite Relaxations of Optimal Power Flow
"... Abstract—The Optimal Power Flow (OPF) problem can be reformulated as a nonconvex Quadratically Constrained Quadratic Program (QCQP). There is a growing body of work on the use of semidefinite programming relaxations to solve OPF. The relaxation is exact if and only if the corresponding optimal solu ..."
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solution set contains a rankone matrix. In this paper, we establish sufficient conditions guaranteeing the nonexistence of a rankone matrix in said optimal solution set. In particular, we show that under mild assumptions on problem nondegeneracy, any optimal solution to the semidefinite relaxation
Characterizing the capacity region in multiradio multichannel wireless mesh networks
 in ACM MobiCom
, 2005
"... Next generation fixed wireless broadband networks are being increasingly deployed as mesh networks in order to provide and extend access to the internet. These networks are characterized by the use of multiple orthogonal channels and nodes with the ability to simultaneously communicate with many nei ..."
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Cited by 244 (0 self)
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network model that captures the key practical aspects of such systems and characterize the constraints binding their behavior. We provide necessary conditions to verify the feasibility of rate vectors in these networks, and use them to derive upper bounds on the capacity in terms of achievable throughput
On Removing Nondegeneracy Assumptions in Computational Geometry (Extended Abstract)
, 1997
"... ) Francisco G'omez 1 , Suneeta Ramaswami 2 and Godfried Toussaint 2 1 Dept. of Applied Mathematics, Universidad Politecnica de Madrid, Madrid, Spain 2 School of Computer Science, McGill University, Montr'eal, Qu'ebec, Canada Abstract Existing methods for removing degeneracies ..."
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Cited by 9 (7 self)
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address an alternative approach that has received little attention in the computational geometry literature. Often a typical computational geometry paper will make a nondegeneracy assumption that can in fact be removed (without perturbing the input) by a global rigid transformation of the input
Results 11  20
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608,548