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Efficient Regularized Proximal Quasi-Newton Methods for Large-Scale Nonconvex Composite Optimization Problems

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arxiv 2210.07644 v1 pith:UU2NZSL4 submitted 2022-10-14 math.OC

classification math.OC
keywords quasi-newtonmethodmethodsproximalcompositeoptimizationproblemsconvex
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Optimization problems with composite functions consist of an objective function which is the sum of a smooth and a (convex) nonsmooth term. This particular structure is exploited by the class of proximal gradient methods and some of their generalizations like proximal Newton and quasi-Newton methods. In this paper, we propose a regularized proximal quasi-Newton method whose main features are: (a) the method is globally convergent to stationary points, (b) the globalization is controlled by a regularization parameter, no line search is required, (c) the method can be implemented very efficiently based on a simple observation which combines recent ideas for the computation of quasi-Newton proximity operators and compact representations of limited-memory quasi-Newton updates. Numerical examples for the solution of convex and nonconvex composite optimization problems indicate that the method outperforms several existing methods.

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Cited by 2 Pith papers

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  1. Convergence rates of regularized quasi-Newton methods without strong convexity

    math.OC 2025-05 conditional novelty 7.0 of 10

    Under the Kurdyka-Lojasiewicz property, regularized SR1 quasi-Newton methods achieve non-asymptotic superlinear convergence without strong convexity.

  2. On the Universality of Simple Trust-Region Algorithms

    math.OC 2026-07 accept novelty 6.0 of 10

    Classical and modified-ratio trust-region methods reach the optimal O(ε^{-1/(1+ν)}) convex and O(ε^{-(2+ν)/(1+ν)}) nonconvex complexity for any Hölder ν∈[0,1] without knowing ν.

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