论文信息 - Quasi-Newton updates with bounds

Quasi-Newton updates with bounds

We develop a quasi-Newton method which preserves known bounds on the Jacobian matrix. We show that this update can be computed with the same amount of work as competitive methods. In particular, we prove that the number of operations required to obtain this update is proportional to the number of nonzeros in the sparsity pattern of the Jacobian matrix. The method is also shown to share the local convergence properties of Broyden’s and Schubert’s method.

J. J. Moré | P. Calamai

[1] C. G. Broyden. A Class of Methods for Solving Nonlinear Simultaneous Equations , 1965 .

[2] Lenhart K. Schubert. Modification of a quasi-Newton method for nonlinear equations with a sparse Jacobian , 1970 .

[3] M. Powell. A New Algorithm for Unconstrained Optimization , 1970 .

[4] Alfred V. Aho,et al. The Design and Analysis of Computer Algorithms , 1974 .

[5] J. J. Moré,et al. Quasi-Newton Methods, Motivation and Theory , 1974 .

[6] J. J. Moré,et al. On the Global Convergence of Broyden''s Method , 1974 .

[7] Arnold Schönhage,et al. Finding the Median , 1976, J. Comput. Syst. Sci..

[8] P. Toint. On sparse and symmetric matrix updating subject to a linear equation , 1977 .

[9] B. Lam. On the convergence of a quasi-Newton method for sparse nonlinear systems , 1978 .

[10] J. H. Avila,et al. Update Methods for Highly Structured Systems of Nonlinear Equations , 1979 .

[11] H. Walker,et al. Convergence Theorems for Least-Change Secant Update Methods, , 1981 .

[12] John E. Dennis,et al. Numerical methods for unconstrained optimization and nonlinear equations , 1983, Prentice Hall series in computational mathematics.

[13] S. Grzegórski. Orthogonal Projections on Convex Sets for Newton-Like Methods , 1985 .