Volume 21, Issue 5
Composite-Step Like Filter Methods for Equality Constraint Problems

J. Comp. Math., 21 (2003), pp. 613-624.

Published online: 2003-10

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• Abstract

In a composite-step approach, a step $s_k$ is computed as the sum of two components $v_k$ and $h_k$. The normal component $v_k$, which is called the vertical step, aims to improve the linearized feasibility, while the tangential compoent $h_k$, which is also called horizontal step, concentrates on reducing a model of the merit functions. As a filter method, it reduces both the infeasibility and the objective function. This is the same property of these two methods. In this paper, one concerns the composite-step like filter approach. That is, a step is tangential component $h_k$ if the infeasibility is reduced. Or else, $s_k$ is a composite step composed of normal component $v_k$ and tangential component $h_k$.

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@Article{JCM-21-613, author = {Nie , Pu-Yan}, title = {Composite-Step Like Filter Methods for Equality Constraint Problems}, journal = {Journal of Computational Mathematics}, year = {2003}, volume = {21}, number = {5}, pages = {613--624}, abstract = {

In a composite-step approach, a step $s_k$ is computed as the sum of two components $v_k$ and $h_k$. The normal component $v_k$, which is called the vertical step, aims to improve the linearized feasibility, while the tangential compoent $h_k$, which is also called horizontal step, concentrates on reducing a model of the merit functions. As a filter method, it reduces both the infeasibility and the objective function. This is the same property of these two methods. In this paper, one concerns the composite-step like filter approach. That is, a step is tangential component $h_k$ if the infeasibility is reduced. Or else, $s_k$ is a composite step composed of normal component $v_k$ and tangential component $h_k$.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/10240.html} }
TY - JOUR T1 - Composite-Step Like Filter Methods for Equality Constraint Problems AU - Nie , Pu-Yan JO - Journal of Computational Mathematics VL - 5 SP - 613 EP - 624 PY - 2003 DA - 2003/10 SN - 21 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/10240.html KW - Composite-step like approaches, Filter methods, Equality constraints, Sequential quadratic programming(SQP) algorithms, Tangential component, Convergence. AB -

In a composite-step approach, a step $s_k$ is computed as the sum of two components $v_k$ and $h_k$. The normal component $v_k$, which is called the vertical step, aims to improve the linearized feasibility, while the tangential compoent $h_k$, which is also called horizontal step, concentrates on reducing a model of the merit functions. As a filter method, it reduces both the infeasibility and the objective function. This is the same property of these two methods. In this paper, one concerns the composite-step like filter approach. That is, a step is tangential component $h_k$ if the infeasibility is reduced. Or else, $s_k$ is a composite step composed of normal component $v_k$ and tangential component $h_k$.

Pu-Yan Nie. (1970). Composite-Step Like Filter Methods for Equality Constraint Problems. Journal of Computational Mathematics. 21 (5). 613-624. doi:
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