{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,1]],"date-time":"2024-08-01T15:16:14Z","timestamp":1722525374465},"reference-count":32,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asia Pac. J. Oper. Res."],"published-print":{"date-parts":[[2020,8]]},"abstract":"<jats:p> In recent years, several convergent variants of the multi-block alternating direction method of multipliers (ADMM) have been proposed for solving the convex quadratic semidefinite programming via its dual, which is inherently a [Formula: see text]-block separable convex optimization problem with coupled linear constraints. Among these multi-block ADMM-type algorithms, the modified [Formula: see text]-block ADMM in [Chang, XK, SY Liu and X Li (2016). Modified alternating direction method of multipliers for convex quadratic semidefinite programming. Neurocomputing, 214, 575\u2013586] bears a peculiar feature that the augmented Lagrangian function is not necessarily to be minimized with respect to the block-variable corresponding to the quadratic term in the objective function. In this paper, we lay the theoretical foundation of this phenomenon by interpreting this modified [Formula: see text]-block ADMM as a special implementation of the Davis\u2013Yin [Formula: see text]-operator splitting [Davis, D and WT Yin (2017). A three-operator splitting scheme and its optimization applications. Set-Valued and Variational Analysis, 25, 829\u2013858]. Based on this perspective, we are able to extend this modified [Formula: see text]-block ADMM to a generalized [Formula: see text]-block ADMM, in the sense of [Eckstein, J and DP Bertsekas (1992). On the Douglas\u2013Rachford splitting method and the proximal point algorithm for maximal monotone operators. Mathematical Programming, 55, 293\u2013318], which not only applies to the more general convex composite quadratic programming problems but also admits the flexibility of achieving even better numerical performance. <\/jats:p>","DOI":"10.1142\/s0217595920400096","type":"journal-article","created":{"date-parts":[[2020,5,19]],"date-time":"2020-05-19T05:37:52Z","timestamp":1589866672000},"page":"2040009","source":"Crossref","is-referenced-by-count":4,"title":["A Three-Operator Splitting Perspective of a Three-Block ADMM for Convex Quadratic Semidefinite Programming and Beyond"],"prefix":"10.1142","volume":"37","author":[{"given":"Liang","family":"Chen","sequence":"first","affiliation":[{"name":"School of Mathematics, Hunan University, Changsha 4100082, P. R. China"}]},{"given":"Xiaokai","family":"Chang","sequence":"additional","affiliation":[{"name":"School of Science, Lanzhou University of Technology, Lanzhou 730050, P. R. China"}]},{"given":"Sanyang","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Xidian University, Xi\u2019an 710071, P. R. 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