The appeals of quadratic majorization–minimization

Marc C. Robini (), Lihui Wang () and Yuemin Zhu ()
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Marc C. Robini: INSA Lyon
Lihui Wang: Guizhou University
Yuemin Zhu: INSA Lyon

Journal of Global Optimization, 2024, vol. 89, issue 3, No 1, 509-558

Abstract: Abstract Majorization–minimization (MM) is a versatile optimization technique that operates on surrogate functions satisfying tangency and domination conditions. Our focus is on differentiable optimization using inexact MM with quadratic surrogates, which amounts to approximately solving a sequence of symmetric positive definite systems. We begin by investigating the convergence properties of this process, from subconvergence to R-linear convergence, with emphasis on tame objectives. Then we provide a numerically stable implementation based on truncated conjugate gradient. Applications to multidimensional scaling and regularized inversion are discussed and illustrated through numerical experiments on graph layout and X-ray tomography. In the end, quadratic MM not only offers solid guarantees of convergence and stability, but is robust to the choice of its control parameters.

Keywords: Differentiable optimization; Majorization–minimization; Tame optimization; Multidimensional scaling; Inverse problems; 65K05; 68W40; 90C26 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10898-023-01361-1

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