TY - JOUR
T1 - On the existence of saddle points for nonlinear second-order cone programming problems
AU - Zhou, Jinchuan
AU - Chen, Jein Shan
N1 - Funding Information:
The author’s work is supported by National Natural Science Foundation of China (11101248, 11171247, 11271233), Shandong Province Natural Science Foundation (ZR2010AQ026, ZR2012AM016), and Young Teacher Support Program of Shandong University of Technology. Jein-Shan Chen work is supported by Ministry of Science and Technology, Taiwan.
Publisher Copyright:
© 2014, Springer Science+Business Media New York.
PY - 2015/11/6
Y1 - 2015/11/6
N2 - In this paper, we study the existence of local and global saddle points for nonlinear second-order cone programming problems. The existence of local saddle points is developed by using the second-order sufficient conditions, in which a sigma-term is added to reflect the curvature of second-order cone. Furthermore, by dealing with the perturbation of the primal problem, we establish the existence of global saddle points, which can be applicable for the case of multiple optimal solutions. The close relationship between global saddle points and exact penalty representations are discussed as well.
AB - In this paper, we study the existence of local and global saddle points for nonlinear second-order cone programming problems. The existence of local saddle points is developed by using the second-order sufficient conditions, in which a sigma-term is added to reflect the curvature of second-order cone. Furthermore, by dealing with the perturbation of the primal problem, we establish the existence of global saddle points, which can be applicable for the case of multiple optimal solutions. The close relationship between global saddle points and exact penalty representations are discussed as well.
KW - Augmented Lagrangian
KW - Exact penalty representations
KW - Local and global saddle points
KW - Second-order sufficient conditions
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U2 - 10.1007/s10898-014-0252-5
DO - 10.1007/s10898-014-0252-5
M3 - Article
AN - SCOPUS:84930485234
SN - 0925-5001
VL - 62
SP - 459
EP - 480
JO - Journal of Global Optimization
JF - Journal of Global Optimization
IS - 3
ER -