Conditions for error bounds and bounded level sets of some merit functions for the second-order cone complementarity problem

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10 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)459-473
Number of pages15
JournalJournal of Optimization Theory and Applications
Volume135
Issue number3
DOIs
Publication statusPublished - 2007 Dec 1

Keywords

  • Error bounds
  • Jordan products
  • Level sets
  • Merit functions
  • Second-order cones
  • Spectral factorization

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

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