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Bound Constrained Quadratic Programming Via Piecewise Quadratic Functions
 Mathematical Programming
, 1999
"... . We consider the strictly convex quadratic programming problem with bounded variables. A dual problem is derived using Lagrange duality. The dual problem is the minimization of an unconstrained, piecewise quadratic function. It involves a lower bound of 1 , the smallest eigenvalue of a symmetric, ..."
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and comparison with other methods for constrained QP are given. Key words. Bound constrained quadratic programming. Huber's Mestimator. Condition estimation. Newton iteration. Factorization update. 1. Introduction The purpose of the present paper is to describe a finite, dual Newton algorithm
An ADMM algorithm for solving a proximal boundconstrained quadratic program
, 2014
"... We consider a proximal operator given by a quadratic function subject to bound constraints and give an optimization algorithm using the alternating direction method of multipliers (ADMM). The algorithm is particularly efficient to solve a collection of proximal operators that share the same quadrati ..."
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We consider a proximal operator given by a quadratic function subject to bound constraints and give an optimization algorithm using the alternating direction method of multipliers (ADMM). The algorithm is particularly efficient to solve a collection of proximal operators that share the same
A New Finite Continuation Algorithm for Bound Constrained Quadratic Programming
 SIAM J. on Optimization
, 1995
"... Abstract. The dual of the strictly convex quadratic programming problem with unit bounds is posed as a linear `1 minimization problem with quadratic terms. A smooth approximation to the linear `1 function is used to obtain a parametric family of piecewisequadratic approximation problems. The unique ..."
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Cited by 2 (1 self)
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Abstract. The dual of the strictly convex quadratic programming problem with unit bounds is posed as a linear `1 minimization problem with quadratic terms. A smooth approximation to the linear `1 function is used to obtain a parametric family of piecewisequadratic approximation problems
ON THE DECREASE OF A QUADRATIC FUNCTION ALONG THE PROJECTEDGRADIENT PATH ∗
"... Abstract. The Euclidean gradient projection is an efficient tool for the expansion of an active set in the activesetbased algorithms for the solution of boundconstrained quadratic programming problems. In this paper we examine the decrease of the convex cost function along the projectedgradient p ..."
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Cited by 1 (0 self)
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Abstract. The Euclidean gradient projection is an efficient tool for the expansion of an active set in the activesetbased algorithms for the solution of boundconstrained quadratic programming problems. In this paper we examine the decrease of the convex cost function along the projected
Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems
 IEEE Journal of Selected Topics in Signal Processing
, 2007
"... Abstract—Many problems in signal processing and statistical inference involve finding sparse solutions to underdetermined, or illconditioned, linear systems of equations. A standard approach consists in minimizing an objective function which includes a quadratic (squared ℓ2) error term combined wi ..."
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Cited by 524 (15 self)
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with a sparsenessinducing (ℓ1) regularization term.Basis pursuit, the least absolute shrinkage and selection operator (LASSO), waveletbased deconvolution, and compressed sensing are a few wellknown examples of this approach. This paper proposes gradient projection (GP) algorithms for the boundconstrained
Subspace accelerated matrix splitting algorithms for boundconstrained quadratic programming and linear complementarity problems
, 2011
"... Abstract. This paper studies the solution of two problems—boundconstrained quadratic programs and linear complementarity problems—by twophase methods that consist of an active set prediction phase and a subspace phase. The algorithms enjoy favorable convergence properties under weaker assumptions ..."
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Cited by 4 (3 self)
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Abstract. This paper studies the solution of two problems—boundconstrained quadratic programs and linear complementarity problems—by twophase methods that consist of an active set prediction phase and a subspace phase. The algorithms enjoy favorable convergence properties under weaker assumptions
A Limited Memory Algorithm for Bound Constrained Optimization
 SIAM Journal on Scientific Computing
, 1994
"... An algorithm for solving large nonlinear optimization problems with simple bounds is described. ..."
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Cited by 557 (9 self)
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An algorithm for solving large nonlinear optimization problems with simple bounds is described.
Benchmarking of boundconstrained optimization software
, 2007
"... In this report we describe a comparison of different algorithms for solving nonlinear optimization problems with simple bounds on the variables. Moreover, we would like to come out with an assessment of the optimization library DOT used in the optimization suite OPTALIA at Airbus for this kind of pr ..."
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In this report we describe a comparison of different algorithms for solving nonlinear optimization problems with simple bounds on the variables. Moreover, we would like to come out with an assessment of the optimization library DOT used in the optimization suite OPTALIA at Airbus for this kind
Learning the Kernel Matrix with SemiDefinite Programming
, 2002
"... Kernelbased learning algorithms work by embedding the data into a Euclidean space, and then searching for linear relations among the embedded data points. The embedding is performed implicitly, by specifying the inner products between each pair of points in the embedding space. This information ..."
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Cited by 780 (22 self)
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problems in machine learning. In this paper we show how the kernel matrix can be learned from data via semidefinite programming (SDP) techniques. When applied
Results 1  10
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505,073