Abstract
<p style='text-indent:20px;'>This paper presents an improved Lagrangian-PPA based prediction correction method to solve linearly constrained convex optimization problem. At each iteration, the predictor is achieved by minimizing the proximal Lagrangian function with respect to the primal and dual variables. These optimization subproblems involved either admit analytical solutions or can be solved by a fast algorithm. The new update is generated by using the information of the current iterate and the predictor, as well as an appropriately chosen stepsize. Compared with the existing PPA based method, the parameters are relaxed. We also establish the convergence and convergence rate of the proposed method. Finally, numerical experiments are conducted to show the efficiency of our Lagrangian-PPA based prediction correction method.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Control and Optimization,Strategy and Management,Business and International Management,Applied Mathematics,Control and Optimization,Strategy and Management,Business and International Management
Reference23 articles.
1. K. J. Arrow, L. Hurwicz and H. Uzawa, Studies in linear and non-linear programming, In Stanford Mathematical Studies in the Social Sciences, II, Stanford University Press, Stanford, 1958.
2. J. F. Cai, E. J. Candès, Z. W. Shen.A singular value thresholding algorithm for matrix completion, SIAM J. Optim., 20 (2010), 1956-1982.
3. E. J. Candès, B. Recht.Exact matrix completion via convex optimization, Foud. Comput. Math., 9 (2008), 717-772.
4. W. Deng, M. J. Lai and W. Yin, On the $o(1/k)$ convergence and parallelization of the alternating direction method of multipliers, preprint, arXiv: 1312.3040.
5. E. Esser, X. Q. Zhang, T. F. Chan.A general framework for a class of first order primal- dual algorithms for convex optimization in imaging science, SIAM J. Imaging Sci, 3 (2010), 1015-1046.
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