Malitsky-Tam forward-reflected-backward splitting method for nonconvex minimization problems

2021/11/17 by Xianfu Wang, Ziyuan Wang, Wang, Xianfu +1
Computer Science · Engineering · Mathematics · #90C26 #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Control (math.OC) #Optimization and Variational Analysis #Primary 49J52 #Secondary 26D10 #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.2111.08852

openalex publication_date 2021/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend the Malitsky-Tam forward-reflected-backward (FRB) splitting method for inclusion problems of monotone operators to nonconvex minimization problems. By assuming the generalized concave Kurdyka-Łojasiewicz (KL) property of a quadratic regularization of the objective, we show that the FRB method converges globally to a stationary point of the objective and enjoys finite length property. The sharpness of our approach is guaranteed by virtue of the exact modulus associated with the generalized concave KL property. Numerical experiments suggest that FRB is competitive compared to the Douglas-Rachford method and the Boţ-Csetnek inertial Tseng's method.

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