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A parameterized Douglas-Rachford splitting algorithm for nonconvex optimization
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DOI：10.1016/j.amc.2021.126425.png)
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Abstract
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In this paper, we study a parameterized Douglas-Rachford splitting method in Wang-Wang (2019)[5] for a class of nonconvex optimization problem. A new merit function is constructed to establish the convergence of the whole sequence generated by the parameterized Douglas-Rachford splitting method. As a by-product, this also provides convergence results of a special case of the adaptive Douglas-Rachford algorithm proposed by Dao and Phan (2019)[22] in nonconvex settings. We then apply the parameterized Douglas-Rachford splitting method to three important classes of nonconvex optimization problems arising in data science: sparsity constrained least squares problem, feasibility problem and low rank matrix completion. Numerical results validate the effectiveness of the parameterized Douglas-Rachford splitting method compared with some other classical methods. (c) 2021 Elsevier Inc. All rights reserved.
Keywords:
Parameterized Douglas-Rachford splitting method
Nonconvex optimization problems
Global convergence
Sparsity constrained least squares problem
Low rank matrix completion
Feasibility problem
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