1996 Fiscal Year Final Research Report Summary
Research on New Global Optimization by Excluding Hyperspheres and Its Applications
| Project/Area Number |
08455175
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
情報通信工学
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
SAKANIWA Kohichi Tokyo Institute of Technology, Faculty of Engineering, Professor, 工学部, 教授 (30114870)
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| Co-Investigator(Kenkyū-buntansha) |
SHIBUYA Tomoharu Tokyo Institute of Technology, Faculty of Engineering, Assistant Professor, 工学部, 助手 (20262280)
YAMADA Isao Tokyo Institute of Technology, Faculty of Engineering, Associate Professor, 工学部, 助教授 (50230446)
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| Project Period (FY) |
1996
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| Keywords | Global Optimization / Excluding Hypersphere / Covering Method / Covering Test / Dimension Reduction / Lipschitz function / Neural Network / Fast Training |
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| Research Abstract |
This research treats the problem of optimizing (minimizing) the multi-dimensional Lipschitz function and applies the newly proposed optimization algorithm to neural network training. The key problem which has been unsolved is :
Give an algorithm which tests if a union of N-dimensional open spheres covers another N-dimensional closed sphere. And if the closed sphere is not covered by the union of N-dimensional open spheres, give a point from the uncovered region.
In this research, we completely solved this problem by developing a fundamental theorem named dimension reduction theorem which states that the covering condition can be reduced to a collection of similar conditions of lower dimension. This reduction theorem is based on a simple observation that the intersection of two spheres of dimension n becomes a sphere of dimension n-1. The covering test algorithm developed in this research judges the covering condition with the computational complexity of O (NK^<N+1>), where K is the number of open spheres. This algorithm repeatedly uses the dimension reduction theorem until the conditions become trivial.
By using the proposed covering test algorithm, we also established a fast learning method for neural networks by developing an estimation method of Lipschitz constant for the neural network objective function.
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Research Products
(17 results)
