A primal–dual prediction–correction algorithm for saddle point optimization

Hongjin He, Jitamitra Desai () and Kai Wang
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Hongjin He: Hangzhou Dianzi University
Jitamitra Desai: Nanyang Technological University
Kai Wang: Nanyang Technological University

Journal of Global Optimization, 2016, vol. 66, issue 3, No 9, 573-583

Abstract: Abstract In this paper, we introduce a new primal–dual prediction–correction algorithm for solving a saddle point optimization problem, which serves as a bridge between the algorithms proposed in Cai et al. (J Glob Optim 57:1419–1428, 2013) and He and Yuan (SIAM J Imaging Sci 5:119–149, 2012). An interesting byproduct of the proposed method is that we obtain an easily implementable projection-based primal–dual algorithm, when the primal and dual variables belong to simple convex sets. Moreover, we establish the worst-case $${\mathcal {O}}(1/t)$$ O ( 1 / t ) convergence rate result in an ergodic sense, where t represents the number of iterations.

Keywords: Saddle point problem; Primal–dual algorithm; Prediction–correction algorithm; Projection method; Convergence rate (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10898-016-0437-1

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