On the behaviour of the underrelaxed Hildreth’s row-action method for computing projections onto polyhedra

Thomas Katsekpor

doi:10.1007/s12597-023-00656-x

On the behaviour of the underrelaxed Hildreth’s row-action method for computing projections onto polyhedra

Thomas Katsekpor

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

A strongly underrelaxed sequential version of the Hildreth’s iterative algorithm for norm minimization over linear inequalities is presented. Proofs are given showing that the algorithm converges from any starting point to its projection onto the linear constraint set in the feasible case and to the nearest least squares solution in the general case.

Original language	English
Pages (from-to)	1757-1776
Number of pages	20
Journal	OPSEARCH
Volume	60
Issue number	4
DOIs	https://doi.org/10.1007/s12597-023-00656-x
Publication status	Published - Dec 2023

Keywords

Hildreth’s iterative algorithm
Inconsistent (Infeasible) case
Least squares solution
Linear inequalities

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10.1007/s12597-023-00656-x

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title = "On the behaviour of the underrelaxed Hildreth{\textquoteright}s row-action method for computing projections onto polyhedra",

abstract = "A strongly underrelaxed sequential version of the Hildreth{\textquoteright}s iterative algorithm for norm minimization over linear inequalities is presented. Proofs are given showing that the algorithm converges from any starting point to its projection onto the linear constraint set in the feasible case and to the nearest least squares solution in the general case.",

keywords = "Hildreth{\textquoteright}s iterative algorithm, Inconsistent (Infeasible) case, Least squares solution, Linear inequalities",

author = "Thomas Katsekpor",

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AB - A strongly underrelaxed sequential version of the Hildreth’s iterative algorithm for norm minimization over linear inequalities is presented. Proofs are given showing that the algorithm converges from any starting point to its projection onto the linear constraint set in the feasible case and to the nearest least squares solution in the general case.

KW - Hildreth’s iterative algorithm

KW - Inconsistent (Infeasible) case

KW - Least squares solution

KW - Linear inequalities

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DO - 10.1007/s12597-023-00656-x

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JO - OPSEARCH

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On the behaviour of the underrelaxed Hildreth’s row-action method for computing projections onto polyhedra

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