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Journal Articles Optimization Letters Year : 2023

Convergence Analysis of Block Majorize-Minimize Subspace Approach

Emilie Chouzenoux
Jean-Baptiste Fest
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Abstract

We consider the minimization of a differentiable Lipschitz gradient but non necessarily convex, function F defined on R N. We propose an accelerated gradient descent approach which combines three strategies, namely (i) a variable metric derived from the majorization-minimization principle ; (ii) a subspace strategy incorporating information from the past iterates ; (iii) a block alternating update. Under the assumption that F satisfies the Kurdyka-Łojasiewicz property, we give conditions under which the sequence generated by the resulting block majorize-minimize subspace algorithm converges to a critical point of the objective function, and we exhibit convergence rates for its iterates.
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hal-04202728 , version 1 (11-09-2023)

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Emilie Chouzenoux, Jean-Baptiste Fest. Convergence Analysis of Block Majorize-Minimize Subspace Approach. Optimization Letters, In press, ⟨10.1007/s11590-023-02055-z⟩. ⟨hal-04202728⟩
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