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

Ping-Qi Pan

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

Published online: 1992-10

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  • 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.

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@Article{JCM-10-77, author = {Pan , Ping-Qi}, 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 AU - Pan , Ping-Qi JO - Journal of Computational Mathematics VL - 1 SP - 77 EP - 92 PY - 1992 DA - 1992/10 SN - 10 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/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.

Pan , Ping-Qi. (1992). New ODE Methods for Equality Constrained Optimization (1) — Equations. Journal of Computational Mathematics. 10 (1). 77-92. doi:
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