Conditions for Error Bounds and Bounded Level Sets of Some Merit Functions for the Second-Order Cone Complementarity Problem |
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Authors: | J-S Chen |
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Institution: | (1) Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan;(2) Mathematics Division, National Center for Theoretical Sciences, Taipei, Taiwan |
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Abstract: | Recently this author studied several merit functions systematically for the second-order cone complementarity problem. These
merit functions were shown to enjoy some favorable properties, to provide error bounds under the condition of strong monotonicity,
and to have bounded level sets under the conditions of monotonicity as well as strict feasibility. In this paper, we weaken
the condition of strong monotonicity to the so-called uniform P
*-property, which is a new concept recently developed for linear and nonlinear transformations on Euclidean Jordan algebra.
Moreover, we replace the monotonicity and strict feasibility by the so-called R
01 or R
02-functions to keep the property of bounded level sets.
This work is partially supported by National Science Council of Taiwan. |
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Keywords: | Error bounds Jordan products Level sets Merit functions Second-order cones Spectral factorization |
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