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

Xianfu Wang () and Ziyuan Wang ()
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Xianfu Wang: University of British Columbia
Ziyuan Wang: University of British Columbia

Computational Optimization and Applications, 2022, vol. 82, issue 2, No 5, 463 pages

Abstract: 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 the finite length property. Convergence rates are also given. 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.

Keywords: Generalized concave Kurdyka-Łojasiewicz property; Proximal mapping; Malitsky-Tam forward-reflected-backward splitting method; Merit function; Global convergence; Nonconvex optimization; Primary 49J52 · 90C26; Secondary 26D10 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10589-022-00364-0

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