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Perturbation Resilience and Superiorization of Iterative Algorithms
Y Censor1, R Davidi, G T Herman
1Department of Mathematics, University of Haifa, Mount Carmel, Haifa 31905, Israel.
Inverse Problems
|July 9, 2010
Summary
This study introduces a method to enhance iterative algorithms for optimization problems. Superiorized versions retain computational efficiency while improving solutions for complex tasks like image reconstruction.
Area of Science:
- Optimization algorithms
- Computational mathematics
- Image processing
Background:
- Iterative algorithms efficiently solve problems like convex set intersection.
- Optimization problems often require more computational resources.
- Existing algorithms may not balance efficiency with optimization effectiveness.
Purpose of the Study:
- To develop a methodology for creating "superiorized" versions of existing iterative algorithms.
- To enhance computational efficiency for optimization tasks.
- To address the limitations of standard iterative methods in solving complex optimization problems.
Main Methods:
- Introduced a methodology to automatically generate "superiorized" iterative algorithms.
- Demonstrated that "perturbation resilient" algorithms, like projection algorithms for convex feasibility, can be superiorized.
- Applied superiorization using perturbations to guide algorithms towards improved feasible points.
Main Results:
- Superiorized algorithms maintain computational efficiency while advancing optimization goals.
- Projection algorithms for consistent convex feasibility problems were shown to be "perturbation resilient".
- Demonstrated superiorized algorithms in image reconstruction using total variation as the objective function.
Conclusions:
- The presented methodology effectively creates computationally efficient "superiorized" algorithms for optimization.
- Superiorization offers a viable approach to enhance iterative methods for problems with limited computational resources.
- The technique shows promise in practical applications such as image reconstruction from projections.
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