Volume 10, Issue 1
New ODE Methods for Equality Constrained Optimization (1)-Equations

Ping-qi Pan

DOI:

J. Comp. Math., 10 (1992), pp. 77-92.

Published online: 1992-10

Preview Full PDF 327 1009
Export citation
  • Abstract

To deal with equality constrained optimization problems (ECP), we introduce in this paper "(ECP)-equation", a class of new systems of ordinary differential equations for (ECP), containing a matrix parameter called (ECP)-direction matrix, which plays a central role in it, and a scalar parameter called (ECP)-rate factor. It is shown that by following the trajectory of the equation, a stationary point or hopefully a local solution can be located under very mild conditions. As examples, several schemes of (ECP)-direction matrices and (ECP)-rate factors are given to construct concrete forms of the (ECP)-equation, including almost all the existing projected gradient type versions as special cases. As will be shown in a subsequent paper where the implementation problems are considered in detail, application of an example of these forms results in encouraging performance in experiments.

  • Keywords

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{JCM-10-77, author = {}, title = {New ODE Methods for Equality Constrained Optimization (1)-Equations}, journal = {Journal of Computational Mathematics}, year = {1992}, volume = {10}, number = {1}, pages = {77--92}, abstract = { To deal with equality constrained optimization problems (ECP), we introduce in this paper "(ECP)-equation", a class of new systems of ordinary differential equations for (ECP), containing a matrix parameter called (ECP)-direction matrix, which plays a central role in it, and a scalar parameter called (ECP)-rate factor. It is shown that by following the trajectory of the equation, a stationary point or hopefully a local solution can be located under very mild conditions. As examples, several schemes of (ECP)-direction matrices and (ECP)-rate factors are given to construct concrete forms of the (ECP)-equation, including almost all the existing projected gradient type versions as special cases. As will be shown in a subsequent paper where the implementation problems are considered in detail, application of an example of these forms results in encouraging performance in experiments. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9342.html} }
TY - JOUR T1 - New ODE Methods for Equality Constrained Optimization (1)-Equations JO - Journal of Computational Mathematics VL - 1 SP - 77 EP - 92 PY - 1992 DA - 1992/10 SN - 10 DO - http://dor.org/ UR - https://global-sci.org/intro/jcm/9342.html KW - AB - To deal with equality constrained optimization problems (ECP), we introduce in this paper "(ECP)-equation", a class of new systems of ordinary differential equations for (ECP), containing a matrix parameter called (ECP)-direction matrix, which plays a central role in it, and a scalar parameter called (ECP)-rate factor. It is shown that by following the trajectory of the equation, a stationary point or hopefully a local solution can be located under very mild conditions. As examples, several schemes of (ECP)-direction matrices and (ECP)-rate factors are given to construct concrete forms of the (ECP)-equation, including almost all the existing projected gradient type versions as special cases. As will be shown in a subsequent paper where the implementation problems are considered in detail, application of an example of these forms results in encouraging performance in experiments.
Ping-qi Pan. (2019). New ODE Methods for Equality Constrained Optimization (1)-Equations. Journal of Computational Mathematics. 10 (1). 77-92. doi:
Copy to clipboard
The citation has been copied to your clipboard