Combining trust-region techniques and rosenbrock methods to compute stationary points

X. L. Luo, C. T. Kelley, Lizhi LIAO*, Hon Wah TAM

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)

Abstract

Rosenbrock methods are popular for solving a stiff initial-value problem of ordinary differential equations. One advantage is that there is no need to solve a nonlinear equation at every iteration, as compared with other implicit methods such as backward difference formulas or implicit Runge-Kutta methods. In this article, we introduce a trust-region technique to select the time steps of a second-order Rosenbrock method for a special initial-value problem, namely, a gradient system obtained from an unconstrained optimization problem. The technique is different from the local error approach. Both local and global convergence properties of the new method for solving an equilibrium point of the gradient system are addressed. Finally, some promising numerical results are also presented.

Original languageEnglish
Pages (from-to)265-286
Number of pages22
JournalJournal of Optimization Theory and Applications
Volume140
Issue number2
DOIs
Publication statusPublished - Feb 2009

Scopus Subject Areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

User-Defined Keywords

  • Gradient system
  • Ordinary differential equations
  • Rosenbrock method
  • Trust-region methods
  • Unconstrained optimization

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