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363,276
Analytic Centers and Repelling Inequalities
 European Journal of Operational Research
, 1999
"... The new concepts of repelling inequalities, repelling paths, and prime analytic centers are introduced. A repelling path is a generalization of the analytic central path for linear programming, and we show that this path has a unique limit. Furthermore, this limit is the prime analytic center if the ..."
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Cited by 6 (4 self)
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The new concepts of repelling inequalities, repelling paths, and prime analytic centers are introduced. A repelling path is a generalization of the analytic central path for linear programming, and we show that this path has a unique limit. Furthermore, this limit is the prime analytic center
An Analytic Center Machine for Regression
, 2002
"... Support vector machines represent a new approach for solving problems in pattern classification and regression analysis. Because of their impressive generalization performance they have attracted much attention in the optimization and machine learning communities. In the version space of hypotheses ..."
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the hypothesis that corresponds to the analytic center of the version space. Preliminary results indicate that a higher level of generalization accuracy can be achieved by this regression estimator.
Abstract Analytic centers and repelling inequalities
, 2000
"... The new concepts of repelling inequalities, repelling paths, and prime analytic centers are introduced. A repelling path is a generalization of the analytic central path for linear programming, and we show that this path has a unique limit. Furthermore, this limit is the prime analytic center if the ..."
Abstract
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The new concepts of repelling inequalities, repelling paths, and prime analytic centers are introduced. A repelling path is a generalization of the analytic central path for linear programming, and we show that this path has a unique limit. Furthermore, this limit is the prime analytic center
Using the analytic center in the feasibility pump Using the analytic center in the feasibility pump
"... Abstract The feasibility pump (FP) has proved to be a successful heuristic for finding feasible solutions of mixed integer linear problems. Briefly, FP alternates between two sequences of points: one of feasible solutions for the relaxed problem, and another of integer points. This short paper exte ..."
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extends FP, such that the integer point is obtained by rounding a point on the (feasible) segment between the computed feasible point and the analytic center for the relaxed linear problem.
Convergence Results of the Analytic Center Estimator
"... The analytic center approach for bounded error parameter estimation was recently proposed as an alternative to the wellknown Chybyshev and least squares estimates. In this paper, we show the asymptotic performance of this approach and prove that the analytic center converges to the true parameter u ..."
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Cited by 3 (0 self)
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The analytic center approach for bounded error parameter estimation was recently proposed as an alternative to the wellknown Chybyshev and least squares estimates. In this paper, we show the asymptotic performance of this approach and prove that the analytic center converges to the true parameter
Using the analytic center in the feasibility pump
, 2010
"... The feasibility pump (FP) [5, 7] has proved to be a successful heuristic for finding feasible solutions of mixed integer linear problems (MILPs). FP was improved in [1] for finding better quality solutions. Briefly, FP alternates between two sequences of points: one of feasible solutions for the rel ..."
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Cited by 2 (0 self)
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, such that the integer point is obtained by rounding a point on the (feasible) segment between the computed feasible point and the analytic center for the relaxed linear problem. Since points in the segment are closer (may be even interior) to the convex hull of integer solutions, it may be expected that the rounded
The Analytic Center Cutting Plane Method with Semidefinite Cuts
 SIAM JOURNAL ON OPTIMIZATION
, 2000
"... We analyze an analytic center cutting plane algorithm for the convex feasibility problems with semidefinite cuts. At each iteration the oracle returns a pdimensional semidefinite cut at an approximate analytic center of the set of localization. The set of localization, which contains the solution s ..."
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Cited by 16 (1 self)
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We analyze an analytic center cutting plane algorithm for the convex feasibility problems with semidefinite cuts. At each iteration the oracle returns a pdimensional semidefinite cut at an approximate analytic center of the set of localization. The set of localization, which contains the solution
The analytic center of LMI's and Riccati equations
, 1999
"... In this paper we derive formulas for constructing the analytic center of the linear matrix inequality defining a positive (parahermitian) transfer function. The Riccati equations that are usually associated with such positive transfer functions, are related to boundary points of the convex set. In ..."
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Cited by 1 (0 self)
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In this paper we derive formulas for constructing the analytic center of the linear matrix inequality defining a positive (parahermitian) transfer function. The Riccati equations that are usually associated with such positive transfer functions, are related to boundary points of the convex set
Multiple Cuts in the Analytic Center Cutting Plane Method
, 1998
"... We analyze the multiple cut generation scheme in the analytic center cutting plane method. We propose an optimal primal and dual updating direction when the cuts are central. The direction is optimal in the sense that it maximizes the product of the new dual slacks and of the new primal variables wi ..."
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Cited by 29 (1 self)
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We analyze the multiple cut generation scheme in the analytic center cutting plane method. We propose an optimal primal and dual updating direction when the cuts are central. The direction is optimal in the sense that it maximizes the product of the new dual slacks and of the new primal variables
Reconstruction and Representation of 3D Objects with Radial Basis Functions
 Computer Graphics (SIGGRAPH ’01 Conf. Proc.), pages 67–76. ACM SIGGRAPH
, 2001
"... We use polyharmonic Radial Basis Functions (RBFs) to reconstruct smooth, manifold surfaces from pointcloud data and to repair incomplete meshes. An object's surface is defined implicitly as the zero set of an RBF fitted to the given surface data. Fast methods for fitting and evaluating RBFs al ..."
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Cited by 505 (1 self)
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allow us to model large data sets, consisting of millions of surface points, by a single RBFpreviously an impossible task. A greedy algorithm in the fitting process reduces the number of RBF centers required to represent a surface and results in significant compression and further computational
Results 1  10
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363,276