Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
A limited memory algorithm for bound constrained optimization
SIAM Journal on Scientific Computing
Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization
ACM Transactions on Mathematical Software (TOMS)
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
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A new conjugate direction (CD) method is proposed, which is based on an orthogonalization procedure and does not make use of line searches for the conjugate vector set construction. This procedure prevents the set of conjugate vectors from degeneracy and eliminates high sensitivity to computation errors pertinent to methods of CDs, resulting in an efficient algorithm for solving large-scale ill-conditioned minimization problems without preconditioning. The advantages of our algorithms are illustrated by results of the extensive numerical experiments with large-scale quadratic functions.