Bibliographic Details
| Title: |
Refining asymptotic complexity bounds for nonconvex optimization methods, including why steepest descent is rather than. |
| Authors: |
Gratton, S.1 (AUTHOR) serge.gratton@enseeiht.fr, Sim, C.-K.2 (AUTHOR) chee-khian.sim@port.ac.uk, Toint, Ph. L.3 (AUTHOR) philippe.toint@unamur.be |
| Source: |
Computational Optimization & Applications. Nov2025, Vol. 92 Issue 2, p515-527. 13p. |
| Subjects: |
Asymptotic analysis, Computational complexity, Method of steepest descent (Numerical analysis), Mathematical bounds, Nonsmooth optimization, Algorithms, Nonconvex programming |
| Abstract: |
We revisit the standard "telescoping sum" argument ubiquitous in the final steps of analyzing evaluation complexity of algorithms for smooth nonconvex optimization, and obtain a refined formulation of the resulting bound as a function of the requested accuracy . While bounds obtained using the standard argument typically are of the form for some positive , the refined results are of the form . We then explore to which known algorithms our refined bounds are applicable and finally describe an example showing how close the standard and refined bounds can be. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
