TY - JOUR
T1 - Solution properties and error bounds for semi-infinite complementarity problems
AU - Zhou, Jinchuan
AU - Xiu, Naihua
AU - Chen, Jein Shan
PY - 2013
Y1 - 2013
N2 - In this paper, we deal with the semi-infinite complementarity problems (SICP), in which several important issues are covered, such as solvability, semismoothness of residual functions, and error bounds. In particular, we characterize the solution set by investigating the relationship between SICP and the classical complementarity problem. Furthermore, we show that the SICP can be equivalently reformulated as a typical semi-infinite min-max programming problem by employing NCP functions. Finally, we study the concept of error bounds and introduce its two variants, ε-error bounds and weak error bounds, where the concept of weak error bounds is highly desirable in that the solution set is not restricted to be nonempty.
AB - In this paper, we deal with the semi-infinite complementarity problems (SICP), in which several important issues are covered, such as solvability, semismoothness of residual functions, and error bounds. In particular, we characterize the solution set by investigating the relationship between SICP and the classical complementarity problem. Furthermore, we show that the SICP can be equivalently reformulated as a typical semi-infinite min-max programming problem by employing NCP functions. Finally, we study the concept of error bounds and introduce its two variants, ε-error bounds and weak error bounds, where the concept of weak error bounds is highly desirable in that the solution set is not restricted to be nonempty.
KW - Error bounds
KW - Semi-infinite complementarity problem
KW - Semidifferentiable and semis-mooth
KW - Weak error bounds
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U2 - 10.3934/jimo.2013.9.99
DO - 10.3934/jimo.2013.9.99
M3 - Article
AN - SCOPUS:84874915240
SN - 1547-5816
VL - 9
SP - 99
EP - 115
JO - Journal of Industrial and Management Optimization
JF - Journal of Industrial and Management Optimization
IS - 1
ER -