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Adaptive Conditional Gradient Method

Author

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  • Z. R. Gabidullina

    (Kazan Federal University)

Abstract

We present a novel fully adaptive conditional gradient method with the step length regulation for solving pseudo-convex constrained optimization problems. We propose some deterministic rules of the step length regulation in a normalized direction. These rules guarantee to find the step length by utilizing the finite procedures and provide the strict relaxation of the objective function at each iteration. We prove that the sequence of the function values for the iterates generated by the algorithm converges globally to the objective function optimal value with sublinear rate.

Suggested Citation

  • Z. R. Gabidullina, 2019. "Adaptive Conditional Gradient Method," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 1077-1098, December.
    • Handle: RePEc:spr:joptap:v:183:y:2019:i:3:d:10.1007_s10957-019-01585-w
    DOI: 10.1007/s10957-019-01585-w
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    References listed on IDEAS

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    1. Yurii Nesterov, 2018. "The Primal-Dual Model of an Objective Function," Springer Optimization and Its Applications, in: Lectures on Convex Optimization, edition 2, chapter 0, pages 423-487, Springer.
    2. Yurii Nesterov, 2018. "Complexity bounds for primal-dual methods minimizing the model of objective function," LIDAM Reprints CORE 2992, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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