Volume 2, Issue 1
Two Modified Schemes for the Primal Dual Fixed Point Method

Ya-Nan Zhu & Xiaoqun Zhang

CSIAM Trans. Appl. Math., 2 (2021), pp. 108-130.

Published online: 2021-02

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  • Abstract

The primal dual fixed point (PDFP) proposed in [7] was designed to solve convex composite optimization problems in imaging and data sciences. The algorithm was shown to have some advantages for simplicity and flexibility for divers applications. In this paper we study two modified schemes in order to accelerate its performance. The first one considered is an inertial variant of PDFP, namely inertial PDFP (iPDFP) and the second one is based on a prediction correction framework proposed in [20], namely Prediction Correction PDFP (PC-PDFP). Convergence analysis on both algorithms is provided. Numerical experiments on sparse signal recovery and CT image reconstruction using TV-$L_2$ model are presented to demonstrate the acceleration of the two proposed algorithms compared to the original PDFP algorithm.

  • AMS Subject Headings

65K10, 49M29, 68U10, 94A08

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COPYRIGHT: © Global Science Press

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@Article{CSIAM-AM-2-108, author = {Zhu , Ya-Nan and Zhang , Xiaoqun}, title = {Two Modified Schemes for the Primal Dual Fixed Point Method}, journal = {CSIAM Transactions on Applied Mathematics}, year = {2021}, volume = {2}, number = {1}, pages = {108--130}, abstract = {

The primal dual fixed point (PDFP) proposed in [7] was designed to solve convex composite optimization problems in imaging and data sciences. The algorithm was shown to have some advantages for simplicity and flexibility for divers applications. In this paper we study two modified schemes in order to accelerate its performance. The first one considered is an inertial variant of PDFP, namely inertial PDFP (iPDFP) and the second one is based on a prediction correction framework proposed in [20], namely Prediction Correction PDFP (PC-PDFP). Convergence analysis on both algorithms is provided. Numerical experiments on sparse signal recovery and CT image reconstruction using TV-$L_2$ model are presented to demonstrate the acceleration of the two proposed algorithms compared to the original PDFP algorithm.

}, issn = {2708-0579}, doi = {https://doi.org/10.4208/csiam-am.2020-0042}, url = {http://global-sci.org/intro/article_detail/csiam-am/18656.html} }
TY - JOUR T1 - Two Modified Schemes for the Primal Dual Fixed Point Method AU - Zhu , Ya-Nan AU - Zhang , Xiaoqun JO - CSIAM Transactions on Applied Mathematics VL - 1 SP - 108 EP - 130 PY - 2021 DA - 2021/02 SN - 2 DO - http://doi.org/10.4208/csiam-am.2020-0042 UR - https://global-sci.org/intro/article_detail/csiam-am/18656.html KW - Inertial iteration, prediction-correction, primal dual fixed point method, acceleration, composite optimization, image restoration. AB -

The primal dual fixed point (PDFP) proposed in [7] was designed to solve convex composite optimization problems in imaging and data sciences. The algorithm was shown to have some advantages for simplicity and flexibility for divers applications. In this paper we study two modified schemes in order to accelerate its performance. The first one considered is an inertial variant of PDFP, namely inertial PDFP (iPDFP) and the second one is based on a prediction correction framework proposed in [20], namely Prediction Correction PDFP (PC-PDFP). Convergence analysis on both algorithms is provided. Numerical experiments on sparse signal recovery and CT image reconstruction using TV-$L_2$ model are presented to demonstrate the acceleration of the two proposed algorithms compared to the original PDFP algorithm.

Zhu , Ya-Nan and Zhang , Xiaoqun. (2021). Two Modified Schemes for the Primal Dual Fixed Point Method. CSIAM Transactions on Applied Mathematics. 2 (1). 108-130. doi:10.4208/csiam-am.2020-0042
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