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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
Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems
 IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING
, 2007
"... 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 with a spa ..."
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Cited by 539 (17 self)
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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
ON THE DECREASE OF A QUADRATIC FUNCTION ALONG THE PROJECTEDGRADIENT PATH
, 2008
"... 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 path and e ..."
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Cited by 1 (1 self)
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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 path
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 2 (1 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
Interiorpoint Methods
, 2000
"... The modern era of interiorpoint methods dates to 1984, when Karmarkar proposed his algorithm for linear programming. In the years since then, algorithms and software for linear programming have become quite sophisticated, while extensions to more general classes of problems, such as convex quadrati ..."
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Cited by 612 (15 self)
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quadratic programming, semidefinite programming, and nonconvex and nonlinear problems, have reached varying levels of maturity. We review some of the key developments in the area, including comments on both the complexity theory and practical algorithms for linear programming, semidefinite programming
SNOPT: An SQP Algorithm For LargeScale Constrained Optimization
, 2002
"... Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first deriv ..."
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Cited by 597 (24 self)
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Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first
On scalable algorithms for numerical solution of variational inequalities based on FETI and semimonotonic augmented Lagrangians
 Proceedings of the 15th International Conference on Domain Decomposition Methods
, 2004
"... Summary. Theoretical and experimental results concerning a new FETI based algorithm for numerical solution of variational inequalities are reviewed. A discretized model problem is first reduced by the duality theory of convex optimization to the quadratic programming problem with bound and equality ..."
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Cited by 2 (2 self)
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for the solution of bound constrained quadratic programming problems. Recent theoretical results are reported that guarantee scalability of the algorithm. The results are confirmed by numerical experiments. 1
A tutorial on support vector regression
, 2004
"... In this tutorial we give an overview of the basic ideas underlying Support Vector (SV) machines for function estimation. Furthermore, we include a summary of currently used algorithms for training SV machines, covering both the quadratic (or convex) programming part and advanced methods for dealing ..."
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Cited by 865 (3 self)
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In this tutorial we give an overview of the basic ideas underlying Support Vector (SV) machines for function estimation. Furthermore, we include a summary of currently used algorithms for training SV machines, covering both the quadratic (or convex) programming part and advanced methods for dealing
Results 1  10
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4,692