The lack of exact worst-case convergence rates
Research gap analysis derived from 3 mathematics papers in our local library.
The gap
The lack of exact worst-case convergence rates for nonconvex and convex functions. The lack of a comprehensive worst-case analysis of gradient descent.
Evidence profile
Sourced from the stated research gap and future-work section of the source papers, classified as general, spanning 3 journals. Those papers have been cited 2 times in total.
Research trend
Established — well-defined area with open sub-problems.
Supporting evidence — 4 representative gaps
- Robust stochastic gradient descent for linearly constrained problems via adaptive barrier amplification (2026) · DOAJ (DOAJ: Directory of Open Access Journals) · doi
The lack of robustness in stochastic gradient descent methods for linearly constrained problems. The need for a novel algorithm to overcome the limitations of existing methods.
generalstated research gapKeywords: lack robustness stochastic gradient descent methods linearly constrained - Reachability of gradient descent (2026) · Optimization Letters · doi
The gap in current research is that it is not known whether gradient descent can converge to any local minimum with sufficiently small step sizes. The paper identifies a need for a theoretical analysis of the reachability of gradient descent.
generalstated research gapevidence 5/5Keywords: gap current research known whether gradient descent converge - Exact worst-case convergence rates of gradient descent: a complete analysis for all constant stepsizes over nonconvex and convex functions (2026) · Mathematical Programming · cited 1× · doi
The lack of exact worst-case convergence rates for nonconvex and convex functions. The lack of a comprehensive worst-case analysis of gradient descent.
generalstated research gapevidence 5/5Keywords: lack exact worst-case convergence rates nonconvex convex functions - Exact worst-case convergence rates of gradient descent: a complete analysis for all constant stepsizes over nonconvex and convex functions (2026) · Mathematical Programming · cited 1× · doi
Future research can focus on extending the results to non-smooth functions. Future research can focus on experimental evaluations of the new variant of gradient descent.
generalfuture-work sectionevidence 5/5Keywords: future research focus extending results non-smooth functions experimental
Questions about this gap
Explore this gap further
Run this gap as a query across open scholarly engines for the latest related literature.
Working on this gap? Review it with us.
Science AI Journal reviews manuscripts in one pass with 8 specialised AI agents calibrated on 69,000+ real peer reviews.
Tools for your next paper
Related gaps in Mathematics
- The lack of efficient numerical methods for solvingThe lack of efficient numerical methods for solving nonlinear time-fractional convection-diffusion problems. The limitations of classical de…
- The lack of a formal proof of the internal mathematicalThe lack of a formal proof of the internal mathematical structure of large language models. The need for a rigorous mathematical framework f…
- Provide a comprehensive comparison with other existingProvide a comprehensive comparison with other existing methods. The numerical tests are limited to a unit square domain and may not be repre…
- The lack of a general nonlinear space-time fractionalThe lack of a general nonlinear space-time fractional formulation of the Fokker-Planck equation. The need for exact analytical solutions for…