Computing the best approximation over the intersection of a polyhedral set and the doubly nonnegative cone

Ying Cui, Defeng Sun, Kim Chuan Toh

Research output: Journal article publicationJournal articleAcademic researchpeer-review

1 Citation (Scopus)


This paper introduces an efficient algorithm for computing the best approximation of a given matrix onto the intersection of linear equalities, inequalities, and the doubly nonnegative cone (the cone of all positive semidefinite matrices whose elements are nonnegative). In contrast to directly applying the block coordinate descent type methods, we propose an inexact accelerated (two-) block coordinate descent algorithm to tackle the four-block unconstrained nonsmooth dual program. The proposed algorithm hinges on the superlinearly convergent semismooth Newton method to solve each of the two subproblems generated from the (two-)block coordinate descent, which have no closed form solutions due to the merger of the original four blocks of variables. The O(1/k2) iteration complexity of the proposed algorithm is established. Extensive numerical results over various large scale semidefinite programming instances from relaxations of combinatorial problems demonstrate the effectiveness of the proposed algorithm.

Original languageEnglish
Pages (from-to)2785-2813
Number of pages29
JournalSIAM Journal on Optimization
Issue number4
Publication statusPublished - 31 Oct 2019


  • Acceleration
  • Complexity
  • Doubly nonnegative cone
  • Semidefinite programming
  • Semismooth Newton

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science

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