Back to Search
Start Over
AN EFFICIENT AND ROBUST SCALAR AUXIALIARY VARIABLE BASED ALGORITHM FOR DISCRETE GRADIENT SYSTEMS ARISING FROM OPTIMIZATIONS.
- Source :
- SIAM Journal on Scientific Computing; 2023, Vol. 45 Issue 5, pA2304-A2324, 21p
- Publication Year :
- 2023
-
Abstract
- We propose in this paper a new minimization algorithm based on a slightly modified version of the scalar auxialiary variable (SAV) approach coupled with a relaxation step and an adaptive strategy. It enjoys several distinct advantages over popular gradient based methods: (i) it is unconditionally energy diminishing with a modified energy which is intrinsically related to the original energy, and thus no parameter tuning is needed for stability; (ii) it allows the use of large step-sizes which can effectively accelerate the convergence rate. We also present a convergence analysis for some SAV based algorithms, which include our new algorithm without the relaxation step as a special case. We apply our new algorithm to several illustrative and benchmark problems and compare its performance with several popular gradient based methods. The numerical results indicate that the new algorithm is very robust, and its adaptive version usually converges significantly faster than those popular gradient decent based methods. [ABSTRACT FROM AUTHOR]
- Subjects :
- DISCRETE systems
BENCHMARK problems (Computer science)
ALGORITHMS
Subjects
Details
- Language :
- English
- ISSN :
- 10648275
- Volume :
- 45
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- SIAM Journal on Scientific Computing
- Publication Type :
- Academic Journal
- Accession number :
- 173571316
- Full Text :
- https://doi.org/10.1137/23M1545744