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A Primal-Dual Fixed Point Algorithm Based on Proximity Operator for Convex Set Constrained Separable Problem(PDF)


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A Primal-Dual Fixed Point Algorithm Based on Proximity Operator for Convex Set Constrained Separable Problem
Chen Peijun12Huang Jianguo1Zhang Xiaoqun13
(1.Department of Mathematics,MOE-LSC,Shanghai Jiao Tong University,Shanghai 200240,China) (2.Department of Mathematics,Taiyuan University of Science and Technology,Taiyuan 030024,China) (3.Institute of Natural Sciences,Shanghai Jiao Tong University,Shanghai 200240,China)
convex constraintconvex separable minimizationproximity operatorfixed point algorithm
O224; O29
In many real problems,the solutions may have constraints arising from their physical requirements.In this paper,we design an efficient algorithm for solving the separable convex minimization on closed convex set based on the algorithm PDFP2O.Precisely speaking,the constraint can be enforced by adding an indicator function to the objective function,and the function are reformulated and can be solved with PDFP2O.Using the separability of the function with respect to its variables,we thus get a primal-dual fixed point algorithm based on proximity operator on closed convex set(PDFP2OC).Since the algorithm PDFP2OC can be recast as the original PDFP2O for unconstrained problem,the convergence and convergence rate analysis can be obtained directly.Finally,we illustrate the efficiency of PDFP2OC through computerized tomographic reconstruction.


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Last Update: 2013-09-30