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A gradient projection algorithm for relaxation methods.
J L Mohammed1, R A Hummel, S W Zucker
1Artificial Intelligence Laboratory, Fair-child Central Research and Development, Palo Alto, CA 94304.
IEEE Transactions on Pattern Analysis and Machine Intelligence
|August 27, 2011
Summary
We developed a simple gradient projection algorithm for optimization problems, particularly useful for artificial intelligence relaxation labeling. This method simplifies Zoutendijk
Area of Science:
- Optimization Theory
- Artificial Intelligence
- Convex Analysis
Background:
- Gradient projection is crucial for constrained optimization and variational inequalities.
- Standard basis unit vectors form a specific convex set relevant to these problems.
- Relaxation labeling in AI heavily relies on these optimization techniques.
Purpose of the Study:
- To simplify the gradient projection method for a specific convex set.
- To develop an efficient algorithm for problems in artificial intelligence.
- To verify the correctness of the proposed simplified algorithm.
Main Methods:
- Applying gradient projection to the convex hull of standard basis unit vectors.
- Utilizing Zoutendijk's method for feasible directions.
- Developing and verifying a simplified finite algorithm.
Main Results:
- A remarkably simple finite algorithm for gradient projection was derived.
- The algorithm is particularly effective for the specified convex set.
- The correctness of the algorithm was independently verified.
Conclusions:
- The proposed algorithm offers a significant simplification for gradient projection.
- This simplification is highly beneficial for AI applications like relaxation labeling.
- The verified algorithm provides a reliable tool for specific optimization tasks.
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