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163
Preconditioning KKT Systems
, 2002
"... This research presents new preconditioners for linear systems. We proceed from the most general case to the very specific problem area of sparse optimal control. In the first most general approach, we assume only that the coefficient matrix is nonsingular. We target highly indefinite, nonsymmetric p ..."
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Cited by 16 (0 self)
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sparse matrices. Our numerical experiments indicate that the reliability and performance of preconditioned iterative solvers are greatly enhanced by such preprocessing. Secondly, we present two new preconditioners for KKT systems. KKT systems arise in areas such as quadratic programming, sparse optimal
Techniques For Solving General KKT Systems
, 2000
"... We consider techniques for solving general KKT systems. In particular, we address the situation of a singular (1,1) block, and focus on ways to eliminate the singularity, either by reducing the system size or by employing an augmented Lagrangian technique. The latter is a parameterdependent approac ..."
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Cited by 4 (2 self)
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We consider techniques for solving general KKT systems. In particular, we address the situation of a singular (1,1) block, and focus on ways to eliminate the singularity, either by reducing the system size or by employing an augmented Lagrangian technique. The latter is a parameter
KKT systems in operative planning for gas distribution networks
 PROC. APPL. MATH. MECH
, 2004
"... Operative planning in gas networks with prescribed binary decisions yields large scale nonlinear programs defined on graphs. We study the structure of the KKT systems arising in interior methods and present a customized direct solution algorithm. Computational results indicate that the algorithm is ..."
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Cited by 3 (2 self)
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Operative planning in gas networks with prescribed binary decisions yields large scale nonlinear programs defined on graphs. We study the structure of the KKT systems arising in interior methods and present a customized direct solution algorithm. Computational results indicate that the algorithm
An LPNewton Method: . . . KKT Systems, and Nonisolated Solutions
, 2011
"... We define a new Newtontype method for the solution of constrained systems of equations and analyze in detail its properties. Under suitable conditions, that do not include differentiability or local uniqueness of solutions, the method converges locally quadratically to a solution of the system of ..."
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of equations, thus filling an important gap in the existing theory. The new algorithm improves on known methods and, when particularized to KKT systems deriving from optimality conditions for constrained optimization or variational inequalities, it has theoretical advantages even over methods specifically
New preconditioners for KKT systems of network flow problems
 SIAM Journal on Optimization
"... Abstract. We propose a new set of preconditioners for the iterative solution, via a preconditioned conjugate gradient (PCG) method, of the KKT systems that must be solved at each iteration of an interior point (IP) algorithm for the solution of linear min cost flow (MCF) problems. These precondition ..."
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Cited by 12 (5 self)
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Abstract. We propose a new set of preconditioners for the iterative solution, via a preconditioned conjugate gradient (PCG) method, of the KKT systems that must be solved at each iteration of an interior point (IP) algorithm for the solution of linear min cost flow (MCF) problems
On the Stability of NullSpace Methods for KKT Systems
 SIAM J. Matrix Anal. Appl
, 1997
"... This paper considers the numerical stability of nullspace methods for KKT systems, particularly in the context of quadratic programming. The methods we consider are based on the direct elimination of variables which is attractive for solving large sparse systems. Illconditioning in a certain su ..."
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This paper considers the numerical stability of nullspace methods for KKT systems, particularly in the context of quadratic programming. The methods we consider are based on the direct elimination of variables which is attractive for solving large sparse systems. Illconditioning in a certain
Solving reduced KKT systems in barrier methods for linear and quadratic programming
, 1991
"... In barrier methods for constrained optimization, the main work lies in solving large linear systems Kp = r, where K is symmetric and indefinite. For linear programs, these KKT systems are usually reduced to smaller positivedefinite systems AH−1ATq = s, where H is a large principal submatrix of K. ..."
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Cited by 27 (8 self)
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In barrier methods for constrained optimization, the main work lies in solving large linear systems Kp = r, where K is symmetric and indefinite. For linear programs, these KKT systems are usually reduced to smaller positivedefinite systems AH−1ATq = s, where H is a large principal submatrix of K
APPROXIMATE NULLSPACE ITERATIONS FOR KKT SYSTEMS IN MODEL BASED OPTIMIZATION
, 2006
"... The aim of the paper is to provide some theoretical basis for approximate reduced SQP methods in contrast to inexact reduced SQP methods, i.e., here the forward and the adjoint problem accuracies are not increased when zooming in to the solution of an optimization problem. Only linearquadratic pr ..."
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Cited by 1 (0 self)
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quadratic problems are treated, where approximate reduced SQP methods can be viewed as nullspace iterations for KKT systems. We give theoretical convergence results and show that certain numerical examples possess convergence properties, even if they do not satisfy the assumptions for the convergence theorems.
REGULARIZATION AND PRECONDITIONING OF KKT SYSTEMS ARISING IN NONNEGATIVE LEASTSQUARES PROBLEMS
"... Abstract. A regularized Newtonlike method for solving nonnegative leastsquares problems is proposed and analysed in this paper. A preconditioner for KKT systems arising in the method is introduced and spectral properties of the preconditioned matrix are analysed. A bound on the condition number of ..."
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Abstract. A regularized Newtonlike method for solving nonnegative leastsquares problems is proposed and analysed in this paper. A preconditioner for KKT systems arising in the method is introduced and spectral properties of the preconditioned matrix are analysed. A bound on the condition number
Results 1  10
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163