-

 

 

 




Optimization Online





 

A Generalized Three-Operator Splitting Algorithm for Convex Quadratic Semidefinite Programming with Nonnegative Constraints

Chang Xiaokai (15293183303***at***163.com)
Liu Sanyang (846188043***at***qq.com)
Deng Zhao (xkchang***at***lut.cn)

Abstract: In this paper, we propose an efficient iterative algorithm for solving the standard convex quadratic semidefinite programming (CQSDP) with nonnegative constraints. In contrast to directly designing multi-block alternating direction method of multipliers (ADMM) for its dual, we take full advantage of the problemís structure, reformulate 4-block dual as 3-block separable problem and propose a semi-proximal ADMM for solving this 3-block reformulation. The proposed algorithm gives a generalization of the three-operator splitting method in [Davis and Yin, Set-Valued Var. Anal, (2017)], and provides an example of the algorithm designed by combining ADMM and operator splitting. To be precise, the proposed algorithm is implemented by an ADMM-based scheme while its convergence analysis is studied by operatorís properties, thus it inherits the advantages of the original ADMM in computation. Under a moderate condition on the penalty parameter, we explore theoretically the nonexpansion property, prove the global convergence and establish the non-ergodic convergence rate o(1/(k +1)) measured by the iterative complexity. Numerical experiments on various classes of CQSDP problems demonstrate that, our iterative algorithm is more efficient than the direct extension of ADMM with the aggressive step-length of 1.618.

Keywords: Quadratic semidefinite programming, Nonnegative constraints, Alternating direction method of multipliers, Generalized operator splitting, Nonexpansive

Category 1: Linear, Cone and Semidefinite Programming

Citation: Xiaokai Chang et al.,A Generalized Three-Operator Splitting Algorithm for Convex Quadratic Semidefinite Programming with Nonnegative Constraints

Download: [PDF]

Entry Submitted: 11/27/2017
Entry Accepted: 11/27/2017
Entry Last Modified: 05/28/2018

Modify/Update this entry


  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository

 

Submit
Update
Policies
Coordinator's Board
Classification Scheme
Credits
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society