Abstract

Given a Lipschitz and convex objective function on a Banach space, we revisit the class of regular vector fields introduced in our previous work on descent methods. We consider continuous descent methods for minimizing our objective function and establish two convergence results for those methods which are generated by regular vector fields. These results improve upon a convergence result which we obtained in our previous work.

Author information

Contact details are reproduced from the original publication and may be historical.

Simeon Reich

Dept. of Mathematics, The Technion – Israel Inst. of Technology, 32000 Haifa, Israel

sreich@technion.ac.il

Alexander J. Zaslavski

Dept. of Mathematics, The Technion – Israel Inst. of Technology, 32000 Haifa, Israel

ajzasl@technion.ac.il

Keywords

  • Banach space
  • complete metric space
  • convex function
  • descent method
  • regular vector field

Mathematics Subject Classification

37L99, 47J35, 49M37, 90C25, 90C30

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Suggested citation

S. Reich, A. J. Zaslavski. “Asymptotic Behavior of Continuous Descent Methods with a Convex Objective Function.” Journal of Convex Analysis 27 (2020), No. 2, 557–564. https://doi.org/10.68381/jca27029

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Published by Heldermann Verlag, 2020. Rights now held by Banach Press LLC.