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Convex optimization based on global lower second-order models

Author

Listed:
  • Doikov, Nikita

    (Université catholique de Louvain, ICTEAM)

  • Nesterov, Yurii

    (Université catholique de Louvain, LIDAM/CORE, Belgium)

Abstract

In this work, we present new second-order algorithms for composite convex optimization, called Contracting-domain Newton methods. These algorithms are affine-invariant and based on global second-order lower approximation for the smooth component of the objective. Our approach has an interpretation both as a second-order generalization of the conditional gradient method, or as a variant of trust-region scheme. Under the assumption, that the problem domain is bounded, we prove O(1/k2)O(1/k2) global rate of convergence in functional residual, where k k is the iteration counter, minimizing convex functions with Lipschitz continuous Hessian. This significantly improves the previously known bound O(1/k)O(1/k) for this type of algorithms. Additionally, we propose a stochastic extension of our method, and present computational results for solving empirical risk minimization problem.

Suggested Citation

  • Doikov, Nikita & Nesterov, Yurii, 2024. "Convex optimization based on global lower second-order models," LIDAM Reprints CORE 3311, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:3311
    Note: In: Advances in Neural Information Processing Systems 33 : 34th Conference on Neural Information Processing Systems (NeurIPS 2020), ed. by H. Larochelle, e.a. ISBN: 9781713829546
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