An Inexact Dual Fast Gradient-Projection Method for Separable Convex Optimization with Linear Coupled Constraints

Jueyou Li (), Zhiyou Wu (), Changzhi Wu (), Qiang Long () and Xiangyu Wang ()
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Jueyou Li: Chongqing Normal University
Zhiyou Wu: Chongqing Normal University
Changzhi Wu: School of Built Environment, Curtin University
Qiang Long: Southwest University of Science and Technology
Xiangyu Wang: School of Built Environment, Curtin University

Journal of Optimization Theory and Applications, 2016, vol. 168, issue 1, No 8, 153-171

Abstract: Abstract In this paper, a class of separable convex optimization problems with linear coupled constraints is studied. According to the Lagrangian duality, the linear coupled constraints are appended to the objective function. Then, a fast gradient-projection method is introduced to update the Lagrangian multiplier, and an inexact solution method is proposed to solve the inner problems. The advantage of our proposed method is that the inner problems can be solved in an inexact and parallel manner. The established convergence results show that our proposed algorithm still achieves optimal convergence rate even though the inner problems are solved inexactly. Finally, several numerical experiments are presented to illustrate the efficiency and effectiveness of our proposed algorithm.

Keywords: Convex optimization; Dual decomposition; Inexact gradient method; Suboptimality and constraint violations; 90C25; 90C46; 65Y05 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-015-0757-1

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