An algorithm for least squares projections onto the intersection of translated, convex cones

A commonly occurring problem is that of minimizing least squares expressions subject to restrictions on the solution. Dykstra (1983) has given a simple algorithm for solving these types of problems when the constraint region can be expressed as a finite intersection of closed, convex cones. Here it...

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Bibliographic Details
Published inJournal of statistical planning and inference Vol. 15; no. 3; pp. 391 - 399
Main Authors Dykstra, Richard L., Boyle, James P.
Format Journal Article
LanguageEnglish
Published Lausanne Elsevier B.V 1986
New York,NY Elsevier Science
Amsterdam
Subjects
Cones constraints
Dual cones
Exact sciences and technology
Iterations
Least squares projections
Linear inference, regression
Mathematics
Minimizations
Probability and statistics
Regression
Sciences and techniques of general use
Statistics
Translations
Dual cones
65015
Regression
49099
Iterations
Translations
Least squares projections
Cones constraints
Minimizations
Least squares method
Algorithm
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ISSN0378-3758
1873-1171
DOI10.1016/0378-3758(86)90111-4

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Summary:A commonly occurring problem is that of minimizing least squares expressions subject to restrictions on the solution. Dykstra (1983) has given a simple algorithm for solving these types of problems when the constraint region can be expressed as a finite intersection of closed, convex cones. Here it is shown that this algorithm must still work correctly even when each cone is allowed to be arbitrarily translated, as long as the intersection is nonempty. This allows the algorithm to be applied to a much larger collection of problems than previously indicated.
ISSN:0378-3758
1873-1171
DOI:10.1016/0378-3758(86)90111-4