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Title: Smoothing functions and algorithm for nonsymmetric circular cone complementarity problems (English)
Author: Tang, Jingyong
Author: Chen, Yuefen
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 67
Issue: 2
Year: 2022
Pages: 209-231
Summary lang: English
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Category: math
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Summary: There has been much interest in studying symmetric cone complementarity problems. In this paper, we study the circular cone complementarity problem (denoted by CCCP) which is a type of nonsymmetric cone complementarity problem. We first construct two smoothing functions for the CCCP and show that they are all coercive and strong semismooth. Then we propose a smoothing algorithm to solve the CCCP. The proposed algorithm generates an infinite sequence such that the value of the merit function converges to zero. Moreover, we show that the iteration sequence must be bounded if the solution set of the CCCP is nonempty and bounded. At last, we prove that the proposed algorithm has local superlinear or quadratical convergence under some assumptions which are much weaker than Jacobian nonsingularity assumption. Some numerical results are reported which demonstrate that our algorithm is very effective for solving CCCPs. (English)
Keyword: circular cone complementarity problem
Keyword: smoothing function
Keyword: smoothing algorithm
Keyword: superlinear/quadratical convergence
MSC: 65K05
MSC: 65K15
MSC: 90C25
MSC: 90C30
MSC: 90C33
idZBL: Zbl 07511502
idMR: MR4396685
DOI: 10.21136/AM.2021.0129-20
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Date available: 2022-03-25T08:23:13Z
Last updated: 2024-05-06
Stable URL: http://hdl.handle.net/10338.dmlcz/149567
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