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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)
Ze Zexian(xkchang***at***lut.cn)

Abstract: In this paper, we propose an efficient iteration algorithm for solving the standard convex quadratic semidefinite programming (CQSDP) with nonnegative constraints, by reformulating its 4-block dual as 3-block separable problem and modifying semi-proximal alternating direc- tion method of multipliers (ADMM) for solving this 3-block reformulation. This method gives a generalization of the three-operator splitting method in [Davis and Yin, Set-Valued Var. Anal, (2017)]. Moreover, our methods provide an example of the algorithm designed by combining ADMM and operator splitting. Under a moderate condition on the penalty parameter, we show theoretically the nonexpansion property, prove the global convergence and establish the worst-case convergence rate measured by the iteration complexity of this iteration algorithm. Numerical experiments on the various classes of CQSDP problems demonstrate that, our iteration 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: 11/27/2017

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