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Minimization of a large-scale quadratic function subject to a spherical constraint. (English) Zbl 0878.65044
An algorithm for solving the large scale trust-region subproblem is proposed that requires a fixed-size limited storage proportional to the order of the quadratic function and relies only upon matrix-vector products. It recasts the problem in terms of a parameterized eigenvalue problem, but only the smallest eigenvalue and corresponding eigenvector needs to be computed using the implicitly restarted Lanczos method.
Reviewer: P.Pan (Nanjing)

65K05 Numerical mathematical programming methods
90C06 Large-scale problems in mathematical programming
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
90C20 Quadratic programming
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