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On the implementation of an algorithm for largescale equality constrained optimization
 SIAM Journal on Optimization
, 1998
"... Abstract. This paper describes a software implementation of Byrd and Omojokun’s trust region algorithm for solving nonlinear equality constrained optimization problems. The code is designed for the efficient solution of large problems and provides the user with a variety of linear algebra techniques ..."
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Cited by 38 (11 self)
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Abstract. This paper describes a software implementation of Byrd and Omojokun’s trust region algorithm for solving nonlinear equality constrained optimization problems. The code is designed for the efficient solution of large problems and provides the user with a variety of linear algebra techniques for solving the subproblems occurring in the algorithm. Second derivative information can be used, but when it is not available, limited memory quasiNewton approximations are made. The performance of the code is studied using a set of difficult test problems from the CUTE collection.
Incomplete Factorization Preconditioning For Linear Least Squares Problems
, 1994
"... this paper is the modified version of GramSchmidt orthogonalization with a rejection test applied right after the formation of the offdiagonal elements of the factor R. For a given rejection parameter 0 / 1, the rejection test is: if r ij ! /= k a ..."
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Cited by 17 (4 self)
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this paper is the modified version of GramSchmidt orthogonalization with a rejection test applied right after the formation of the offdiagonal elements of the factor R. For a given rejection parameter 0 / 1, the rejection test is: if r ij ! /= k a
Finding Good Column Orderings for Sparse QR Factorization
 In Second SIAM Conference on Sparse Matrices
, 1996
"... For sparse QR factorization, finding a good column ordering of the matrix to be factorized, is essential. Both the amount of fill in the resulting factors, and the number of floatingpoint operations required by the factorization, are highly dependent on this ordering. A suitable column ordering of ..."
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Cited by 17 (0 self)
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For sparse QR factorization, finding a good column ordering of the matrix to be factorized, is essential. Both the amount of fill in the resulting factors, and the number of floatingpoint operations required by the factorization, are highly dependent on this ordering. A suitable column ordering of the matrix A is usually obtained by minimum degree analysis on A T A. The objective of this analysis is to produce low fill in the resulting triangular factor R. We observe that the efficiency of sparse QR factorization is also dependent on other criteria, like the size and the structure of intermediate fill, and the size and the structure of the frontal matrices for the multifrontal method, in addition to the amount of fill in R. An important part of this information is lost when A T A is formed. However, the structural information from A is important to consider in order to find good column orderings. We show how a suitable equivalent reordering of an initial fillreducing ordering can...
The Solution of Augmented Systems
, 1993
"... We examine the solution of sets of linear equations for which the coefficient matrix has the form / H A A T 0 ! where the matrix H is symmetric. We are interested in the case when the matrices H and A are sparse. These augmented systems occur in many application areas, for example in the solu ..."
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Cited by 12 (3 self)
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We examine the solution of sets of linear equations for which the coefficient matrix has the form / H A A T 0 ! where the matrix H is symmetric. We are interested in the case when the matrices H and A are sparse. These augmented systems occur in many application areas, for example in the solution of linear programming problems, structural analysis, magnetostatics, differential algebraic systems, constrained optimization, electrical networks, and computational fluid dynamics. We discuss in some detail how they arise in the last three of these applications and consider particular characteristics and methods of solution. We then concentrate on direct methods of solution. We examine issues related to conditioning and scaling, and discuss the design and performance of a code for solving these systems. Keywords: augmented systems, constrained optimization, Stokes problem, indefinite sparse matrices, KKT systems, systems matrix, equilibrium problems, electrical networks, interior poi...
A Projection Method for the Solution of Rectangular Systems
, 1996
"... We present a general method for the linear leastsquares solution of overdetermined and underdetermined systems. The method is particularly efficient when the coefficient matrix is quasisquare, that is when the number of rows and number of columns is almost the same. The numerical methods proposed ..."
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We present a general method for the linear leastsquares solution of overdetermined and underdetermined systems. The method is particularly efficient when the coefficient matrix is quasisquare, that is when the number of rows and number of columns is almost the same. The numerical methods proposed in the literature for linear leastsquares problems and minimumnorm solutions do not generally take account of this special characteristic. The proposed method is based on an LU factorization of the original quasisquare matrix A, assuming that A has full rank. In the overdetermined case, the LU factors are used to compute a basis for the null space of A T . The righthand side vector b is then projected onto this subspace and the leastsquares solution is obtained from the solution of this reduced problem. In the case of underdetermined systems, the desired solution is again obtained through the solution of a reduced system. The use of this method may lead to important savings in comput...