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primaldual methods
, 2010
"... On distributed optimization under inequality constraints via Lagrangian ..."
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On distributed optimization under inequality constraints via Lagrangian
The primaldual method for approximation algorithms and its application to network design problems.
, 1997
"... Abstract In this survey, we give an overview of a technique used to design and analyze algorithms that provide approximate solutions to N P hard problems in combinatorial optimization. Because of parallels with the primaldual method commonly used in combinatorial optimization, we call it the prim ..."
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Cited by 137 (5 self)
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Abstract In this survey, we give an overview of a technique used to design and analyze algorithms that provide approximate solutions to N P hard problems in combinatorial optimization. Because of parallels with the primaldual method commonly used in combinatorial optimization, we call
A Nonlinear PrimalDual Method For Total VariationBased Image Restoration
, 1995
"... . We present a new method for solving total variation (TV) minimization problems in image restoration. The main idea is to remove some of the singularity caused by the nondifferentiability of the quantity jruj in the definition of the TVnorm before we apply a linearization technique such as Newton ..."
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Cited by 232 (22 self)
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such as Newton's method. This is accomplished by introducing an additional variable for the flux quantity appearing in the gradient of the objective function. Our method can be viewed as a primaldual method as proposed by Conn and Overton [8] and Andersen [3] for the minimization of a sum of Euclidean
Augmented PrimalDual Method Boundary Point Method
"... X, Z symmetric n × n matrices The linear equations A(X) =b read 〈Ai,X 〉 = bi for given symmetric matrices Ai,i=1,...,m. The adjoint map A T is given by A T (y) = ∑ yiAi. We assume that both the primal and the dual problem have strictly feasible points (X, Z ≻ 0), so that strong duality holds, and ..."
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X, Z symmetric n × n matrices The linear equations A(X) =b read 〈Ai,X 〉 = bi for given symmetric matrices Ai,i=1,...,m. The adjoint map A T is given by A T (y) = ∑ yiAi. We assume that both the primal and the dual problem have strictly feasible points (X, Z ≻ 0), so that strong duality holds
PrimalDual Methods for Vertex and Facet Enumeration
 Discrete and Computational Geometry
, 1998
"... Every convex polytope can be represented as the intersection of a finite set of halfspaces and as the convex hull of its vertices. Transforming from the halfspace (respectively vertex) to the vertex (respectively halfspace) representation is called vertex enumeration (respectively facet enumeration) ..."
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Cited by 42 (7 self)
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class of algorithms that take advantage of this phenomenon. Loosely speaking, primaldual ...
Global Convergence of PrimalDual Methods for Nonlinear Programming
, 2008
"... We propose a new globalization strategy for primaldual interiorpoint methods in nonlinear programming that relaxes the requirement of closely following the central path and lends itself to dynamic updates of the barrier parameter. The latter promote better synchonization between the barrier param ..."
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We propose a new globalization strategy for primaldual interiorpoint methods in nonlinear programming that relaxes the requirement of closely following the central path and lends itself to dynamic updates of the barrier parameter. The latter promote better synchonization between the barrier
An augmented primaldual method for linear conic programs
, 2007
"... We propose a new iterative approach for solving linear programs over convex cones. Assuming that Slaters condition is satisfied, the conic problem is transformed to the minimization of a convex differentiable function. This “agumented primaldual function” or “apdfunction” is restricted to an affin ..."
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Cited by 10 (2 self)
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We propose a new iterative approach for solving linear programs over convex cones. Assuming that Slaters condition is satisfied, the conic problem is transformed to the minimization of a convex differentiable function. This “agumented primaldual function” or “apdfunction” is restricted
Column Generation with a PrimalDual Method
, 1997
"... A simple column generation scheme that employs an interior point method to solve underlying restricted master problems is presented. In contrast with the classical column generation approach where restricted master problems are solved exactly, the method presented in this paper consists in solving i ..."
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Cited by 10 (4 self)
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it to a predetermined optimality tolerance (loose at the beginning and appropriately tightened when the optimum is approached). An infeasible primaldual interior point method which employs the notion of ¯center to control the distance to optimality is used to solve the restricted master problem
PrimalDual methods for sparse constrained matrix completion
"... We develop scalable algorithms for regular and nonnegative matrix completion. In particular, we base the methods on tracenorm regularization that induces a low rank predicted matrix. The regularization problem is solved via a constraint generation method that explicitly maintains a sparse dual and ..."
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Cited by 1 (1 self)
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and the corresponding low rank primal solution. We provide a new dual block coordinate descent algorithm for solving the dual problem with a few spectral constraints. Empirical results illustrate the effectiveness of our method in comparison to recently proposed alternatives. 1
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