Variable metric methods for unconstrained optimization and nonlinear least squares

[摘要] Variable metric or quasi-Newton methods are well known and commonly used in connection with unconstrained optimization, since they have good theoretical and practical convergence properties. Although these methods were originally developed for small- and moderate-size dense problems, their modifications based either on sparse, partitioned or limited-memory updates are very efficient on large-scale sparse problems. Very significant applications of these methods also appear in nonlinear least-squares approximation and nonsmooth optimization. In this contribution, we give an extensive review of variable metric methods and their use in various optimization fields. (C) 2000 Elsevier Science B.V. All rights reserved.

[发布日期] 2000-12-01

[关键词] quasi-Newton methods;variable metric methods;unconstrained optimization;nonlinear least squares;sparse problems;partially separable problems;limited-memory methods