Constructions of complementarity functions and merit functions for circular cone complementarity problem

In this paper, we consider complementarity problem associated with circular cone, which is a type of nonsymmetric cone complementarity problem. The main purpose of this paper is to show the readers how to construct complementarity functions for such nonsymmetric cone complementarity problem, and pro...

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Bibliographic Details
Published in:Computational optimization and applications 2016-03, Vol.63 (2), p.495-522
Main Authors: Miao, Xin-He, Guo, Shengjuan, Qi, Nuo, Chen, Jein-Shan
Format: Article
Language:English
Subjects:
Accumulation
Algorithms
Circular cones
Construction
Convex and Discrete Geometry
Error analysis
Management Science
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Operations Research
Operations Research/Decision Theory
Optimization
Readers
Statistics
Studies
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Summary:In this paper, we consider complementarity problem associated with circular cone, which is a type of nonsymmetric cone complementarity problem. The main purpose of this paper is to show the readers how to construct complementarity functions for such nonsymmetric cone complementarity problem, and propose a few merit functions for solving such a complementarity problem. In addition, we study the conditions under which the level sets of the corresponding merit functions are bounded, and we also show that these merit functions provide an error bound for the circular cone complementarity problem. These results ensure that the sequence generated by descent methods has at least one accumulation point, and build up a theoretical basis for designing the merit function method for solving circular cone complementarity problem.
ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-015-9781-1