Second-order global optimality conditions for convex composite optimization

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Abstract

In recent years second-order sufficient conditions of an isolated local minimizer for convex composite optimization problems have been established. In this paper, second-order optimality conditions are obtained of a global minimizer for convex composite problems with a nonfinite valued convex function and a twice strictly differentiable function by introducing a generalized representation condition. This result is applied to a minimization problem with a closed convex set constraint which is shown to satisfy the basic constraint qualification. In particular, second-order necessary and sufficient conditions of a solution for a variational inequality problem with convex composite inequality constraints are obtained. Published by Elsevier Science B.V.
Original languageEnglish
Pages (from-to)327-347
Number of pages21
JournalMathematical Programming, Series B
Volume81
Issue number3
DOIs
Publication statusPublished - 1 May 1998
Externally publishedYes

Keywords

  • Convex composite function
  • Second-order duality
  • Second-order global optimality
  • Variational inequality

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

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