TY - JOUR
T1 - Singly Diagonally Implicit Runge-Kutta Methods Combining Line Search Techniques for Unconstrained Optimization
AU - Xin-Long Luo
JO - Journal of Computational Mathematics
VL - 2
SP - 153
EP - 164
PY - 2005
DA - 2005/04
SN - 23
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8803.html
KW - Global convergence, Superlinear convergence, Runge-Kutta method, Unconstrained optimization.
AB - <p style="text-align: justify;">There exists a strong connection between numerical methods for the integration of ordinary differential equations and optimization problems. In this paper, we try to discover further their links. And we transform unconstrained problems to the equivalent ordinary differential equations and construct the LRKOPT method to solve them by combining the second order singly diagonally implicit Runge-Kutta formulas and line search techniques. Moreover, we analyze the global convergence and the local convergence of the LRKOPT method. Promising numerical results are also reported.</p>