Geometric views of the generalized Fischer-Burmeister function and its induced merit function

Huai Yin Tsai; Jein Shan Chen

doi:10.1016/j.amc.2014.03.089

Geometric views of the generalized Fischer-Burmeister function and its induced merit function

Huai Yin Tsai, Jein Shan Chen^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

In this paper, we study geometric properties of surfaces of the generalized Fischer-Burmeister function and its induced merit function. Then, a visualization is proposed to explain how the convergent behaviors are influenced by two descent directions in merit function approach. Based on the geometric properties and visualization, we have more intuitive ideas about how the convergent behavior is affected by changing parameter. Furthermore, geometric view indicates how to improve the algorithm to achieve our goal by setting proper value of the parameter in merit function approach.

Original language	English
Pages (from-to)	31-59
Number of pages	29
Journal	Applied Mathematics and Computation
Volume	237
DOIs	https://doi.org/10.1016/j.amc.2014.03.089
Publication status	Published - 2014 Jun 15

Keywords

Curvature
Level curve
Merit function
NCP-function
Surface

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2014.03.089

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abstract = "In this paper, we study geometric properties of surfaces of the generalized Fischer-Burmeister function and its induced merit function. Then, a visualization is proposed to explain how the convergent behaviors are influenced by two descent directions in merit function approach. Based on the geometric properties and visualization, we have more intuitive ideas about how the convergent behavior is affected by changing parameter. Furthermore, geometric view indicates how to improve the algorithm to achieve our goal by setting proper value of the parameter in merit function approach.",

keywords = "Curvature, Level curve, Merit function, NCP-function, Surface",

author = "Tsai, {Huai Yin} and Chen, {Jein Shan}",

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language = "English",

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journal = "Applied Mathematics and Computation",

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N2 - In this paper, we study geometric properties of surfaces of the generalized Fischer-Burmeister function and its induced merit function. Then, a visualization is proposed to explain how the convergent behaviors are influenced by two descent directions in merit function approach. Based on the geometric properties and visualization, we have more intuitive ideas about how the convergent behavior is affected by changing parameter. Furthermore, geometric view indicates how to improve the algorithm to achieve our goal by setting proper value of the parameter in merit function approach.

AB - In this paper, we study geometric properties of surfaces of the generalized Fischer-Burmeister function and its induced merit function. Then, a visualization is proposed to explain how the convergent behaviors are influenced by two descent directions in merit function approach. Based on the geometric properties and visualization, we have more intuitive ideas about how the convergent behavior is affected by changing parameter. Furthermore, geometric view indicates how to improve the algorithm to achieve our goal by setting proper value of the parameter in merit function approach.

KW - Curvature

KW - Level curve

KW - Merit function

KW - NCP-function

KW - Surface

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SP - 31

EP - 59

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

Geometric views of the generalized Fischer-Burmeister function and its induced merit function

Abstract

Keywords

ASJC Scopus subject areas

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