Successive Projection under a Quasi-Cyclic Order

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Abstract:

A classical method for finding a point in the intersection of a finite collection of closed convex sets is the successive projection method. It is well-known that this method is convergent if each convex sets is chosen for projection in a cyclical manner. In this note we show that this method is still convergent if the length of the cycle grows without bound, provided that the growth is not too fast. Our argument is based on an interesting application of the Cauchy-Schwartz inequality.

Author(s):
Tseng, Paul
Author Organization(s):
MASSACHUSETTS INST OF TECH CAMBRIDGE LAB FOR INFORMATION AND DECISION SYSTEMS
Descriptive Note:
Technical rept.
Supplementary Note:
DOI: 10.21236/ADA458804
Pagination:
0012

Security Markings

DOCUMENT & CONTEXTUAL SUMMARY

Distribution:
Approved For Public Release
Distribution Statement:
Approved For Public Release; Distribution Is Unlimited.

RECORD

Collection: TR
Identifying Numbers
Report Number(s):
LIDS-P-1938
Contract/Grant Number(s):
DAAL03-86-K-0171
Monitor Series:
ARO
 Subject Terms
Joint Capability Areas:
JCA_5_Command and Control; JCA_5.3_Planning; JCA_1.2.5_Lessons Learned; JCA_6_Net Centric; JCA_8_Building Partnerships
Modernization Areas:
Autonomy
Communities of Interest:
Autonomy
Descriptor(s):
*CONVEX SETS, *DISTRIBUTION THEORY, CAUCHY PROBLEM, FACTOR ANALYSIS
Field(s)/Group(s):
Theoretical Mathematics, Statistics and Probability
Keyword(s):
QUASI CYCLIC ORDER, CAUCHY SCHWARTZ INEQUALITY
Report Date:
1990 Jan 06
Creation Date:
2007 Jan 03