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One-Rank Linear Transformations and Fejer-Type Methods: An Overview.
- Source :
-
Mathematics (2227-7390) . May2024, Vol. 12 Issue 10, p1527. 26p. - Publication Year :
- 2024
-
Abstract
- Subgradient methods are frequently used for optimization problems. However, subgradient techniques are characterized by slow convergence for minimizing ravine convex functions. To accelerate subgradient methods, special linear non-orthogonal transformations of the original space are used. This paper provides an overview of these transformations based on Shor's original idea. Two one-rank linear transformations of Euclidean space are considered. These simple transformations form the basis of variable metric methods for convex minimization that have a natural geometric interpretation in the transformed space. Along with the space transformation, a search direction and a corresponding step size must be defined. Subgradient Fejer-type methods are analyzed to minimize convex functions, and Polyak step size is used for problems with a known optimal objective value. Convergence theorems are provided together with the results of numerical experiments. Directions for future research are discussed. [ABSTRACT FROM AUTHOR]
- Subjects :
- *SUBGRADIENT methods
*CONVEX functions
*CONVEX programming
Subjects
Details
- Language :
- English
- ISSN :
- 22277390
- Volume :
- 12
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- Mathematics (2227-7390)
- Publication Type :
- Academic Journal
- Accession number :
- 177488302
- Full Text :
- https://doi.org/10.3390/math12101527