Volume 32, Issue 1
A New Generalized FB Complementarity Function for Symmetric Cone Complementarity Problems

Commun. Math. Res., 32 (2016), pp. 39-46.

Published online: 2021-03

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• Abstract

We establish that the generalized Fischer-Burmeister (FB) function and penalized Generalized Fischer-Burmeister (FB) function defined on symmetric cones are complementarity functions (C-functions), in terms of Euclidean Jordan algebras, and the Generalized Fischer-Burmeister complementarity function for the symmetric cone complementarity problem (SCCP). It provides an affirmative answer to the open question by Kum and Lim (Kum S H, Lim Y. Penalized complementarity functions on symmetric cones. $J$. $Glob$. $Optim$.. 2010, 46: 475–485) for any positive integer.

• Keywords

complementarity problem, complementarity function, symmetric cone, generalized Fischer-Burmeister function.

90C33

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@Article{CMR-32-39, author = {Zhang , Yunsheng and Gao , Leifu}, title = {A New Generalized FB Complementarity Function for Symmetric Cone Complementarity Problems}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {32}, number = {1}, pages = {39--46}, abstract = {

We establish that the generalized Fischer-Burmeister (FB) function and penalized Generalized Fischer-Burmeister (FB) function defined on symmetric cones are complementarity functions (C-functions), in terms of Euclidean Jordan algebras, and the Generalized Fischer-Burmeister complementarity function for the symmetric cone complementarity problem (SCCP). It provides an affirmative answer to the open question by Kum and Lim (Kum S H, Lim Y. Penalized complementarity functions on symmetric cones. $J$. $Glob$. $Optim$.. 2010, 46: 475–485) for any positive integer.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2016.01.02}, url = {http://global-sci.org/intro/article_detail/cmr/18661.html} }
TY - JOUR T1 - A New Generalized FB Complementarity Function for Symmetric Cone Complementarity Problems AU - Zhang , Yunsheng AU - Gao , Leifu JO - Communications in Mathematical Research VL - 1 SP - 39 EP - 46 PY - 2021 DA - 2021/03 SN - 32 DO - http://doi.org/10.13447/j.1674-5647.2016.01.02 UR - https://global-sci.org/intro/article_detail/cmr/18661.html KW - complementarity problem, complementarity function, symmetric cone, generalized Fischer-Burmeister function. AB -

We establish that the generalized Fischer-Burmeister (FB) function and penalized Generalized Fischer-Burmeister (FB) function defined on symmetric cones are complementarity functions (C-functions), in terms of Euclidean Jordan algebras, and the Generalized Fischer-Burmeister complementarity function for the symmetric cone complementarity problem (SCCP). It provides an affirmative answer to the open question by Kum and Lim (Kum S H, Lim Y. Penalized complementarity functions on symmetric cones. $J$. $Glob$. $Optim$.. 2010, 46: 475–485) for any positive integer.

Yunsheng Zhang & Leifu Gao. (2021). A New Generalized FB Complementarity Function for Symmetric Cone Complementarity Problems. Communications in Mathematical Research . 32 (1). 39-46. doi:10.13447/j.1674-5647.2016.01.02
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