Comparative study of two fast algorithms for projecting a point to the standard simplex

We consider two algorithms for orthogonal projection of a point to the standard simplex. These algorithms are fundamentally different; however, they are related to each other by the following fact: When one of them has the maximum run time, the run time of the other is minimal. Some particular domai...

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Published inJournal of applied and industrial mathematics Vol. 10; no. 2; pp. 288 - 301
Main Authors Tamasyan, G. Sh, Prosolupov, E. V., Angelov, T. A.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.04.2016
Springer Nature B.V
Subjects
Algorithms
Approximation
Java (programming language)
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Matlab
Programming languages
Projection
Quadratic programming
Run time (computers)
Simplex method
Studies
optimality conditions
quadratic programming
projecting a point to a simplex
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Summary:We consider two algorithms for orthogonal projection of a point to the standard simplex. These algorithms are fundamentally different; however, they are related to each other by the following fact: When one of them has the maximum run time, the run time of the other is minimal. Some particular domains are presented whose points are projected by the considered algorithms in the minimum and maximum number of iterations. The correctness of the conclusions is confirmed by the numerical experiments independently implemented in the MatLab environment and the Java programming language.
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ISSN:1990-4789
1990-4797
DOI:10.1134/S1990478916020137