# Complexity Estimation for an Algorithm of Searching for Zero of a Piecewise Linear Convex Function

Complexity Estimation for an Algorithm of Searching for Zero of a Piecewise Linear Convex Function It is known that the problem of the orthogonal projection of a point to the standard simplex can be reduced to solution of a scalar equation. In this article, the complexity is analyzed of an algorithm of searching for zero of a piecewise linear convex function which is proposed in [30]. The analysis is carried out of the best and worst cases of the input data for the algorithm. To this end, the largest and smallest numbers of iterations of the algorithm are studied as functions of the size of the input data. It is shown that, in the case of equality of elements of the input set, the algorithm performs the smallest number of iterations. In the case of different elements of the input set, the number of iterations is maximal and depends rather weakly on the particular values of the elements of the set. The results of numerical experiments with random input data of large dimension are presented. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied and Industrial Mathematics Springer Journals

# Complexity Estimation for an Algorithm of Searching for Zero of a Piecewise Linear Convex Function

, Volume 12 (2) – May 29, 2018
9 pages

/lp/springer_journal/complexity-estimation-for-an-algorithm-of-searching-for-zero-of-a-lnZkB2J0Br
Publisher
Subject
Mathematics; Mathematics, general
ISSN
1990-4789
eISSN
1990-4797
D.O.I.
10.1134/S1990478918020126
Publisher site
See Article on Publisher Site

### Abstract

It is known that the problem of the orthogonal projection of a point to the standard simplex can be reduced to solution of a scalar equation. In this article, the complexity is analyzed of an algorithm of searching for zero of a piecewise linear convex function which is proposed in [30]. The analysis is carried out of the best and worst cases of the input data for the algorithm. To this end, the largest and smallest numbers of iterations of the algorithm are studied as functions of the size of the input data. It is shown that, in the case of equality of elements of the input set, the algorithm performs the smallest number of iterations. In the case of different elements of the input set, the number of iterations is maximal and depends rather weakly on the particular values of the elements of the set. The results of numerical experiments with random input data of large dimension are presented.

### Journal

Journal of Applied and Industrial MathematicsSpringer Journals

Published: May 29, 2018

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