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Volume 23, Issue 2
Singly Diagonally Implicit Runge-Kutta Methods Combining Line Search Techniques for Unconstrained Optimization

Xin-Long Luo

J. Comp. Math., 23 (2005), pp. 153-164.

Published online: 2005-04

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  • Abstract

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.

  • Keywords

Global convergence, Superlinear convergence, Runge-Kutta method, Unconstrained optimization.

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COPYRIGHT: © Global Science Press

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@Article{JCM-23-153, author = {Xin-Long Luo}, title = {Singly Diagonally Implicit Runge-Kutta Methods Combining Line Search Techniques for Unconstrained Optimization}, journal = {Journal of Computational Mathematics}, year = {2005}, volume = {23}, number = {2}, pages = {153--164}, abstract = {

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.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8803.html} }
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 -

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.

Xin-Long Luo. (2005). Singly Diagonally Implicit Runge-Kutta Methods Combining Line Search Techniques for Unconstrained Optimization. Journal of Computational Mathematics. 23 (2). 153-164. doi:
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