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Journal of Optimization Theory and Applications

, Volume 183, Issue 3, pp 1077–1098 | Cite as

Adaptive Conditional Gradient Method

  • Z. R. GabidullinaEmail author
Article
  • 117 Downloads

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.

Keywords

Optimization problems Pseudo-convex function Adaptation Descent direction Normalization Step length Regulation Rate of convergence 

Mathematics Subject Classification

90C30 65K05 

Notes

Acknowledgements

The author thanks the anonymous referees and the editor for their helpful comments and remarks on a previous version of the paper.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Data Analysis and Operations ResearchKazan Federal UniversityKazanRussia

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